Title: Some Distributions from the 'Boost' Library and More
Version: 1.0.0
Description: Make some distributions from the 'C++' library 'Boost' available in 'R'. In addition, the normal-inverse Gaussian distribution and the generalized inverse Gaussian distribution are provided. The distributions are represented by 'R6' classes. The method to sample from the generalized inverse Gaussian distribution is the one given in "Random variate generation for the generalized inverse Gaussian distribution" Luc Devroye (2012) <doi:10.1007/s11222-012-9367-z>.
License: GPL-3
URL: https://github.com/stla/boodist
BugReports: https://github.com/stla/boodist/issues
Imports: R6, Rcpp, RcppNumerical, stats
LinkingTo: BH, Rcpp, RcppEigen, RcppNumerical
Suggests: plotly
Encoding: UTF-8
RoxygenNote: 7.2.3
SystemRequirements: C++17
NeedsCompilation: yes
Packaged: 2023-08-09 13:14:44 UTC; SDL96354
Author: Stéphane Laurent [aut, cre]
Maintainer: Stéphane Laurent <laurent_step@outlook.fr>
Repository: CRAN
Date/Publication: 2023-08-10 10:00:02 UTC

Generalized inverse Gaussian distribution

Description

A R6 class to represent a generalized inverse Gaussian distribution.

Details

See Wikipedia.

Active bindings

theta

Get or set the value of theta.

eta

Get or set the value of eta.

lambda

Get or set the value of lambda.

Methods

Public methods

Method new()

New generalized inverse Gaussian distribution.

Usage
GeneralizedInverseGaussian$new(theta, eta, lambda)
Arguments
theta

concentration parameter, >0

eta

scale parameter, >0

lambda

parameter (denoted by p on Wikipedia)

Returns

A GeneralizedInverseGaussian object.

Method d()

Density function of the generalized inverse Gaussian distribution.

Usage
GeneralizedInverseGaussian$d(x, log = FALSE)
Arguments
x

vector of positive numbers

log

Boolean, whether to return the log-density

Returns

The density or the log-density evaluated at x.

Method p()

Cumulative distribution function of the generalized inverse Gaussian distribution.

Usage
GeneralizedInverseGaussian$p(q)
Arguments
q

numeric vector of quantiles (>= 0)

Returns

The cumulative probabilities corresponding to q, with two attributes (see the Note).

Method q()

Quantile function of the generalized inverse Gaussian distribution.

Usage
GeneralizedInverseGaussian$q(p, bounds = NULL)
Arguments
p

numeric vector of probabilities

bounds

bounds enclosing the quantiles to be found (see the Note), or NULL for automatic bounds

Returns

The quantiles corresponding to p.

Method r()

Sampling from the generalized inverse Gaussian distribution.

Usage
GeneralizedInverseGaussian$r(n)
Arguments
n

number of simulations

Returns

A numeric vector of length n.

Method mean()

Mean of the generalized inverse Gaussian distribution.

Usage
GeneralizedInverseGaussian$mean()
Returns

The mean of the generalized inverse Gaussian distribution.

Method mode()

Mode of the generalized inverse Gaussian distribution.

Usage
GeneralizedInverseGaussian$mode()
Returns

The mode of the generalized inverse Gaussian distribution.

Method sd()

Standard deviation of the generalized inverse Gaussian distribution.

Usage
GeneralizedInverseGaussian$sd()
Returns

The standard deviation of the generalized inverse Gaussian distribution.

Method variance()

Variance of the generalized inverse Gaussian distribution.

Usage
GeneralizedInverseGaussian$variance()
Returns

The variance of the generalized inverse Gaussian distribution.

Method clone()

The objects of this class are cloneable with this method.

Usage
GeneralizedInverseGaussian$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Note

The cumulative distribution function is evaluated by integrating the density function (in C++). Its returned value has two attributes: a numeric vector "error_estimate" and an integer vector "error_code". The error code is 0 if no problem is detected. If an error code is not 0, a warning is thrown. The quantile function is evaluated by root-finding and then the user must provide some bounds enclosing the values of the quantiles or choose the automatic bounds. A maximum number of iterations is fixed in the root-finding algorithm. If it is reached, a warning is thrown.

