lmomco (version 2.0.1)

pdfst3: Probability Density Function of the 3-Parameter Student T Distribution

Description

This function computes the probability density of the 3-parameter Student T distribution given parameters ($\xi$, $\alpha$, $\nu$) of the distribution computed by parst3. The probability density function has an explicit solution but not shown here. For value X, the built-in Rfunctions can be used. For $\nu \ge 1000$, dnorm(X, mean=U, sd=A) for U = $\xi$ and A=$\alpha$ for $1.000001 \le \nu \le 1000$, dt((X-U)/A, N)/A for N=$\nu$ and where dnorm() is for the Normal distribution and dt() is the 1-parameter Student T distribution.

Usage

pdfst3(x, para, paracheck=TRUE)

Arguments

x

A real value.

para

The parameters from parst3 or similar.

paracheck

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

Value

• Probability density ($f$) 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.

See Also

cdfst3, quast3, parst3

Examples

xs <- -200:200
   para <- vec2par(c(37,25,114), type="st3")
plot(xs, pdfst3(xs, para), type='l')
   para <- vec2par(c(11,36,1000), type="st3")
lines(xs, pdfst3(xs, para), lty=2)
   para <- vec2par(c(-7,60,40), type="st3")
lines(xs, pdfst3(xs, para), lty=3)