Cumulative Distribution Function of the 3-Parameter Student t Distribution

Share:

Description

This function computes the cumulative probability or nonexceedance probability of the 3-parameter Student t distribution given parameters (ξ, α, ν) computed by parst3. There is no explicit solution for the cumulative distribution function for value X but built-in R functions can be used. For ν ≥ 1000, one can use pnorm(X, mean=U, sd=A) for U = ξ and A = α and for 1.000001 ≤ ν ≤ 1000, one can use pt((X-U)/A, N) for N = ν and where the R function pnorm is for the Normal distribution and the R function pt is the 1-parameter Student t distribution.

Usage

1
cdfst3(x, para, paracheck=TRUE)

Arguments

x

A real value vector.

para

The parameters from parst3 or vec2par.

paracheck

A logical on whether the parameter should be check for validity.

Value

Nonexceedance probability (F) for x.

Author(s)

W.H. Asquith

References

Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978–146350841–8.

See Also

pdfst3, quast3, lmomst3, parst3

Examples

1
2
  lmr <- lmoms(c(123,34,4,654,37,78))
  cdfst3(191.5143, parst3(lmr)) # 75th percentile

Want to suggest features or report bugs for rdrr.io? Use the GitHub issue tracker.