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.