Find The Best Fitting Distribution

Description

It finds the best fitting distribution from supported univariate continuous distributions for given data.

Usage

find_best_fit(
  x,
  positive = FALSE,
  plot = TRUE,
  legend.pos = "topright",
  dlc = NULL,
  dlw = 1,
  ...
)

Arguments

Details

This function is supported following univariate distributions:

• for positive random variables: Log normal, Exponential, Gamma and Weibull.

• for all random variables: Normal, Cauchy, Log normal, Exponential, Gamma, Weibull and Uniform.

Legends of the plot are ordered by p-values of the test.

Value

A list containing the following items:

distribution

the name of the best fitting distribution.

ks.statistic

the Kolmogorov-Smirnov test statistic for the distribution.

p.value

the p-value of the test.

summary

results similar to above for other distributions.

x

given data.

n

the sample size.

References

1. William J. Conover (1971). Practical Nonparametric Statistics. New York: John Wiley & Sons. Pages 295–301.

2. Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

ks.test, fitdistr, hist

Examples

petal.length <- datasets::iris$Petal.Length[datasets::iris$Species == "setosa"]
simukde::find_best_fit(x = petal.length, positive = TRUE)

Simulation with Kernel Density Estimation

Description

The simukde package provides a function which generates random values from a univariate and multivariate continuous distribution by using kernel density estimation based on a sample. The function uses the Accept-Reject method.

Note

Funding: This package has been done within the framework of the project Statistics and Optimization Based Methods for Identification of Cancer-Activated Biological Processes (P2017-2519) supported by the Asia Research Center, Mongolia and Korea Foundation for Advanced Studies, Korea.

The funders had no role in study design, analysis, decision to publish, or preparation of the package.

Author(s)

MAKHGAL Ganbold and BAYARBAATAR Amgalan, National University of Mongolia

References

Duong (2017) <doi:10.18637/jss.v021.i07>, Christian P. Robert and George Casella (2010 ISBN:978-1-4419-1575-7) <doi:10.1007/978-1-4419-1576-4>.

Simulation with Kernel Density Estimation

Description

Generates random values from a univariate and multivariate continuous distribution by using kernel density estimation based on a sample. The function uses the Accept-Reject method.

Usage

simulate_kde(
  x,
  n = 100,
  distr = "norm",
  const.only = FALSE,
  seed = NULL,
  parallel = FALSE,
  ...
)

Arguments

Details

Such function uses the function kde as kernel density estimator.

The Accept-Reject method is used to simulate random variables. Following code named distributions can be used as a value of the argument distr and an instrumental or candidate distribution of the simulation method. For univariate distributions:

norm

normal distribution (default), (-\infty,+\infty)

cauchy

Cauchy distribution, (-\infty,+\infty)

lnorm

log-normal distribution, (0,+\infty)

exp

exponential distribution, (0,+\infty)

gamma

gamma distribution, (0,+\infty)

weibull

Weibull distribution, (0,+\infty)

unif

uniform distribution, (a,b)

And you can choose the best fitting instrumental distribution to simulate random variables more effectively by using find_best_fit. See examples.

For multivariate distributions, "norm" (multivariate normal distribution) is used.

Value

list of given data, simulated values, kernel density estimation and the constant of the Accept-Reject method when const.only is FALSE (default).

References

• Tarn Duong (2018). ks: Kernel Smoothing. R package version 1.11.2. https://CRAN.R-project.org/package=ks

• Christian P. Robert and George Casella (2010) Introducing Monte Carlo Methods with R. Springer. Pages 51-57.

See Also

find_best_fit, kde

Examples

## 1-dimensional data
data(faithful)
hist(faithful$eruptions)
res <- simukde::simulate_kde(x = faithful$eruptions, n = 100, parallel = FALSE)
hist(res$random.values)

## Simulation with the best fitting instrumental distribution
data(faithful)
par(mfrow = c(1, 3))
hist(faithful$eruptions)
fit <- simukde::find_best_fit(x = faithful$eruptions, positive = TRUE)
res <- simukde::simulate_kde(
  x = faithful$eruptions, n = 100,
  distr = fit$distribution, parallel = FALSE
)
hist(res$random.values)
par(mfrow = c(1, 1))

## 2-dimensional data
data(faithful)
res <- simukde::simulate_kde(x = faithful, n = 100)
plot(res$kde, display = "filled.contour")
points(x = res$random.values, cex = 0.25, pch = 16, col = "green")
points(x = faithful, cex = 0.25, pch = 16, col = "black")