CharFun (version 0.1.0)

cfX_Gamma: Characteristic function of Gamma distribution

Description

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

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

Usage

cfX_Gamma(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 Gamma distribution

See Also

For more details see WIKIPEDIA: https://en.wikipedia.org/wiki/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_InverseGamma, cfX_LogNormal, cfX_Normal, cfX_PearsonV, cfX_Rectangular, cfX_Triangular

Examples

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

## EXAMPLE2 (PDF/CDF of the Gamma distribution with alpha = 2, beta = 2)
alpha <- 2
beta <- 2
cf <- function(t)
  cfX_Gamma(t, alpha, beta)
x <- seq(0, 5, length.out = 101)
prob <- c(0.9, 0.95, 0.99)
result <- cf2DistGP(cf, x, prob, xMin = 0, N = 2 ^ 14)

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