Description Usage Arguments Value Note See Also Examples
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)
1 | cfS_StudentT(t, df)
|
t |
numerical values (number, vector...) |
df |
df degrees of freedom, df > 0 |
characteristic function cf(t) of the Student's t-distribution
bessel function nefunguje dobre
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
1 2 3 4 5 6 7 8 9 10 11 12 13 | ## 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)
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