Type: Package
Title: Statistical Functions for Probability Distributions and Regression
Version: 0.2.3
Description: A collection of miscellaneous statistical functions for probability distributions: 'dbern()', 'pbern()', 'qbern()', 'rbern()' for the Bernoulli distribution, and 'distr2name()', 'name2distr()' for distribution names; probability density estimation: 'densityfun()'; most frequent value estimation: 'mfv()', 'mfv1()'; other statistical measures of location: 'cv()' (coefficient of variation), 'midhinge()', 'midrange()', 'trimean()'; construction of histograms: 'histo()', 'find_breaks()'; calculation of the Hellinger distance: 'hellinger()'; use of classical kernels: 'kernelfun()', 'kernel_properties()'; univariate piecewise-constant regression: 'picor()'.
License: GPL-3
LazyData: TRUE
Depends: R (≥ 3.1.3)
Imports: clue, graphics, rpart, stats
Suggests: knitr, testthat
URL: https://github.com/paulponcet/statip
BugReports: https://github.com/paulponcet/statip/issues
RoxygenNote: 7.0.0
NeedsCompilation: yes
Packaged: 2019-11-17 21:21:11 UTC; YL1101
Author: Paul Poncet [aut, cre], The R Core Team [aut, cph] (C function 'BinDist' copied from package 'stats'), The R Foundation [cph] (C function 'BinDist' copied from package 'stats'), Adrian Baddeley [ctb] (C function 'BinDist' copied from package 'stats')
Maintainer: Paul Poncet <paulponcet@yahoo.fr>
Repository: CRAN
Date/Publication: 2019-11-17 21:40:02 UTC

Bandwidth calculation

Description

bandwidth computes the bandwidth to be used in the densityfun function.

Usage

bandwidth(x, rule)

Arguments

x

numeric. The data from which the estimate is to be computed.

rule

character. A rule to choose the bandwidth. See bw.nrd.

Value

A numeric value.

Coefficient of variation

Description

Compute the coefficient of variation of a numeric vector x, defined as the ratio between the standard deviation and the mean.

Usage

cv(x, na_rm = FALSE, ...)

Arguments

x

numeric. A numeric vector.

na_rm

logical. Should missing values be removed before computing the coefficient of variation?

...

Additional arguments to be passed to mean().

Value

A numeric value, the coefficient of variation.

References

https://en.wikipedia.org/wiki/Coefficient_of_variation.

The Bernoulli distribution

Description

Density, distribution function, quantile function and random generation for the Bernoulli distribution.

Usage

dbern(x, prob, log = FALSE)

qbern(p, prob, lower.tail = TRUE, log.p = FALSE)

pbern(q, prob, lower.tail = TRUE, log.p = FALSE)

rbern(n, prob)

Arguments

x

numeric. Vector of quantiles.

prob

Probability of success on each trial.

log

logical. If TRUE, probabilities p are given as log(p).

p

numeric in [0, 1]. Vector of probabilities.

lower.tail

logical. If TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].

log.p

logical. If TRUE, probabilities p are given as log(p).

q

numeric. Vector of quantiles.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

See Also

See the help page of the Binomial distribution.

Kernel density estimation

Description

Return a function performing kernel density estimation. The difference between density and densityfun is similar to that between approx and approxfun.

Usage

densityfun(
  x,
  bw = "nrd0",
  adjust = 1,
  kernel = "gaussian",
  weights = NULL,
  window = kernel,
  width,
  n = 512,
  from,
  to,
  cut = 3,
  na.rm = FALSE,
  ...
)

Arguments

x

numeric. The data from which the estimate is to be computed.

bw

numeric. The smoothing bandwidth to be used. See the eponymous argument of density.

adjust

numeric. The bandwidth used is actually adjust*bw. This makes it easy to specify values like 'half the default' bandwidth.

kernel, window

character. A string giving the smoothing kernel to be used. Authorized kernels are listed in .kernelsList(). See also the eponymous argument of density.

weights

numeric. A vector of non-negative observation weights, hence of same length as x. See the eponymous argument of density.

width

this exists for compatibility with S; if given, and bw is not, will set bw to width if this is a character string, or to a kernel-dependent multiple of width if this is numeric.

n

The number of equally spaced points at which the density is to be estimated. See the eponymous argument of density.

from, to

The left and right-most points of the grid at which the density is to be estimated; the defaults are cut * bw outside of range(x).

cut

By default, the values of from and to are cut bandwidths beyond the extremes of the data. This allows the estimated density to drop to approximately zero at the extremes.

na.rm

logical. If TRUE, missing values are removed from x. If FALSE any missing values cause an error.

