About the parameters for generating grains based on a pdf

[mario-renderos]

Hello, good morning.

I have a question about the parameters when using probability distribution functions to generate grains shape. For the skewnormal distribution there are three parameters (mean, sigma and gamma).
I am clear that sigma is the square root of the variance of X (sigma=sqrt(variance)), mean is the first moment of X (mean = E(X)). What I am not clear about is what the gamma parameter corresponds to. Is gamma the skewness (generally denoted as gamma_1), or is it the kurtosis (usually denoted as gamma_2)?

Thank you very much for the help, Mario.

[rquey]

I don't know (this distribution was contributed), but here is the code:

neper/src/contrib/ut/src/ut_fct/ut_fct.c

Lines 468 to 477 in 27841d7

	else if (!strcmp (Fct.type, "skewnormal"))
	{
	const double factor = (x - Fct.mean) / (Fct.sigma * sqrt (2.));
	val =
	(1. +
	erf (factor * Fct.gamma)) * exp (-pow (factor,
	2)) / (Fct.sigma * sqrt (2. *
	M_PI));
	}

[mario-renderos]

Hello.
There is an error in the way the parameters for the skewnormal probability density function are defined.
In the manual:

• mu appears as the mean, it is actually the location factor (xi).
• sigma as the standard deviation, but it is the scale factor (omega).
• gamma, is supposed to be sigma?, but it is actually the shape factor (alpha).
  https://en.wikipedia.org/wiki/Skew_normal_distribution

It would be interesting to correct that in the manual, otherwise very important errors are generated.

Kind regards, Mario.