Probability and Conditional Probability Calculates probability and conditional probability of events.

Description

Probability and Conditional Probability Calculates probability and conditional probability of events.

Usage

Prob(x, ...)

Arguments

Details

This function calculates the probability of events or subsets of a given sample space. Conditional probability is also implemented. In essence, the Prob() function operates by summing the probs column of its argument. It will find subsets on the fly if desired. The event argument is used to define a subset of x, that is, the only outcomes used in the probability calculation will be those that are elements of x and satisfy event simultaneously. In other words, Prob(x,event) calculates Prob(intersect(x, subset(x, event))). Consequently, x should be the entire probability space in the case that event is non-null. There is some flexibility in the given argument in that it can be either a data frame or it can be a logical expression that defines the subset. However, that flexibility is limited. In particular, if given is a logical expression, then event must also be specified (also a logical expression). And in this case, the argument x should be the entire sample space, not a subset thereof.

Value

A number in the interval [0,1].

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

probspace, iidspace

Examples

S <- rolldie(times = 3, makespace = TRUE )
Prob(S, X1+X2 > 9 )
Prob(S, X1+X2 > 9, given = X1+X2+X3 > 7 )

Probability and Conditional Probability Calculates probability and conditional probability of events.

Description

Probability and Conditional Probability Calculates probability and conditional probability of events.

Usage

## Default S3 method:
Prob(x, event = NULL, given = NULL, ...)

Arguments

Details

This function calculates the probability of events or subsets of a given sample space. Conditional probability is also implemented. In essence, the Prob() function operates by summing the probs column of its argument. It will find subsets on the fly if desired. The event argument is used to define a subset of x, that is, the only outcomes used in the probability calculation will be those that are elements of x and satisfy event simultaneously. In other words, Prob(x,event) calculates Prob(intersect(x, subset(x, event))). Consequently, x should be the entire probability space in the case that event is non-null. There is some flexibility in the given argument in that it can be either a data frame or it can be a logical expression that defines the subset. However, that flexibility is limited. In particular, if given is a logical expression, then event must also be specified (also a logical expression). And in this case, the argument x should be the entire sample space, not a subset thereof.

Value

A number in the interval [0,1].

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

probspace, iidspace

Examples

S <- rolldie(times = 3, makespace = TRUE )
Prob(S, X1+X2 > 9 )
Prob(S, X1+X2 > 9, given = X1+X2+X3 > 7 )

Probability and Conditional Probability Calculates probability and conditional probability of events.

Description

Probability and Conditional Probability Calculates probability and conditional probability of events.

Usage

## S3 method for class 'ps'
Prob(x, event = NULL, given = NULL, ...)

Arguments

Details

This function calculates the probability of events or subsets of a given sample space. Conditional probability is also implemented. In essence, the Prob() function operates by summing the probs column of its argument. It will find subsets on the fly if desired. The event argument is used to define a subset of x, that is, the only outcomes used in the probability calculation will be those that are elements of x and satisfy event simultaneously. In other words, Prob(x,event) calculates Prob(intersect(x, subset(x, event))). Consequently, x should be the entire probability space in the case that event is non-null. There is some flexibility in the given argument in that it can be either a data frame or it can be a logical expression that defines the subset. However, that flexibility is limited. In particular, if given is a logical expression, then event must also be specified (also a logical expression). And in this case, the argument x should be the entire sample space, not a subset thereof.

Value

A number in the interval [0,1].

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

probspace, iidspace

Examples

S <- rolldie(times = 3, makespace = TRUE )
Prob(S, X1+X2 > 9 )
Prob(S, X1+X2 > 9, given = X1+X2+X3 > 7 )

Adding Random Variables to a Probability Space

Description

Adds a column to a data frame probability space containing the values of a random variable computed from the existing columns of the space.

Usage

addrv(space, FUN = NULL, invars = NULL, name = NULL, ...)

Arguments

Details

There are two ways to add a random variable to a data frame probability space; see the examples. The argument FUN has precedence and will be used if specified. If name is not specified, then the new random variable will be called X. Note that this function only works for data frames, as a method for objects of class ps has not been implemented.

Value

The input data frame with an additional column called name.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

See transform to add a column to a data frame of outcomes (not yet a probability space).

Examples

S <- rolldie(3, makespace = TRUE)
addrv(S, sum, name = "Y")
addrv(S, Z = X3 - X2)

A Standard Set of Playing Cards

Description

The title says it all.

Usage

cards(jokers = FALSE, makespace = FALSE)

Arguments

Details

This generates a data frame sample space of a standard deck of 52 playing cards. Optionally, the user can specify that Jokers be included, which have a rank but with suit a missing value.

Value

A data frame with columns rank and suit, and optionally a column of equally likely probs.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

rolldie, tosscoin, and roulette

Examples

cards()
cards(makespace = TRUE)

Count Repetitions Counts the number of repetitions of vals in a given vector x.

