quast3 {lmomco}

Quantile Function of the 3-Parameter Student t Distribution

Description

This function computes the quantiles of the 3-parameter Student t distribution given parameters (\xi, \alpha, \nu) computed by parst3. There is no explicit solution for the quantile function for nonexceedance probability F but built-in R functions can be used. The implementation is U = \xi and A = \alpha for 1.001 \le \nu \le 10^5.5, one can use U + A*qt(F, N) where qt is the 1-parameter Student t quantile function. The numerically accessible range of implementation here and consistency to the \tau_4 and \tau_6 is 10.001 \le \nu \le 10^5.5. The limits for \nu stem from study of ability for theoretical integration of the quantile function to produce viable \tau_4 and \tau_6 (see inst/doc/t4t6/studyST3.R).

Usage

quast3(f, para, paracheck=TRUE)

Arguments

f

Nonexceedance probability (0 \le F \le 1).

para

The parameters from parst3 or vec2par.

paracheck

A logical on whether the parameters are checked for validity. Overriding of this check might be extremely important and needed for use of the quantile function in the context of TL-moments with nonzero trimming.

Value

Quantile value for nonexceedance probability F.

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

cdfst3, pdfst3, lmomst3, parst3

Examples

lmr <- lmoms(c(123, 34, 4, 654, 37, 78))
quast3(0.75, parst3(lmr))