# cdfgno: Cumulative Distribution Function of the Generalized Normal... In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

 cdfgno R Documentation

## 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 (ξ, α, and κ) computed by pargno. The cumulative distribution function is

F(x) = Φ(Y) \mbox{,}

where Φ is the cumulative distribution function of the Standard Normal distribution and Y is

Y = -κ^{-1} \log≤ft(1 - \frac{κ(x-ξ)}{α}\right)\mbox{,}

for κ \ne 0 and

Y = (x-ξ)/α\mbox{,}

for κ = 0, where F(x) is the nonexceedance probability for quantile x, ξ is a location parameter, α is a scale parameter, and κ is a shape parameter.

### Usage

cdfgno(x, para)


### Arguments

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

### Value

Nonexceedance probability (F) for x.

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.

pdfgno, quagno, lmomgno, pargno, cdfln3
  lmr <- lmoms(c(123,34,4,654,37,78))