Description

Count Repetitions Counts the number of repetitions of vals in a given vector x.

Usage

countrep(x, ...)

Arguments

Details

This is a generic function, with methods supplied for data frames and vectors. The default behavior counts the number of pairs of elements of x. One can find the number of triples, etc., by changing the nrep argument. If there are specific values for which one is looking for repeats, these can be specified with the vals argument. Note that the function only checks for exactly nrep instances, so two pairs of a specific element would be counted as 0 pairs and 1 quadruple. See the examples.

Value

If x is a vector, then the value is an integer. If x is a data frame then the value is a vector, with entries the corresponding value for the respective rows of x

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

isrep

Examples

x <- c(3,3,2,2,3,3,4,4)
countrep(x)  # one pair each of 2s and 4s
countrep(x, nrep = 4)
countrep(x, vals = 4) # one pair of 4s

Count Repetitions Counts the number of repetitions of vals in a given vector x.

Description

Count Repetitions Counts the number of repetitions of vals in a given vector x.

Usage

## S3 method for class 'data.frame'
countrep(x, ...)

Arguments

Details

This is a generic function, with methods supplied for data frames and vectors. The default behavior counts the number of pairs of elements of x. One can find the number of triples, etc., by changing the nrep argument. If there are specific values for which one is looking for repeats, these can be specified with the vals argument. Note that the function only checks for exactly nrep instances, so two pairs of a specific element would be counted as 0 pairs and 1 quadruple. See the examples.

Value

If x is a vector, then the value is an integer. If x is a data frame then the value is a vector, with entries the corresponding value for the respective rows of x

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

isrep

Examples

x <- c(3,3,2,2,3,3,4,4)
countrep(x)  # one pair each of 2s and 4s
countrep(x, nrep = 4)
countrep(x, vals = 4) # one pair of 4s

Count Repetitions Counts the number of repetitions of vals in a given vector x.

Description

Count Repetitions Counts the number of repetitions of vals in a given vector x.

Usage

## Default S3 method:
countrep(x, vals = unique(x), nrep = 2, ...)

Arguments

Details

This is a generic function, with methods supplied for data frames and vectors. The default behavior counts the number of pairs of elements of x. One can find the number of triples, etc., by changing the nrep argument. If there are specific values for which one is looking for repeats, these can be specified with the vals argument. Note that the function only checks for exactly nrep instances, so two pairs of a specific element would be counted as 0 pairs and 1 quadruple. See the examples.

Value

If x is a vector, then the value is an integer. If x is a data frame then the value is a vector, with entries the corresponding value for the respective rows of x

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

isrep

Examples

x <- c(3,3,2,2,3,3,4,4)
countrep(x)  # one pair each of 2s and 4s
countrep(x, nrep = 4)
countrep(x, vals = 4) # one pair of 4s

Empirical Summary of a Simulation

Description

Calculates relative frequencies of the rows of a data frame.

Usage

empirical(x)

Arguments

Details

The function works by adding a probs column to x with equally likely entries of 1/n, where n is the number of rows. Then it aggregates the duplicated rows of x while accumulating the probabilities associated with each.

Value

A data frame formed by aggregating the rows of x. A probs column is added giving the relative frequencies of each of the rows.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

sim

Examples

S <- tosscoin(2, makespace = TRUE)
sims <- sim(S, ntrials = 50000)
empirical(sims)

A Deck of Playing Cards for Euchre

Description

The title says it all.

Usage

euchredeck(benny = FALSE, makespace = FALSE)

Arguments

Details

This is a conventional Euchre deck which uses a deck of 24 standard playing cards consisting of Ace, King, Queen, Jack, 10, and 9 of each of the four suits. If benny = TRUE then a Joker is added to the deck.

Value

A data frame with columns value and suit, and optionally a column of equally likely probs.

See Also

cards, tosscoin, and roulette

Examples

euchredeck()
euchredeck(benny = TRUE, makespace = TRUE)

Generate Two-way Tables

Description

A function to randomly generate arbitrary two-way tables.

Usage

gen2wayTable(
  n = sample(100:500, size = 1),
  pmatrix = matrix(1:12, nrow = 3),
  dmnames = list(X = paste("x", 1:nrow(pmatrix), sep = ""), Y = paste("y",
    1:ncol(pmatrix), sep = "")),
  addmargins = TRUE,
  as.df = FALSE,
  untable = TRUE
)

Arguments

Value

An object of class table containing the generated values.

Author(s)

G. Jay Kerns

Generate Independent Two-way Table

Description

A function to generate a two-way table with independent margins.

Usage

genIndepTable(
  n = sample(100:500, size = 1),
  prow = 1:3,
  pcol = 1:4,
  dmnames = list(X = paste("x", 1:length(prow), sep = ""), Y = paste("y", 1:length(pcol),
    sep = "")),
  addmargins = TRUE,
  as.df = FALSE,
  untable = TRUE
)

Arguments

Details

This function will generate a two-way table with independent marginal distributions.

