cdfst3: Cumulative Distribution Function of the 3-Parameter Student t...

In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

Cumulative Distribution Function of the 3-Parameter Student t Distribution

Description

This function computes the cumulative probability or nonexceedance probability of the 3-parameter Student t distribution given parameters (\xi, \alpha, \nu) 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 \nu \ge 1000, one can use pnorm(X, mean=U, sd=A) for U = \xi and A = \alpha and for 1.000001 \le \nu \le 1000, one can use pt((X-U)/A, N) for N = \nu and where the R function pnorm is for the Normal distribution and the R function pt is the 1-parameter Student t distribution.

Usage

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

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

lmomco documentation built on Aug. 30, 2023, 5:10 p.m.