...

Additional arguments for (non-default) methods.

Value

A function that can be called to generate a density.

Author(s)

Adapted from the density function of package stats. The C code of BinDist is copied from package stats and authored by the R Core Team with contributions from Adrian Baddeley.

See Also

density and approxfun from package stats.

Examples

x <- rlnorm(1000, 1, 1)
f <- densityfun(x, from = 0)
curve(f(x), xlim = c(0, 20))

Conversion between abbreviated distribution names and proper names

Description

The function distr2name() converts abbreviated distribution names to proper distribution names (e.g. "norm" becomes "Gaussian").

The function name2distr() does the reciprocal operation.

Usage

distr2name(x)

name2distr(x)

Arguments

x

character. A vector of abbreviated distribution names or proper distribution names.

Value

A character vector of the same length as x. Elements of x that are not recognized are kept unchanged (yet in lowercase).

Examples

distr2name(c("norm", "dnorm", "rhyper", "ppois"))
name2distr(c("Cauchy", "Gaussian", "Generalized Extreme Value"))

Error function

Description

The function erf() encodes the error function, defined as erf(x) = 2 * F(x * sqrt(2)) - 1, where F is the Gaussian distribution function.

Usage

erf(x, ...)

Arguments

x

numeric. A vector of input values.

...

Additional arguments to be passed to pnorm.

Value

A numeric vector of the same length as x.

References

https://en.wikipedia.org/wiki/Error_function.

See Also

pnorm from package stats.

Breakpoints to be passed to a Histogram

Description

The function find_breaks() isolates a piece of code of the function truehist() from package MASS that is used to compute the set of breakpoints to be applied for the construction of the histogram.

Usage

find_breaks(x, nbins = "Scott", h, x0 = -h/1000)

Arguments

x

numeric. A vector.

nbins

integer or character. The suggested number of bins. Either a positive integer, or a character string naming a rule: "Scott" (the default) or "Freedman-Diaconis" or "FD". (Case is ignored.)

h

numeric. The bin width, a strictly positive number (takes precedence over nbins).

x0

numeric. Shift for the bins - the breaks are at x0 + h * (..., -1, 0, 1, ...).

Value

A numeric vector.

See Also

histo() in this package; truehist() from package MASS; hist() from package graphics.

Hellinger distance

Description

Estimate the Hellinger distance between two random samples whose underdyling distributions are continuous.

Usage

hellinger(x, y, lower = -Inf, upper = Inf, method = 1, ...)

Arguments

x

numeric. A vector giving the first sample.

y

numeric. A vector giving the second sample.

lower

numeric. Lower limit passed to integrate.

upper

numeric. Upper limit passed to integrate.

method

integer. If method = 1, the usual definition of the Hellinger distance is used; if method = 2, an alternative formula is used.

...

Additional parameters to be passed to densityfun.

Details

Probability density functions are estimated with densityfun. Then numeric integration is performed with integrate.

Value

A numeric value, the Hellinger distance.

References

https://en.wikipedia.org/wiki/Hellinger_distance.

See Also

HellingerDist in package distrEx.

Examples

x <- rnorm(200, 0, 2)
y <- rnorm(1000, 10, 15)
hellinger(x, y, -Inf, Inf)
hellinger(x, y, -Inf, Inf, method = 2)

Alternative Histograms

Description

A simplified version of hist() from package graphics.

Usage

histo(x, breaks, ...)

Arguments

x

numeric. A vector.

breaks

numeric. A vector of breakpoints to build the histogram, possibly given by find_breaks().

