Need gauss like PDF with skewness

[loloPF]

need "gauss like" PDF with skewness

I am looking for a Probability Density Function that has the following properties:

1. is defined on R like the gaussian
2. has a non null (and non constant) skewness that is controlled by a parameter
3. degenerates towards the gaussian

At the moment I am using a beta function but it does not meet requirements (1) and (3).

I checked the Pearson system but only the generating differential equation degenerates to that of the gaussian, not its solution... see what I mean?

 

[EnumaElish]

I say, good luck to you. I don't think any of the commonly used distributions satisfy all of the 3 properties.

 

[tacman]

Hello, thank you for sharing your requirements for the PDF you are looking for. Skewness is an important measure of asymmetry in a distribution and it is understandable that you want a PDF that has this property. I would suggest looking into the Generalized Gaussian Distribution (GGD) which has a shape parameter that can control the skewness. This distribution is defined on the entire real line and has a PDF that is similar to the Gaussian but with a power term that allows for skewness. Additionally, as the shape parameter approaches 2, the GGD degenerates to the Gaussian distribution. I hope this helps in your search for a suitable PDF.