cfX_InverseGamma: Characteristic function of Inverse Gamma distribution

In CharFun: Numerical Computation Cumulative Distribution Function and Probability Density Function from Characteristic Function

Description

cfX_InverseGamma(t,alpha,beta) evaluates the characteristic function cf(t) of the Inverse Gamma distribution with the parameters alpha (shape, alpha > 0) and beta (rate, beta > 0), i.e.

cfX_InverseGamma(t, alpha, beta) = (1 - it/beta)^(-alpha)

Usage

cfX_InverseGamma(t, alpha = 1, beta = 1)

Arguments

t	numerical values (number, vector...)
alpha	shape, alpha > 0, default value alpha = 1
beta	rate > 0, default value beta = 1

Value

characteristic function cf(t) of the Inverse Gamma distribution

See Also

For more details see WIKIPEDIA: https://en.wikipedia.org/wiki/Inverse-gamma_distribution

Other Continuous Probability distribution: cfS_Arcsine, cfS_Beta, cfS_Gaussian, cfS_Rectangular, cfS_StudentT, cfS_Trapezoidal, cfS_Triangular, cfX_Beta, cfX_ChiSquared, cfX_Exponential, cfX_Gamma, cfX_LogNormal, cfX_Normal, cfX_PearsonV, cfX_Rectangular, cfX_Triangular

Examples

## EXAMPLE1 (CF of the InverseGamma distribution with alpha = 2, beta = 2)
alpha <- 2
beta <- 2
t <- seq(-20, 20, length.out = 501)
plotGraf(function(t)
  cfX_InverseGamma(t, alpha, beta), t,
  title = "CF of the InverseGamma distribution with alpha = 2, beta = 2")

## EXAMPLE2 (PDF/CDF of the InverseGamma distribution with alpha = 2, beta = 2)
alpha <- 2
beta <- 2
cf <- function(t)
  cfX_InverseGamma(t, alpha, beta)
x <- seq(0, 15, length.out = 101)
prob <- c(0.9, 0.95, 0.99)
result <- cf2DistGP(cf, x, prob, xMin = 0, N = 2 ^ 10)

## EXAMPLE3 (PDF/CDF of the compound Binomial-InverseGamma distribution)
p <- 0.3
n <- 25
alpha <- 2
beta <- 2
cfX <- function(t)
  cfX_InverseGamma(t, alpha, beta)
cf <- function(t)
  cfN_Binomial(t, n, p, cfX)
x <- seq(0, 70, length.out = 101)
prob <- c(0.9, 0.95, 0.99)
result <- cf2DistGP(cf, x, prob, isCompound = TRUE, N = 2 ^ 10)

CharFun documentation built on May 2, 2019, 9:18 a.m.