...

Additional parameters (currently not used).

Value

An object of class "histogram", which can be plotted by plot.histogram from package graphics. This object is a list with components:

See Also

find_breaks() in this package; truehist() from package MASS; hist() from package graphics.

Smoothing kernels

Description

The generic function kernelfun creates a smoothing kernel function.

Usage

kernel_properties(name, derivative = FALSE)

kernelfun(name, ...)

## S3 method for class ''function''
kernelfun(name, ...)

## S3 method for class 'character'
kernelfun(name, derivative = FALSE, ...)

.kernelsList()

Arguments

name

character. The name of the kernel to be used. Authorized kernels are listed in .kernelsList().

derivative

logical. If TRUE, the derivative of the kernel is returned.

...

Additional arguments to be passed to the kernel function.

Value

A function.

See Also

density in package stats.

Examples

kernel_properties("gaussian")

k <- kernelfun("epanechnikov")
curve(k(x), xlim = c(-1, 1))

Lag a vector

Description

This function computes a lagged vector, shifting it back or forward.

Usage

lagk(x, k, na = FALSE, cst = FALSE)

Arguments

x

A vector.

k

integer. The number of lags. If k < 0, la serie est avancee au lieu d'etre retardee.

na

logical. If na = TRUE and k > 0 (resp. k < 0), the |k| holes created in the lagged vector are put to NA; otherwise, the imputation depends on cst.

cst

logical. If na = FALSE and cst = TRUE, the |k| holes created in the lagged vector are put to x[[1L]] (or to x[[length(x)]] if k < 0). If na = FALSE and cst = FALSE, these |k| holes are imputed by the k first values of x (or the k last values if k < 0).

Value

A vector of the same type and length as x.

Examples

v <- sample(1:10)
print(v)
lagk(v, 1)
lagk(v, 1, na = TRUE)
lagk(v, -2)
lagk(v, -3, na = TRUE)
lagk(v, -3, na = FALSE, cst = TRUE)
lagk(v, -3, na = FALSE)

Most frequent value(s)

Description

The function mfv() returns the most frequent value(s) (or mode(s)) found in a vector. The function mfv1 returns the first of these values, so that mfv1(x) is identical to mfv(x)[[1L]].

Usage

mfv(x, ...)

## Default S3 method:
mfv(x, na_rm = FALSE, ...)

## S3 method for class 'tableNA'
mfv(x, na_rm = FALSE, ...)

mfv1(x, na_rm = FALSE, ...)

Arguments

x

Vector of observations (of type numeric, integer, character, factor, or logical). x is to come from a discrete distribution.

...

Additional arguments (currently not used).

na_rm

logical. If TRUE, missing values do not interfer with the result, see 'Details'.

Details

See David Smith' blog post here to understand the philosophy followed in the code of mfv for missing values treatment.

Value

The function mfv returns a vector of the same type as x. One should be aware that this vector can be of length > 1, in case of multiple modes. mfv1 always returns a vector of length 1 (the first of the modes found).

Note

mfv() calls the function tabulate.

References

Examples

# Basic examples:
mfv(integer(0))                      # NaN
mfv(c(3, 3, 3, 2, 4))                # 3
mfv(c(TRUE, FALSE, TRUE))            # TRUE
mfv(c("a", "a", "b", "a", "d"))      # "a"

mfv(c("a", "a", "b", "b", "d"))      # c("a", "b")
mfv1(c("a", "a", "b", "b", "d"))     # "a"

# With missing values: 
mfv(c(3, 3, 3, 2, NA))               # 3
mfv(c(3, 3, 2, NA))                  # NA
mfv(c(3, 3, 2, NA), na_rm = TRUE)    # 3
mfv(c(3, 3, 2, 2, NA))               # NA
mfv(c(3, 3, 2, 2, NA), na_rm = TRUE) # c(2, 3)
mfv1(c(3, 3, 2, 2, NA), na_rm = TRUE)# 2

# With only missing values: 
mfv(c(NA, NA))                   # NA
mfv(c(NA, NA), na_rm = TRUE)     # NaN

# With factors
mfv(factor(c("a", "b", "a")))
mfv(factor(c("a", "b", "a", NA)))
mfv(factor(c("a", "b", "a", NA)), na_rm = TRUE)

Midhinge

Description

Compute the midhinge of a numeric vector x, defined as the average of the first and third quartiles.

