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

Details

Feasible values for input must have abs(gamma1)<0.5*(4-pi)*(2/(pi-2))^1.5, 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.

Value

A numeric vector of the corresponding shape parameters.

References

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

See Also

dsn

Examples

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