cdfpe3 {lmomco}R Documentation

Cumulative Distribution Function of the Pearson Type III Distribution

Description

This function computes the cumulative probability or nonexceedance probability of the Pearson Type III distribution given parameters (xi, α, and gamma) of the distribution computed by parpe3. The cumulative distribution function of the distribution is

F(x) = frac{G(α,frac{x - xi}{gamma})}{Γ(α)} mbox{,}

where F(x) is the nonexceedance probability for quantile x, G is the incomplete gamma function, Γ is the gamma function, xi is a location parameter, α is a scale parameter, and gamma is a shape parameter.

Usage

cdfpe3(x, para)

Arguments

x A real value.
para The parameters from parpe3 or similar.

Value

Nonexceedance probability (F) for x.

Author(s)

W.H. Asquith

References

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105–124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

See Also

quape3, parpe3

Examples

  lmr <- lmom.ub(c(123,34,4,654,37,78))
  cdfpe3(50,parpe3(lmr))

[Package lmomco version 0.6 Index]