cdfgno: Cumulative Distribution Function of the Generalized Normal Distribution

Description

This function computes the cumulative probability or nonexceedance probability of the Generalized Normal distribution given parameters ($\xi$, $\alpha$, and $\kappa$) computed by pargno. The cumulative distribution function is $$F(x) = \Phi(Y) \mbox{,} $$ where $\Phi$ is the cumulative distribution function of the Standard Normal distribution and $Y$ is $$Y = -\kappa^{-1} \log\left(1 - \frac{\kappa(x-\xi)}{\alpha}\right)\mbox{,}$$ for $\kappa \ne 0$ and $$Y = (x-\xi)/\alpha\mbox{,}$$ for $\kappa = 0$, where $F(x)$ is the nonexceedance probability for quantile $x$, $\xi$ is a location parameter, $\alpha$ is a scale parameter, and $\kappa$ is a shape parameter.

Usage

cdfgno(x, para)

Value

Nonexceedance probability ($F$) for $x$.

Arguments

x: A real value vector.
para: The parameters from pargno or vec2par.

Author

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, v. 52, pp. 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.

Examples

Run this code

  lmr <- lmoms(c(123,34,4,654,37,78))
  cdfgno(50,pargno(lmr))

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