CharFun (version 0.1.0)

cfS_StudentT: Characteristic function of Student's t-distribution

Description

cfS_StudentT(t, df) evaluates the characteristic function cf(t) of the Student's t-distribution with the parameters df (degrees of freedom, df > 0) computed for real vector argument t, i.e.

cfS_StudentT(t,df) = besselK(df/2,abs(t)*sqrt(df),1) * exp(-abs(t)*sqrt(df)) * (sqrt(df)*abs(t))^(df/2) / 2^(df/2-1)/gamma(df/2)

Usage

cfS_StudentT(t, df)

Arguments

t

numerical values (number, vector...)

df

df degrees of freedom, df > 0

Value

characteristic function cf(t) of the Student's t-distribution

See Also

For more details see WIKIPEDIA: https://en.wikipedia.org/wiki/Student's_t-distribution

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

Other Symetric Probability distribution: cfS_Arcsine, cfS_Gaussian, cfS_Rectangular, cfS_Trapezoidal, cfS_Triangular

Examples

## EXAMPLE1 (CF of the Student t-distribution with df = 2)
df <- 2
t <- seq(-5, 5, length.out = 501)
plotGraf(function(t)
  cfS_StudentT(t, df), t, title = "CF of the Student t-distribution with df = 2")

## EXAMPLE2 (PDF/CDF of the Student t-distribution with df = 3)
df <- 2
cf <- function(t)
  cfS_StudentT(t, df)
x <- seq(-8, 8, length.out = 101)
prob <- c(0.9, 0.95, 0.99)
result <- cf2DistGP(cf, x, prob, SixSigmaRule = 8)