Value

Either an object of class table or a data frame.

Author(s)

G. Jay Kerns

Generate data for logistic regression

Description

This function generates data ready for a logistic regression model.

Usage

genLogRegData(xdata, beta = rep(1, ncol(xdata)), yname = "y")

Arguments

Details

This function generates data ready for a logistic regression model.

Value

A data frame with the model matrix and the generated y values added.

Author(s)

G. Jay Kerns

Generate continuous model matrix data

Description

This function generates correlated normal data to serve as a model matrix in a regression model.

Usage

genXdata(
  n,
  nvar = 1,
  mu = rep(0, nvar),
  Sigma = diag(length(mu)),
  varnames = paste("x", 1:length(mu), sep = ""),
  roundto = NULL
)

Arguments

Details

This function generates correlated normal data to serve as a model matrix in a regression model.

Value

A data frame of generated data

Author(s)

G. Jay Kerns

Independent Identical Experiments Sets up a probability space corresponding to independent, identical experiments.

Description

Independent Identical Experiments Sets up a probability space corresponding to independent, identical experiments.

Usage

iidspace(x, ntrials, probs = NULL)

Arguments

Details

The elementary experiment to be repeated consists of drawing an element of x according to the probabilities contained in probs. The entries of probs need not sum to one, but they will be normalized before any computations. If probs is not specified, the equally likely model will be assumed.

Value

A data frame, with a probs column, where probs is calculated to be the probability of observing the outcome in its row under the assumption of independence and identical distribution of draws from x.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

probspace

Examples

iidspace( 1:6, ntrials = 3) # same as rolldie(3)
iidspace( 1:6, ntrials = 3, probs = 3:8 ) # unbalanced die

Intersection of Subsets Calculates the intersection of subsets of a probability space. Comparisons are made row-wise, so that in the data frame case, intersect(A,B) is a data frame with those rows that are both in A and in B.

Description

Intersection of Subsets Calculates the intersection of subsets of a probability space. Comparisons are made row-wise, so that in the data frame case, intersect(A,B) is a data frame with those rows that are both in A and in B.

Usage

intersect(x, ...)

Arguments

Details

This is a generic function, extended from the intersect function in the base package. The elements of intersect(x,y) are those elements in x and in y. The original definition is preserved in the case that x and y are vectors of the same mode.

Value

A vector, data frame, or subset of a probability space of the same type as its arguments.

Author(s)

G. Jay Kerns gkerns@ysu.edu, based on a suggestion made by Brian Ripley in R-devel, 12/11/07.

See Also

union, setdiff

Examples

S <- cards()
A <- subset(S, suit == "Heart")
B <- subset(S, rank == "A" )
intersect(A, B)

Intersection of Subsets Calculates the intersection of subsets of a probability space. Comparisons are made row-wise, so that in the data frame case, intersect(A,B) is a data frame with those rows that are both in A and in B.

Description

Intersection of Subsets Calculates the intersection of subsets of a probability space. Comparisons are made row-wise, so that in the data frame case, intersect(A,B) is a data frame with those rows that are both in A and in B.

Usage

## S3 method for class 'data.frame'
intersect(x, y, ...)

Arguments

Details

This is a generic function, extended from the intersect function in the base package. The elements of intersect(x,y) are those elements in x and in y. The original definition is preserved in the case that x and y are vectors of the same mode.

Value

A vector, data frame, or subset of a probability space of the same type as its arguments.

Author(s)

G. Jay Kerns gkerns@ysu.edu, based on a suggestion made by Brian Ripley in R-devel, 12/11/07.

See Also

union, setdiff

Examples

S <- cards()
A <- subset(S, suit == "Heart")
B <- subset(S, rank == "A" )
intersect(A, B)

Intersection of Subsets Calculates the intersection of subsets of a probability space. Comparisons are made row-wise, so that in the data frame case, intersect(A,B) is a data frame with those rows that are both in A and in B.

Description

Intersection of Subsets Calculates the intersection of subsets of a probability space. Comparisons are made row-wise, so that in the data frame case, intersect(A,B) is a data frame with those rows that are both in A and in B.

Usage

## Default S3 method:
intersect(x, y, ...)

Arguments

Details

This is a generic function, extended from the intersect function in the base package. The elements of intersect(x,y) are those elements in x and in y. The original definition is preserved in the case that x and y are vectors of the same mode.

Value

A vector, data frame, or subset of a probability space of the same type as its arguments.

Author(s)

G. Jay Kerns gkerns@ysu.edu, based on a suggestion made by Brian Ripley in R-devel, 12/11/07.

See Also

union, setdiff

Examples

S <- cards()
A <- subset(S, suit == "Heart")
B <- subset(S, rank == "A" )
intersect(A, B)

Intersection of Subsets Calculates the intersection of subsets of a probability space. Comparisons are made row-wise, so that in the data frame case, intersect(A,B) is a data frame with those rows that are both in A and in B.

