Need gauss like PDF with skewness

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In summary, the conversation discussed the need for a Probability Density Function that has similar properties to the Gaussian distribution, but with a non-null and parameter-controlled skewness. The use of a beta function was mentioned, but it did not meet all the requirements. The Pearson system was also considered, but it only degenerates to the Gaussian distribution in terms of its differential equation, not its solution. The conversation concluded with the acknowledgement that it may be difficult to find a distribution that satisfies all three properties.
  • #1
loloPF
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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?
 
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  • #2
I say, good luck to you. I don't think any of the commonly used distributions satisfy all of the 3 properties.
 
  • #3


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.
 

What is a Gaussian distribution?

A Gaussian distribution, also known as a normal distribution, is a statistical distribution that is often used to model random events in nature. It is characterized by a bell-shaped curve and is symmetrical around its mean.

What is skewness in a PDF?

Skewness is a measure of the asymmetry of a probability distribution. It indicates the degree to which the distribution is skewed to one side or the other. A PDF with skewness would have a non-symmetrical shape, with a longer or fatter tail on one side compared to the other.

Why might someone need a Gaussian-like PDF with skewness?

There are many situations in which a Gaussian distribution with skewness may be useful. For example, in finance, stock prices often follow a skewed distribution, as do many natural phenomena such as earthquake magnitudes. By using a Gaussian-like PDF with skewness, scientists can better model and understand these real-world phenomena.

How is skewness calculated in a PDF?

There are several methods for calculating skewness, but the most commonly used is the Pearson's moment coefficient of skewness. This involves using the mean, median, and standard deviation of the data to determine the degree of asymmetry in the distribution.

Can a Gaussian-like PDF have negative skewness?

Yes, a Gaussian-like PDF can have negative skewness. This would indicate that the tail of the distribution is longer on the left side, while the right side is shorter and more concentrated. Negative skewness is often referred to as left-skewed or negatively skewed.

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