cdfst3 {lmomco}

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 U = \xi and A = \alpha and for 1.001 \le \nu \le 10^5.5, one can use pt((X-U)/A, N) for N = \nu. The R function pt is used for the 1-parameter Student t cumulative distribution function. 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

cdfst3(x, para, paracheck=TRUE)

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.

Value

Nonexceedance probability (F) for x.

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

pdfst3, quast3, lmomst3, parst3

Examples

  lmr <- lmoms(c(123, 34, 4, 654, 37, 78))
  cdfst3(191.5143, parst3(lmr)) # 75th percentile