Description

Intersection of Subsets Calculates the intersection of subsets of a probability space. Comparisons are made row-wise, so that in the data frame case, intersect(A,B) is a data frame with those rows that are both in A and in B.

Usage

## S3 method for class 'ps'
intersect(x, y, ...)

Arguments

Details

This is a generic function, extended from the intersect function in the base package. The elements of intersect(x,y) are those elements in x and in y. The original definition is preserved in the case that x and y are vectors of the same mode.

Value

A vector, data frame, or subset of a probability space of the same type as its arguments.

Author(s)

G. Jay Kerns gkerns@ysu.edu, based on a suggestion made by Brian Ripley in R-devel, 12/11/07.

See Also

union, setdiff

Examples

S <- cards()
A <- subset(S, suit == "Heart")
B <- subset(S, rank == "A" )
intersect(A, B)

Testing for a Probability Space Decides whether a given object is a probability space.

Description

Testing for a Probability Space Decides whether a given object is a probability space.

Usage

is.probspace(x)

Arguments

Details

It first checks if the class of the object includes ps, and if so TRUE is returned. If not, then it checks that the object is a data frame and contains a probs column. Lastly, it checks whether all entries of probs are nonnegative. Note that it does not check whether the sum of probs is one, to allow for the possibility that the input object is a proper subset of a probability space.

Value

Logical.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

probspace

Examples

S <- rolldie(3, makespace = TRUE)
is.probspace(S)

Test Whether One Vector Is In Another Vector

Description

Test Whether One Vector Is In Another Vector

Usage

isin(x, ...)

Arguments

Details

The function will only return TRUE if every element of y is present in the vector x, counting multiplicity. See the examples below. Of ordered = TRUE, then elements must be in the vector x in the order specified in y. Compare this to the behavior of the %in% function in the base package. This is a generic function with a method for data frames, which applies isin() to each row of the data frame, with a vector as a result.

Value

Logical, or a vector of logicals.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

isrep

Examples

x <- 1:10
y <- 3:7
z <- c(3,3,7)
isin(x,y)
isin(x,z)
isin(x, c(3,4,5), ordered = TRUE)
isin(x, c(3,5,4), ordered = TRUE)

S <- rolldie(4)
subset(S, isin(S, c(2,2,6), ordered = TRUE))

Test Whether One Vector Is In Another Vector

Description

Test Whether One Vector Is In Another Vector

Usage

## S3 method for class 'data.frame'
isin(x, ...)

Arguments

Details

The function will only return TRUE if every element of y is present in the vector x, counting multiplicity. See the examples below. Of ordered = TRUE, then elements must be in the vector x in the order specified in y. Compare this to the behavior of the %in% function in the base package. This is a generic function with a method for data frames, which applies isin() to each row of the data frame, with a vector as a result.

Value

Logical, or a vector of logicals.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

isrep

Examples

x <- 1:10
y <- 3:7
z <- c(3,3,7)
isin(x,y)
isin(x,z)
isin(x, c(3,4,5), ordered = TRUE)
isin(x, c(3,5,4), ordered = TRUE)

S <- rolldie(4)
subset(S, isin(S, c(2,2,6), ordered = TRUE))

Test Whether One Vector Is In Another Vector

Description

Test Whether One Vector Is In Another Vector

Usage

## Default S3 method:
isin(x, y, ordered = FALSE, ...)

Arguments

Details

The function will only return TRUE if every element of y is present in the vector x, counting multiplicity. See the examples below. Of ordered = TRUE, then elements must be in the vector x in the order specified in y. Compare this to the behavior of the %in% function in the base package. This is a generic function with a method for data frames, which applies isin() to each row of the data frame, with a vector as a result.

Value

Logical, or a vector of logicals.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

isrep

Examples

x <- 1:10
y <- 3:7
z <- c(3,3,7)
isin(x,y)
isin(x,z)
isin(x, c(3,4,5), ordered = TRUE)
isin(x, c(3,5,4), ordered = TRUE)

S <- rolldie(4)
subset(S, isin(S, c(2,2,6), ordered = TRUE))

Is Repeated in a Vector Tests for a certain number of repetitions of vals in a given vector x.

Description

Is Repeated in a Vector Tests for a certain number of repetitions of vals in a given vector x.

Usage

isrep(x, ...)

Arguments

Details

This is a generic function, with methods supplied for data frames and vectors. The default behavior tests for existence of pairs of elements of x. One can test existence of triples, etc., by changing the nrep argument. If there are specific values for which one is looking for repeats, these can be specified with the vals argument. Note that the function only checks for exactly nrep instances, so two pairs of a specific element would be counted as 0 pairs and 1 quadruple. See the examples. The data frame method uses apply to apply isrep.default to each row of the data frame.