Examples

if(require("plotly")) {
library(boodist)

x_ <- seq(0, 3, length.out = 100L)
lambda_ <- seq(-1, 1, length.out = 100L)
dsty <- vapply(lambda_, function(lambda) {
  GeneralizedInverseGaussian$new(theta = 1, eta = 1, lambda)$d(x_)
}, numeric(length(x_)))
#
txt <- matrix(NA_character_, nrow = length(x_), ncol = length(lambda_))
for(i in 1L:nrow(txt)) {
  for(j in 1L:ncol(txt)) {
    txt[i, j] <- paste0(
      "x: ", formatC(x_[i]),
      "<br> lambda: ", formatC(lambda_[j]),
      "<br> density: ", formatC(dsty[i, j])
    )
  }
}
#
plot_ly(
  x = ~lambda_, y = ~x_, z = ~dsty, type = "surface",
  text = txt, hoverinfo = "text", showscale = FALSE
) %>% layout(
  title = "Generalized inverse Gaussian distribution",
  margin = list(t = 40, r= 5, b = 5, l = 5),
  scene = list(
    xaxis = list(
      title = "lambda"
    ),
    yaxis = list(
      title = "x"
    ),
    zaxis = list(
      title = "density"
    )
  )
)
}

Gumbel distribution

Description

A R6 class to represent a Gumbel distribution.

Details

See Wikipedia.

Active bindings

a

Get or set the value of a.

b

Get or set the value of b.

Methods

Public methods

Method new()

New Gumbel distribution.

Usage
Gumbel$new(a, b)
Arguments
a

location parameter

b

scale parameter, >0

Returns

A Gumbel object.

Method d()

Density function of the Gumbel distribution.

Usage
Gumbel$d(x, log = FALSE)
Arguments
x

numeric vector

log

Boolean, whether to return the logarithm of the density

Returns

The density or the log-density evaluated at x.

Method p()

Cumulative distribution function of the Gumbel distribution.

Usage
Gumbel$p(q, lower = TRUE)
Arguments
q

numeric vector of quantiles

lower

Boolean, whether to deal with the lower tail

Returns

The cumulative probabilities corresponding to q.

Method q()

Quantile function of the Gumbel distribution.

Usage
Gumbel$q(p, lower = TRUE)
Arguments
p

numeric vector of probabilities

lower

Boolean, whether to deal with the lower tail

Returns

The quantiles corresponding to p.

Method r()

Sampling from the Gumbel distribution.

Usage
Gumbel$r(n)
Arguments
n

number of simulations

Returns

A numeric vector of length n.

Method mean()

Mean of the Gumbel distribution.

Usage
Gumbel$mean()
Returns

The mean of the Gumbel distribution.

Method median()

Median of the Gumbel distribution.

Usage
Gumbel$median()
Returns

The median of the Gumbel distribution.

Method mode()

Mode of the Gumbel distribution.

Usage
Gumbel$mode()
Returns

The mode of the Gumbel distribution.

Method sd()

Standard deviation of the Gumbel distribution.

Usage
Gumbel$sd()
Returns

The standard deviation of the Gumbel distribution.

Method variance()

Variance of the Gumbel distribution.

Usage
Gumbel$variance()
Returns

The variance of the Gumbel distribution.

Method skewness()

Skewness of the Gumbel distribution.

Usage
Gumbel$skewness()
Returns

The skewness of the Gumbel distribution.

Method kurtosis()

Kurtosis of the Gumbel distribution.

Usage
Gumbel$kurtosis()
Returns

The kurtosis of the Gumbel distribution.

Method kurtosisExcess()

Kurtosis excess of the Gumbel distribution.

Usage
Gumbel$kurtosisExcess()
Returns

The kurtosis excess of the Gumbel distribution.

Method clone()

The objects of this class are cloneable with this method.

Usage
Gumbel$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Hyperexponential distribution

Description

A R6 class to represent a hyperexponential distribution.

Details

See Wikipedia.

Active bindings

probs

Get or set the value of probs.

rates

Get or set the value of rates.

Methods

Public methods

Method new()

New hyperexponential distribution.

Usage
Hyperexponential$new(probs, rates)
Arguments
probs

probabilities (weights), a vector of positive numbers

rates

rate parameters, vector of positive numbers of the same length as the probs vector

Returns

A Hyperexponential object.

Method d()

Density function of the hyperexponential distribution.

Usage
Hyperexponential$d(x)
Arguments
x

vector of positive numbers

Returns

The density evaluated at x.

Method p()

Cumulative distribution function of the hyperexponential distribution.

Usage
Hyperexponential$p(q, lower = TRUE)
Arguments
q

numeric vector of quantiles

lower

Boolean, whether to deal with the lower tail

Returns

The cumulative probabilities corresponding to q.

