Description Usage Arguments Value See Also Examples
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)
1 | cfX_InverseGamma(t, alpha = 1, beta = 1)
|
t |
numerical values (number, vector...) |
alpha |
shape, alpha > 0, default value alpha = 1 |
beta |
rate > 0, default value beta = 1 |
characteristic function cf(t) of the Inverse Gamma distribution
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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 | ## 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)
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