Value

Logical.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

countrep

Examples

x <- c(3,3,2,2,3,3,4,4)
isrep(x)  # one pair each of 2s and 4s
isrep(x, nrep = 4)
isrep(x, vals = 4) # one pair of 4s

Is Repeated in a Vector Tests for a certain number of repetitions of vals in a given vector x.

Description

Is Repeated in a Vector Tests for a certain number of repetitions of vals in a given vector x.

Usage

## S3 method for class 'data.frame'
isrep(x, ...)

Arguments

Details

This is a generic function, with methods supplied for data frames and vectors. The default behavior tests for existence of pairs of elements of x. One can test existence of triples, etc., by changing the nrep argument. If there are specific values for which one is looking for repeats, these can be specified with the vals argument. Note that the function only checks for exactly nrep instances, so two pairs of a specific element would be counted as 0 pairs and 1 quadruple. See the examples. The data frame method uses apply to apply isrep.default to each row of the data frame.

Value

Logical.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

countrep

Examples

x <- c(3,3,2,2,3,3,4,4)
isrep(x)  # one pair each of 2s and 4s
isrep(x, nrep = 4)
isrep(x, vals = 4) # one pair of 4s

Is Repeated in a Vector Tests for a certain number of repetitions of vals in a given vector x.

Description

Is Repeated in a Vector Tests for a certain number of repetitions of vals in a given vector x.

Usage

## Default S3 method:
isrep(x, vals = unique(x), nrep = 2, ...)

Arguments

Details

This is a generic function, with methods supplied for data frames and vectors. The default behavior tests for existence of pairs of elements of x. One can test existence of triples, etc., by changing the nrep argument. If there are specific values for which one is looking for repeats, these can be specified with the vals argument. Note that the function only checks for exactly nrep instances, so two pairs of a specific element would be counted as 0 pairs and 1 quadruple. See the examples. The data frame method uses apply to apply isrep.default to each row of the data frame.

Value

Logical.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

countrep

Examples

x <- c(3,3,2,2,3,3,4,4)
isrep(x)  # one pair each of 2s and 4s
isrep(x, nrep = 4)
isrep(x, vals = 4) # one pair of 4s

Marginal Distributions

Description

Computes the marginal distribution of a set of variables.

Usage

marginal(space, vars = NULL)

Arguments

Details

If vars is not specified, then marginal() will set vars to be all non-probs columns, which can be useful in the case that it is desired to aggregate duplicated rows.

Value

A data frame with a probs column.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

See addrv for adding random variables to a data frame probability space.

Examples

S <- rolldie(3, makespace = TRUE)
marginal(S, vars = c("X1", "X2"))

Sort and Merge Probability Space Outcomes

Description

This function sorts the rows (outcomes) of a data frame probability space, effectively removing the original order present and aggregates the sorted rows into a new probability data frame with unique, sorted outcomes.

Usage

noorder(space)

Arguments

Details

The data frame space must have at least two non-probs columns or an error will result.

Value

A data frame with a probs column and sorted, unique rows.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

addrv, marginal

Examples

S <- tosscoin(3, makespace = TRUE)
noorder(S)

Number of Samples from an Urn

Description

Calculates the number of samples from an urn under different sampling scenarios.

Usage

nsamp(n, k, replace = FALSE, ordered = FALSE)

Arguments

Details

The nsamp() function will calculate the number of samples from an urn under assorted assumptions on the sampling procedure. The arguments are: n, the number of (distinguishable) objects in the urn, k, the sample size, and replace, ordered as documented in urnsamples.

nsamp() is vectorized, so that entering vectors instead of numbers for n, k, replace, and ordered results in a vector of corresponding answers.

The formulas used in the four possible combinations of replace and ordered are as follows:

• When replace = TRUE and ordered = TRUE, the value is n^k.

• When replace = FALSE and ordered = TRUE, the value is n!/(n-k)!.

• When replace = FALSE and ordered = FALSE, the value is n!/[k!(n-k)!].

• When replace = TRUE and ordered = FALSE, the value is (n-1+k)!/[(n-1)!k!].

Value

A number.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

urnsamples

Examples

nsamp(n = 3, k = 2, replace = TRUE, ordered = TRUE)
nsamp(n = 3, k = 2, replace = TRUE, ordered = FALSE)
nsamp(n = 3, k = 2, replace = FALSE, ordered = FALSE)
nsamp(n = 3, k = 2, replace = FALSE, ordered = TRUE)

Generate All Permutations of x Elements Taken m at a Time

Description

Generate all permutations of the elements of x taken m at a time. If x is a positive integer, returns all permutations of the elements of seq(x) taken m at a time.

Usage

permsn(x, m)

Arguments

Value

a list or array (in nondegenerate cases).