Method q()

Quantile function of the hyperexponential distribution.

Usage
Hyperexponential$q(p, lower = TRUE)
Arguments
p

numeric vector of probabilities

lower

Boolean, whether to deal with the lower tail

Returns

The quantiles corresponding to p.

Method r()

Sampling from the hyperexponential distribution.

Usage
Hyperexponential$r(n)
Arguments
n

number of simulations

Returns

A numeric vector of length n.

Method mean()

Mean of the hyperexponential distribution.

Usage
Hyperexponential$mean()
Returns

The mean of the hyperexponential distribution.

Method mode()

Mode of the hyperexponential distribution.

Usage
Hyperexponential$mode()
Returns

The mode of the hyperexponential distribution.

Method sd()

Standard deviation of the hyperexponential distribution.

Usage
Hyperexponential$sd()
Returns

The standard deviation of the hyperexponential distribution.

Method variance()

Variance of the hyperexponential distribution.

Usage
Hyperexponential$variance()
Returns

The variance of the hyperexponential distribution.

Method skewness()

Skewness of the hyperexponential distribution.

Usage
Hyperexponential$skewness()
Returns

The skewness of the hyperexponential distribution.

Method kurtosis()

Kurtosis of the hyperexponential distribution.

Usage
Hyperexponential$kurtosis()
Returns

The kurtosis of the hyperexponential distribution.

Method kurtosisExcess()

Kurtosis excess of the hyperexponential distribution.

Usage
Hyperexponential$kurtosisExcess()
Returns

The kurtosis excess of the hyperexponential distribution.

Method clone()

The objects of this class are cloneable with this method.

Usage
Hyperexponential$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Inverse Gamma distribution

Description

A R6 class to represent an inverse Gamma distribution.

Details

See Wikipedia.

Active bindings

alpha

Get or set the value of alpha.

beta

Get or set the value of beta.

Methods

Public methods

Method new()

New inverse Gamma distribution.

Usage
InverseGamma$new(alpha, beta)
Arguments
alpha

shape parameter, >0

beta

scale parameter, >0

Returns

An inverseGamma object.

Method d()

Density function of the inverse Gamma distribution.

Usage
InverseGamma$d(x, log = FALSE)
Arguments
x

vector of positive numbers

log

Boolean, whether to return the logarithm of the density

Returns

The density or the log-density evaluated at x.

Method p()

Cumulative distribution function of the inverse Gamma distribution.

Usage
InverseGamma$p(q, lower = TRUE)
Arguments
q

numeric vector of quantiles

lower

Boolean, whether to deal with the lower tail

Returns

The cumulative probabilities corresponding to q.

Method q()

Quantile function of the inverse Gamma distribution.

Usage
InverseGamma$q(p, lower = TRUE)
Arguments
p

numeric vector of probabilities

lower

Boolean, whether to deal with the lower tail

Returns

The quantiles corresponding to p.

Method r()

Sampling from the inverse Gamma distribution.

Usage
InverseGamma$r(n)
Arguments
n

number of simulations

Returns

A numeric vector of length n.

Method mean()

Mean of the inverse Gamma distribution.

Usage
InverseGamma$mean()
Returns

The mean of the inverse Gamma distribution.

Method median()

Median of the inverse Gamma distribution.

Usage
InverseGamma$median()
Returns

The median of the inverse Gamma distribution.

Method mode()

Mode of the inverse Gamma distribution.

Usage
InverseGamma$mode()
Returns

The mode of the inverse Gamma distribution.

Method sd()

Standard deviation of the inverse Gamma distribution.

Usage
InverseGamma$sd()
Returns

The standard deviation of the inverse Gamma distribution.

Method variance()

Variance of the inverse Gamma distribution.

Usage
InverseGamma$variance()
Returns

The variance of the inverse Gamma distribution.

Method skewness()

Skewness of the inverse Gamma distribution.

Usage
InverseGamma$skewness()
Returns

The skewness of the inverse Gamma distribution.

Method kurtosis()

Kurtosis of the inverse Gamma distribution.

Usage
InverseGamma$kurtosis()
Returns

The kurtosis of the inverse Gamma distribution.

Method kurtosisExcess()

Kurtosis excess of the inverse Gamma distribution.

Usage
InverseGamma$kurtosisExcess()
Returns

The kurtosis excess of the inverse Gamma distribution.

Method clone()

The objects of this class are cloneable with this method.

