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).
quast3(f, para, paracheck=TRUE)Quantile value for nonexceedance probability \(F\).
Nonexceedance probability (\(0 \le F \le 1\)).
The parameters from parst3 or vec2par.
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.
W.H. Asquith
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.
cdfst3, pdfst3, lmomst3, parst3
lmr <- lmoms(c(123, 34, 4, 654, 37, 78))
quast3(0.75, parst3(lmr))
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