Author(s)

G. Jay Kerns gkerns@ysu.edu, modified from the combn function in the package utils.

See Also

combn

Examples

permsn(3, 2)

Probability Spaces Forms a probability space from a set of outcomes and (optional) vector of probabilities.

Description

Probability Spaces Forms a probability space from a set of outcomes and (optional) vector of probabilities.

Usage

probspace(x, ...)

Arguments

Details

The elements of probs will be normalized to ensure that their sum is one. If probs is not specified, then the equally likely model is assumed in which every outcome has the same probability.

Value

If outcomes is a vector or data frame, then the value is a data frame with an added probs column. If outcomes is a list, then the value is a list with components outcomes (the supplied list) and a probs component.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

Examples

R <- rolldie(3)
probspace(R)

Probability Spaces Forms a probability space from a set of outcomes and (optional) vector of probabilities.

Description

Probability Spaces Forms a probability space from a set of outcomes and (optional) vector of probabilities.

Usage

## Default S3 method:
probspace(x, probs, ...)

Arguments

Details

The elements of probs will be normalized to ensure that their sum is one. If probs is not specified, then the equally likely model is assumed in which every outcome has the same probability.

Value

If outcomes is a vector or data frame, then the value is a data frame with an added probs column. If outcomes is a list, then the value is a list with components outcomes (the supplied list) and a probs component.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

Examples

R <- rolldie(3)
probspace(R)

Probability Spaces Forms a probability space from a set of outcomes and (optional) vector of probabilities.

Description

Probability Spaces Forms a probability space from a set of outcomes and (optional) vector of probabilities.

Usage

## S3 method for class 'list'
probspace(x, probs, ...)

Arguments

Details

The elements of probs will be normalized to ensure that their sum is one. If probs is not specified, then the equally likely model is assumed in which every outcome has the same probability.

Value

If outcomes is a vector or data frame, then the value is a data frame with an added probs column. If outcomes is a list, then the value is a list with components outcomes (the supplied list) and a probs component.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

Examples

R <- rolldie(3)
probspace(R)

Rolling a Die

Description

Sets up a sample space for the experiment of rolling a die repeatedly.

Usage

rolldie(times, nsides = 6, makespace = FALSE)

Arguments

Details

The function uses expand.grid() to generate all possible rolls resulting from the experiment of rolling a die. Sides on the die are 1:nsides. Columns of the data frame are called X1, X2, up to Xtimes.

Value

A data frame, with an equally likely probs column if makespace is TRUE.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

tosscoin

Examples

rolldie(2)
rolldie(3, nsides = 4)
rolldie(3, nsides = 4, makespace = TRUE)

Roulette

Description

Sets up a sample space for the experiment of spinning a roulette wheel once.

Usage

roulette(european = FALSE, makespace = FALSE)

Arguments

Details

If european is TRUE, then a traditional EU roulette wheel with 37 pockets is used, otherwise, a standard US roulette wheel with 38 pockets is used. Entries in the data frame are ordered in the customary way to facilitate the calculation probabilities regarding called bets.

Value

A data frame, with columns num and color, and an equally likely probs column if makespace is TRUE.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

cards

Examples

roulette()
roulette(european = TRUE, makespace = TRUE)

Set Difference of Subsets Calculates the (nonsymmetric) set difference of subsets of a probability space.

Description

Set Difference of Subsets Calculates the (nonsymmetric) set difference of subsets of a probability space.

Usage

setdiff(x, ...)

Arguments

Details

This function operates row-wise on dataframes, and element-wise among the outcomes of ps objects. The elements of setdiff(x,y) are those elements in x but not in y. The definition is taken to match the version in the base package.

Value

A data frame or subset of a probability space of the same type as its arguments.

Author(s)

G. Jay Kerns gkerns@ysu.edu, essentially verbatim from a suggestion made by Brian Ripley on R-devel, 12/11/07

See Also

intersect, union

Examples

S <- cards()
A <- subset(S, suit == "Heart")
B <- subset(S, rank == "A" )
setdiff(B, A)

Set Difference of Subsets Calculates the (nonsymmetric) set difference of subsets of a probability space.

Description

Set Difference of Subsets Calculates the (nonsymmetric) set difference of subsets of a probability space.

Usage

## S3 method for class 'data.frame'
setdiff(x, y, ...)

Arguments

Details

This function operates row-wise on dataframes, and element-wise among the outcomes of ps objects. The elements of setdiff(x,y) are those elements in x but not in y. The definition is taken to match the version in the base package.

Value

A data frame or subset of a probability space of the same type as its arguments.

Author(s)

G. Jay Kerns gkerns@ysu.edu, essentially verbatim from a suggestion made by Brian Ripley on R-devel, 12/11/07

See Also

intersect, union

Examples

S <- cards()
A <- subset(S, suit == "Heart")
B <- subset(S, rank == "A" )
setdiff(B, A)

Set Difference of Subsets Calculates the (nonsymmetric) set difference of subsets of a probability space.