Usage
InverseGamma$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Examples

if(require("plotly")) {
x_ <- seq(0, 2, length.out = 100L)
alpha_ <- seq(0.5, 2.5, length.out = 100L)
dsty <- vapply(alpha_, function(alpha) {
  InverseGamma$new(alpha, beta = 1)$d(x_)
}, numeric(length(x_)))
#
txt <- matrix(NA_character_, nrow = length(x_), ncol = length(alpha_))
for(i in 1L:nrow(txt)) {
  for(j in 1L:ncol(txt)) {
    txt[i, j] <- paste0(
      "x: ", formatC(x_[i]),
      "<br> alpha: ", formatC(alpha_[j]),
      "<br> density: ", formatC(dsty[i, j])
    )
  }
}
#
plot_ly(
  x = ~alpha_, y = ~x_, z = ~dsty, type = "surface",
  text = txt, hoverinfo = "text", showscale = FALSE
) %>% layout(
  title = "Inverse Gamma distribution",
  margin = list(t = 40, r= 5, b = 5, l = 5),
  scene = list(
    xaxis = list(
      title = "alpha"
    ),
    yaxis = list(
      title = "x"
    ),
    zaxis = list(
      title = "density"
    )
  )
)
}

Inverse Gaussian distribution

Description

A R6 class to represent an inverse Gaussian distribution.

Details

See Wikipedia.

Active bindings

mu

Get or set the value of mu.

lambda

Get or set the value of lambda.

Methods

Public methods

Method new()

New inverse Gaussian distribution.

Usage
InverseGaussian$new(mu, lambda)
Arguments
mu

parameter, the mean, >0

lambda

shape parameter, >0

Returns

An inverseGaussian object.

Method d()

Density function of the inverse Gaussian distribution.

Usage
InverseGaussian$d(x, log = FALSE)
Arguments
x

vector of positive numbers

log

Boolean, whether to return the logarithm of the density

Returns

The density or the log-density evaluated at x.

Method p()

Cumulative distribution function of the inverse Gaussian distribution.

Usage
InverseGaussian$p(q, lower = TRUE)
Arguments
q

numeric vector of quantiles

lower

Boolean, whether to deal with the lower tail

Returns

The cumulative probabilities corresponding to q.

Method q()

Quantile function of the inverse Gaussian distribution.

Usage
InverseGaussian$q(p, lower = TRUE)
Arguments
p

numeric vector of probabilities

lower

Boolean, whether to deal with the lower tail

Returns

The quantiles corresponding to p.

Method r()

Sampling from the inverse Gaussian distribution.

Usage
InverseGaussian$r(n)
Arguments
n

number of simulations

Returns

A numeric vector of length n.

Method mean()

Mean of the inverse Gaussian distribution.

Usage
InverseGaussian$mean()
Returns

The mean of the inverse Gaussian distribution.

Method median()

Median of the inverse Gaussian distribution.

Usage
InverseGaussian$median()
Returns

The median of the inverse Gaussian distribution.

Method mode()

Mode of the inverse Gaussian distribution.

Usage
InverseGaussian$mode()
Returns

The mode of the inverse Gaussian distribution.

Method sd()

Standard deviation of the inverse Gaussian distribution.

Usage
InverseGaussian$sd()
Returns

The standard deviation of the inverse Gaussian distribution.

Method variance()

Variance of the inverse Gaussian distribution.

Usage
InverseGaussian$variance()
Returns

The variance of the inverse Gaussian distribution.

Method skewness()

Skewness of the inverse Gaussian distribution.

Usage
InverseGaussian$skewness()
Returns

The skewness of the inverse Gaussian distribution.

Method kurtosis()

Kurtosis of the inverse Gaussian distribution.

Usage
InverseGaussian$kurtosis()
Returns

The kurtosis of the inverse Gaussian distribution.

Method kurtosisExcess()

Kurtosis excess of the inverse Gaussian distribution.

Usage
InverseGaussian$kurtosisExcess()
Returns

The kurtosis excess of the inverse Gaussian distribution.

Method clone()

The objects of this class are cloneable with this method.

Usage
InverseGaussian$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Normal-inverse Gaussian distribution

Description

A R6 class to represent a normal-inverse Gaussian distribution.

Details

See Wikipedia.

Active bindings

mu

Get or set the value of mu.

alpha

Get or set the value of alpha.

beta

Get or set the value of beta.

delta

Get or set the value of delta.

Methods

Public methods

Method new()

New normal-inverse Gaussian distribution.