Usage

midhinge(x, na_rm = FALSE, ...)

Arguments

x

numeric. A numeric vector.

na_rm

logical. Should missing values be removed before computing the midhinge?

...

Additional arguments to be passed to quantile().

Value

A numeric value, the midhinge.

References

https://en.wikipedia.org/wiki/Midhinge.

Mid-range

Description

Compute the mid-range of a numeric vector x, defined as the mean of the minimum and the maximum.

Usage

midrange(x, na_rm = FALSE)

Arguments

x

numeric. A numeric vector.

na_rm

logical. Should missing values be removed before computing the mid-range?

Value

A numeric value, the mid-range.

References

https://en.wikipedia.org/wiki/Mid-range.

Piecewise-constant regression

Description

picor looks for a piecewise-constant function as a regression function. The regression is necessarily univariate. This is essentially a wrapper for rpart (regression tree) and isoreg.

Usage

picor(formula, data, method, min_length = 0, ...)

## S3 method for class 'picor'
knots(Fn, ...)

## S3 method for class 'picor'
predict(object, newdata, ...)

## S3 method for class 'picor'
plot(x, ...)

## S3 method for class 'picor'
print(x, ...)

Arguments

formula

formula of the model to be fitted.

data

optional data frame.

method

character. If method = "isotonic", then isotonic regression is applied with the isoreg from package stats. Otherwise, rpart is used, with the corresponding method argument.

min_length

integer. The minimal distance between two consecutive knots.

...

Additional arguments to be passed to rpart.

object, x, Fn

An object of class "picor".

newdata

data.frame to be passed to the predict method.

Value

An object of class "picor", which is a list composed of the following elements:

Examples

## Not run: 
s <- stats::stepfun(c(-1,0,1), c(1., 2., 4., 3.))
x <- stats::rnorm(1000)
y <- s(x)
p <- picor(y ~ x, data.frame(x = x, y = y))
print(p)
plot(p)

## End(Not run)

Basic plot of a loess object

Description

Plots a loess object adjusted on one unique explanatory variable.

Usage

## S3 method for class 'loess'
plot(x, ...)

Arguments

x

An object of class "loess".

...

Additional graphical arguments.

See Also

loess from package stats.

Examples

reg <- loess(dist ~ speed, cars)
plot(reg)

Default model predictions

Description

Default method of the predict generic function, which can be used when the model object is empty.

Usage

## Default S3 method:
predict(object, newdata, ...)

Arguments

object

A model object, possibly empty.

newdata

An optional data frame in which to look for variables with which to predict. If omitted, the fitted values are used.

...

Additional arguments.

Value

A vector of predictions.

See Also

predict from package stats.

Examples

stats::predict(NULL)
stats::predict(NULL, newdata = data.frame(x = 1:2, y = 2:3))

Objects exported from other packages

Description

These objects are imported from other packages. Follow the links below to see their documentation.

graphics

plot

stats

as.stepfun, knots, na.pass, predict, predict

Alternative Table Creation

Description

Count the occurrences of each factor level or value in a vector.

Usage

tableNA(x)

Arguments

x

numeric. An atomic vector or a factor.

Value

An object of class "tableNA", which is the result of tabulate() with three attributes:

The number of missing values is always reported.

Examples

tableNA(c(1,2,2,1,3))
tableNA(c(1,2,2,1,3, NA))

Tukey's trimean

Description

Compute the trimean of a numeric vector x.

Usage

trimean(x, na_rm = FALSE, ...)

Arguments

x

numeric. A numeric vector.

na_rm

logical. Should missing values be removed before computing the trimean?

...

Additional arguments to be passed to quantile().

Value

A numeric value, the trimean.

References

https://en.wikipedia.org/wiki/Trimean