Description

Set Difference of Subsets Calculates the (nonsymmetric) set difference of subsets of a probability space.

Usage

## Default S3 method:
setdiff(x, y, ...)

Arguments

Details

This function operates row-wise on dataframes, and element-wise among the outcomes of ps objects. The elements of setdiff(x,y) are those elements in x but not in y. The definition is taken to match the version in the base package.

Value

A data frame or subset of a probability space of the same type as its arguments.

Author(s)

G. Jay Kerns gkerns@ysu.edu, essentially verbatim from a suggestion made by Brian Ripley on R-devel, 12/11/07

See Also

intersect, union

Examples

S <- cards()
A <- subset(S, suit == "Heart")
B <- subset(S, rank == "A" )
setdiff(B, A)

Set Difference of Subsets Calculates the (nonsymmetric) set difference of subsets of a probability space.

Description

Set Difference of Subsets Calculates the (nonsymmetric) set difference of subsets of a probability space.

Usage

## S3 method for class 'ps'
setdiff(x, y, ...)

Arguments

Details

This function operates row-wise on dataframes, and element-wise among the outcomes of ps objects. The elements of setdiff(x,y) are those elements in x but not in y. The definition is taken to match the version in the base package.

Value

A data frame or subset of a probability space of the same type as its arguments.

Author(s)

G. Jay Kerns gkerns@ysu.edu, essentially verbatim from a suggestion made by Brian Ripley on R-devel, 12/11/07

See Also

intersect, union

Examples

S <- cards()
A <- subset(S, suit == "Heart")
B <- subset(S, rank == "A" )
setdiff(B, A)

Simulate Draws from a Sample Space

Description

Simulates the experiment of drawing from a sample space.

Simulates the experiment of drawing from a sample space.

Simulates the experiment of drawing from a sample space.

Usage

sim(x, ...)

## Default S3 method:
sim(x, ntrials, ...)

## S3 method for class 'ps'
sim(x, ntrials, ...)

Arguments

Details

The sim() function is a wrapper for sample(), except that it strips the probs component from the result and (if x is a data frame) renames the rownames of the data frame consecutively from 1:ntrials.

The sim() function is a wrapper for sample(), except that it strips the probs component from the result and (if x is a data frame) renames the rownames of the data frame consecutively from 1:ntrials.

The sim() function is a wrapper for sample(), except that it strips the probs component from the result and (if x is a data frame) renames the rownames of the data frame consecutively from 1:ntrials.

Value

A data frame if space is a data frame, or a list if space is of class ps.

A data frame if space is a data frame, or a list if space is of class ps.

A data frame if space is a data frame, or a list if space is of class ps.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

empirical

empirical

empirical

Examples

S <- cards(makespace = TRUE)
sim(S, ntrials = 5)

T <- urnsamples(S, 2)
U <- probspace(T)
sim(U, ntrials = 4)

S <- cards(makespace = TRUE)
sim(S, ntrials = 5)

T <- urnsamples(S, 2)
U <- probspace(T)
sim(U, ntrials = 4)

S <- cards(makespace = TRUE)
sim(S, ntrials = 5)

T <- urnsamples(S, 2)
U <- probspace(T)
sim(U, ntrials = 4)

Subsets of Probability Spaces This is a method for subset() for the case when the input object is a probability space of class ps.

Description

Subsets of Probability Spaces This is a method for subset() for the case when the input object is a probability space of class ps.

Usage

## S3 method for class 'ps'
subset(x, subset, ...)

Arguments

Details

This function simply extends the existing subset() function to ps objects.

Value

A ps object, a subset of a probability space.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

Examples

L <- tosscoin(2)
M <- urnsamples(L, 3)
N <- probspace(M)
subset(N, all(toss1=="H"))
subset(N, any(toss2=="T"))

Tossing a Coin

Description

Sets up a sample space for the experiment of tossing a coin repeatedly with the outcomes "H" or "T".

Usage

tosscoin(times, makespace = FALSE)

Arguments

Details

The function uses expand.grid() to generate all possible sequences of flips resulting from the experiment of tossing a coin. Columns of the dataframe are denoted toss1, toss2, up to tosstimes.

Value

A data frame, with an equally likely probs column if makespace is TRUE.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

See Also

rolldie

Examples

tosscoin(2)
tosscoin(3, makespace = TRUE)

Union of Subsets Calculates the union of subsets of a probability space.

Description

Union of Subsets Calculates the union of subsets of a probability space.

Usage

union(x, ...)

Arguments

Details

This function operates row-wise on dataframes, and element-wise among the outcomes of ps objects. The elements of union(x,y) are those elements in x or y, or both. The definition is taken to match the version in the base package.

Value

A data frame or subset of a probability space of the same type as its arguments.

