lmomco (version 2.4.14)

cdfst3: 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)

Value

Nonexceedance probability ($F$) for $x$.

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.

Author

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