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 ($\xi$, $\alpha$, $\nu$) of the distribution computed by parst3. There is no explicit solution for the cumulative distribution function for value X but built-in Rfunctions can be used. For $\nu \ge 1000$, pnorm(X, mean=U, sd=A) for U = $\xi$ and A = $\alpha$ for $1.000001 \le \nu \le 1000$, pt((X-U)/A, N) for N = $\nu$ and where pnorm() is for the Normal distribution and pt() is the 1-parameter Student T distribution.
A logical on whether the parameter should be check for validity.
Value
Nonexceedance probability ($F$) for $x$.
References
Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: CreateSpace Independent Publishing Platform, 2nd printing, ISBN 978-1463508418.