Author(s)

G. Jay Kerns gkerns@ysu.edu, based on a suggestion made by Brian Ripley in R-devel, 12/11/07.

Examples

S <- cards()
A <- subset(S, suit == "Heart")
B <- subset(S, rank == "A" )
union(A, B)

Union of Subsets Calculates the union of subsets of a probability space.

Description

Union of Subsets Calculates the union of subsets of a probability space.

Usage

## S3 method for class 'data.frame'
union(x, y, ...)

Arguments

Details

This function operates row-wise on dataframes, and element-wise among the outcomes of ps objects. The elements of union(x,y) are those elements in x or y, or both. The definition is taken to match the version in the base package.

Value

A data frame or subset of a probability space of the same type as its arguments.

Author(s)

G. Jay Kerns gkerns@ysu.edu, based on a suggestion made by Brian Ripley in R-devel, 12/11/07.

Examples

S <- cards()
A <- subset(S, suit == "Heart")
B <- subset(S, rank == "A" )
union(A, B)

Union of Subsets Calculates the union of subsets of a probability space.

Description

Union of Subsets Calculates the union of subsets of a probability space.

Usage

## Default S3 method:
union(x, y, ...)

Arguments

Details

This function operates row-wise on dataframes, and element-wise among the outcomes of ps objects. The elements of union(x,y) are those elements in x or y, or both. The definition is taken to match the version in the base package.

Value

A data frame or subset of a probability space of the same type as its arguments.

Author(s)

G. Jay Kerns gkerns@ysu.edu, based on a suggestion made by Brian Ripley in R-devel, 12/11/07.

Examples

S <- cards()
A <- subset(S, suit == "Heart")
B <- subset(S, rank == "A" )
union(A, B)

Union of Subsets Calculates the union of subsets of a probability space.

Description

Union of Subsets Calculates the union of subsets of a probability space.

Usage

## S3 method for class 'ps'
union(x, y, ...)

Arguments

Details

This function operates row-wise on dataframes, and element-wise among the outcomes of ps objects. The elements of union(x,y) are those elements in x or y, or both. The definition is taken to match the version in the base package.

Value

A data frame or subset of a probability space of the same type as its arguments.

Author(s)

G. Jay Kerns gkerns@ysu.edu, based on a suggestion made by Brian Ripley in R-devel, 12/11/07.

Examples

S <- cards()
A <- subset(S, suit == "Heart")
B <- subset(S, rank == "A" )
union(A, B)

Sampling from Urns This function creates a sample space associated with the experiment of sampling distinguishable objects from an urn.

Description

Sampling from Urns This function creates a sample space associated with the experiment of sampling distinguishable objects from an urn.

Usage

urnsamples(x, ...)

Arguments

Details

The function operates on the indices of the urn (or rows, in the case urn is a data frame). It then takes those samples and substitutes back into urn to generate the entries of the data frame (or list, respectively). In the case that urn has repeated values, the result will be repeated values in the output. Note that urnsamples strips x of any existing probs column before sampling.

Value

A data frame if urn is a vector, and a list if urn is a data frame.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

Examples

urnsamples(1:10, size = 5)
S <- cards()
 urnsamples(S, size = 2)

Sampling from Urns This function creates a sample space associated with the experiment of sampling distinguishable objects from an urn.

Description

Sampling from Urns This function creates a sample space associated with the experiment of sampling distinguishable objects from an urn.

Usage

## S3 method for class 'data.frame'
urnsamples(x, size, replace = FALSE, ordered = FALSE, ...)

Arguments

Details

The function operates on the indices of the urn (or rows, in the case urn is a data frame). It then takes those samples and substitutes back into urn to generate the entries of the data frame (or list, respectively). In the case that urn has repeated values, the result will be repeated values in the output. Note that urnsamples strips x of any existing probs column before sampling.

Value

A data frame if urn is a vector, and a list if urn is a data frame.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

Examples

urnsamples(1:10, size = 5)
S <- cards()
 urnsamples(S, size = 2)

Sampling from Urns This function creates a sample space associated with the experiment of sampling distinguishable objects from an urn.

Description

Sampling from Urns This function creates a sample space associated with the experiment of sampling distinguishable objects from an urn.

Usage

## Default S3 method:
urnsamples(x, size, replace = FALSE, ordered = FALSE, ...)

Arguments

Details

The function operates on the indices of the urn (or rows, in the case urn is a data frame). It then takes those samples and substitutes back into urn to generate the entries of the data frame (or list, respectively). In the case that urn has repeated values, the result will be repeated values in the output. Note that urnsamples strips x of any existing probs column before sampling.

Value

A data frame if urn is a vector, and a list if urn is a data frame.

Author(s)

G. Jay Kerns gkerns@ysu.edu.

Examples

urnsamples(1:10, size = 5)
S <- cards()
 urnsamples(S, size = 2)