gamma1.to.lambda: Converts skewness to shape parameter of skew-normal distribution

Description

For a given value of the index of skewness (standardized third cumulant), the function finds the corresponding shape parameter of a skew-normal distribution.

Usage

gamma1.to.lambda(gamma1)

Arguments

gamma1

a numeric vector of indices of skewness.

Value

A numeric vector of the corresponding shape parameters.

Details

Feasible values for input must have

abs(gamma1)<0.5*(4-pi)*(2 (pi-2))^1.5<="" code="">,
which is about 0.99527.
If some values of gamma1 are not in the feasible region, a warning
message is issued, and NAs are returned.

See the reference below for the expression of the index of skewnnes
of a skew-normal distribution.

References

Azzalini, A. (1985). A class of distributions which includes the normal ones. Scand. J. Statist. 12, 171-178.

Examples

Run this code

gamma1.to.lambda(seq(-0.95, 0.95, length=11))

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