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.