S Archive: Zero Cumulant Distribution

dzeroc Zero Cumulant Distribution

DESCRIPTION

Density of the Zero Cumulant Distribution of order 6. The first six cumulants are specified, and the others are assumed zero.

USAGE

dzeroc(x,kappa)

REQUIRED ARGUMENTS

`x`		vector of quantiles.
`kappa`		vector of length 6 holding the cumulants of the distribution.

VALUE

Vector of same length as x giving the density of the distribution with cumulants given by kappa.

DETAILS

Uses 400-point Gaussian quadrature to invert the moment generating function.

REFERENCE

Smyth, G. K. (1993). Zero cumulant distribitions. Unpublished manuscript.

EXAMPLES

The normal distribution is determined exactly by its first two cumulants:

> dzeroc(x=c(0,1,2,3),kappa=c(0,1,0,0,0,0)) [1] 0.398942280 0.241970725 0.053990967 0.004431848 > dnorm(x=c(0,1,2,3)) [1] 0.398942280 0.241970725 0.053990967 0.004431848

The gamma distribution can be approximated by its first 6 cumulants:

> dzeroc(x=5,kappa=rep(5,6)) [1] 0.1754872 > dgamma(x=5,shape=5) [1] 0.1754674

S-Archive

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