Description Usage Arguments Value See Also Examples
cfX_PearsonV(t, alpha, beta) evaluates the characteristic function cf(t) of the Pearson type V distribution with the parameters alpha (shape, alpha > 0) and beta (scale, beta > 0), computed for real vector argument t, i.e.
cfX_PearsonV(t, alpha, beta) = (2/gamma(alpha)) * (-1i*t/beta)^(alpha/2) * besselk(alpha,2*sqrt(-1i*t/beta)), where besselk(a,z) denotes the modified Bessel function of the second.
1 | cfX_PearsonV(t, alpha = 1, beta = 1)
|
t |
numerical real values (number, vector...) |
alpha |
shape, alpha > 0, default value alpha = 1 |
beta |
scale > 0, default value beta = 1 |
characteristic function cf(t) of the Gamma distribution
For more details see WIKIPEDIA: https://en.wikipedia.org/wiki/Pearson_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_InverseGamma
,
cfX_LogNormal
, cfX_Normal
,
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 30 31 32 33 34 35 36 | ## EXAMPLE1 ((CF of the PearsonV distribution)
alpha <- 3 / 2
beta <- 2 / 3
t <- seq(-10, 10, length.out = 1001)
plotGraf(function(t)
cfX_PearsonV(t, alpha, beta), t,
title = "CF of the PearsonV distribution with alpha = 3/2, beta = 2/3")
## EXAMPLE2 (PDF/CDF of the Beta distribution with alpha = 3/2, beta = 2/3)
alpha <- 3 / 2
beta <- 2 / 3
prob <- c(0.9, 0.95, 0.99)
x <- seq(0, 40, length.out = 101)
cf <- function(t)
cfX_PearsonV(t, alpha, beta)
result <-
cf2DistGP(cf,
x,
prob,
xMin = 0,
N = 2 ^ 10,
SixSigmaRule = 10)
## EXAMPLE3 (PDF/CDF of the compound Binomial-PearsonV distribution)
n <- 25
p <- 0.3
alpha <- 3 / 2
beta <- 2 / 3
prob <- c(0.9, 0.95, 0.99)
x <- seq(0, 200, length.out = 101)
cfX <- function(t)
cfX_PearsonV(t, alpha, beta)
cf <- function(t)
cfN_Binomial(t, n, p, cfX)
result <- cf2DistGP(cf, x, prob, isCompound = TRUE, N = 2 ^ 10)
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