Usage
NormalInverseGaussian$new(mu, alpha, beta, delta)
Arguments
mu

location parameter

alpha

tail heaviness parameter, >0

beta

asymmetry parameter

delta

scale parameter, >0

Returns

A NormalInverseGaussian object.

Method d()

Density function of the normal-inverse Gaussian distribution.

Usage
NormalInverseGaussian$d(x, log = FALSE)
Arguments
x

numeric vector

log

Boolean, whether to return the logarithm of the density

Returns

The density or the log-density evaluated at x.

Method p()

Cumulative distribution function of the normal-inverse Gaussian distribution.

Usage
NormalInverseGaussian$p(q)
Arguments
q

numeric vector of quantiles

Returns

The cumulative probabilities corresponding to q, with two attributes (see the Note).

Method q()

Quantile function of the normal-inverse Gaussian distribution.

Usage
NormalInverseGaussian$q(p, bounds = NULL)
Arguments
p

numeric vector of probabilities

bounds

bounds enclosing the quantiles to be found (see the Note), or NULL for automatic bounds

Returns

The quantiles corresponding to p.

Method r()

Sampling from the normal-inverse Gaussian distribution.

Usage
NormalInverseGaussian$r(n)
Arguments
n

number of simulations

Returns

A numeric vector of length n.

Method mean()

Mean of the normal-inverse Gaussian distribution.

Usage
NormalInverseGaussian$mean()
Returns

The mean of the normal-inverse Gaussian distribution.

Method sd()

Standard deviation of the normal-inverse Gaussian distribution.

Usage
NormalInverseGaussian$sd()
Returns

The standard deviation of the normal-inverse Gaussian distribution.

Method variance()

Variance of the normal-inverse Gaussian distribution.

Usage
NormalInverseGaussian$variance()
Returns

The variance of the normal-inverse Gaussian distribution.

Method skewness()

Skewness of the normal-inverse Gaussian distribution.

Usage
NormalInverseGaussian$skewness()
Returns

The skewness of the normal-inverse Gaussian distribution.

Method kurtosis()

Kurtosis of the normal-inverse Gaussian distribution.

Usage
NormalInverseGaussian$kurtosis()
Returns

The kurtosis of the normal-inverse Gaussian distribution.

Method kurtosisExcess()

Kurtosis excess of the normal-inverse Gaussian distribution.

Usage
NormalInverseGaussian$kurtosisExcess()
Returns

The kurtosis excess of the normal-inverse Gaussian distribution.

Method clone()

The objects of this class are cloneable with this method.

Usage
NormalInverseGaussian$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Note

The cumulative distribution function is evaluated by integrating the density function (in C++). Its returned value has two attributes: a numeric vector "error_estimate" and an integer vector "error_code". The error code is 0 if no problem is detected. If an error code is not 0, a warning is thrown. The quantile function is evaluated by root-finding and then the user must provide some bounds enclosing the values of the quantiles or choose the automatic bounds. A maximum number of iterations is fixed in the root-finding algorithm. If it is reached, a warning is thrown.

Skew normal distribution

Description

A R6 class to represent a skew normal distribution.

Details

See Wikipedia.

Active bindings

xi

Get or set the value of xi.

omega

Get or set the value of omega.

alpha

Get or set the value of alpha.

Methods

Public methods

Method new()

New skew normal distribution.

Usage
SkewNormal$new(xi, omega, alpha)
Arguments
xi

location parameter

omega

scale parameter, >0

alpha

shape parameter

Returns

A SkewNormal object.

Method d()

Density function of the skew normal distribution.

Usage
SkewNormal$d(x)
Arguments
x

numeric vector

Returns

The density evaluated at x.

Method p()

Cumulative distribution function of the skew normal distribution.

Usage
SkewNormal$p(q, lower = TRUE)
Arguments
q

numeric vector of quantiles

lower

Boolean, whether to deal with the lower tail

Returns

The cumulative probabilities corresponding to q.

Method q()

Quantile function of the skew normal distribution.

Usage
SkewNormal$q(p, lower = TRUE)
Arguments
p

numeric vector of probabilities

lower

Boolean, whether to deal with the lower tail

Returns

The quantiles corresponding to p.

Method r()

Sampling from the skew normal distribution.

Usage
SkewNormal$r(n)
Arguments
n

number of simulations

Returns

A numeric vector of length n.

Method mean()

Mean of the skew normal distribution.

Usage
SkewNormal$mean()
Returns

The mean of the skew normal distribution.

Method mode()

Mode of the skew normal distribution.

Usage
SkewNormal$mode()
Returns

The mode of the skew normal distribution.

Method sd()

Standard deviation of the skew normal distribution.

Usage
SkewNormal$sd()
Returns

The standard deviation of the skew normal distribution.

Method variance()

Variance of the skew normal distribution.

Usage
SkewNormal$variance()
Returns

The variance of the skew normal distribution.

Method skewness()

Skewness of the skew normal distribution.

Usage
SkewNormal$skewness()
Returns

The skewness of the skew normal distribution.

Method kurtosis()

Kurtosis of the skew normal distribution.

Usage
SkewNormal$kurtosis()
Returns

The kurtosis of the skew normal distribution.

Method kurtosisExcess()

Kurtosis excess of the skew normal distribution.

Usage
SkewNormal$kurtosisExcess()
Returns

The kurtosis excess of the skew normal distribution.

Method clone()

The objects of this class are cloneable with this method.

Usage
SkewNormal$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Non-central Student distribution

Description

A R6 class to represent a non-central Student distribution.

Active bindings

nu

Get or set the value of nu.

delta

Get or set the value of delta.

Methods

Public methods

Method new()

New Student distribution.

Usage
Student$new(nu, delta)
Arguments
nu

degrees of freedom parameter, >0

delta

non-centrality parameter

Returns

A Student object.

Method d()

Density function of the Student distribution.

Usage
Student$d(x)
Arguments
x

numeric vector

Returns

The density evaluated at x.

Method p()

Cumulative distribution function of the Student distribution.

Usage
Student$p(q, lower = TRUE)
Arguments
q

numeric vector of quantiles

lower

Boolean, whether to deal with the lower tail

Returns

The cumulative probabilities corresponding to q.

Method q()

Quantile function of the Student distribution.

Usage
Student$q(p, lower = TRUE)
Arguments
p

numeric vector of probabilities

lower

Boolean, whether to deal with the lower tail

Returns

The quantiles corresponding to p.

Method r()

Sampling from the Student distribution.

Usage
Student$r(n)
Arguments
n

number of simulations

Returns

A numeric vector of length n.

Method mean()

Mean of the Student distribution.

Usage
Student$mean()
Returns

The mean of the Student distribution.

Method median()

Median of the Student distribution.

Usage
Student$median()
Returns

The median of the Student distribution.

Method mode()

Mode of the Student distribution.

Usage
Student$mode()
Returns

The mode of the Student distribution.

Method sd()

Standard deviation of the Student distribution.

Usage
Student$sd()
Returns

The standard deviation of the Student distribution.

Method variance()

Variance of the Student distribution.

Usage
Student$variance()
Returns

The variance of the Student distribution.

Method skewness()

Skewness of the Student distribution.

Usage
Student$skewness()
Returns

The skewness of the Student distribution.

Method kurtosis()

Kurtosis of the Student distribution.

Usage
Student$kurtosis()
Returns

The kurtosis of the Student distribution.

Method kurtosisExcess()

Kurtosis excess of the Student distribution.

Usage
Student$kurtosisExcess()
Returns

The kurtosis excess of the Student distribution.

Method clone()

The objects of this class are cloneable with this method.

Usage
Student$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Note

The non-centrality parameter of the Student distribution in the stats package is limited to abs(ncp) <= 37.62. The present implementation allows a larger range.

Find degrees of freedom

Description

Find the degrees of freedom parameter of a non-central Chi-squared distribution given a quantile, its corresponding probability, and the non-centrality parameter.

Usage

findChi2df(ncp, q, p)

Arguments

ncp

non-centrality parameter, a non-negative number

q

a quantile

p

probability corresponding to the quantile q

Value

The degrees of freedom parameter of the non-central Chi-squared distribution with non-centrality parameter ncp and with cumulative probability p at the quantile q.

Examples

library(boodist)
nu <- findChi2df(ncp = 10, q = 3, p = 0.1)
pchisq(3, df = nu, ncp = 10) # should be 0.1

Find non-centrality parameter

Description

Find the non-centrality parameter of a Chi-squared distribution given a quantile, its corresponding probability, and the degrees of freedom.

Usage

findChi2ncp(df, q, p)

Arguments

df

degrees of freedom, a positive number

q

a quantile

p

probability corresponding to the quantile q

Value

The non-centrality parameter of the Chi-squared distribution with degrees of freedom parameter df and with cumulative probability p at the quantile q.

Examples

library(boodist)
ncp <- findChi2ncp(df = 1, q = 3, p = 0.1)
pchisq(3, df = 1, ncp = ncp) # should be 0.1