Need gauss like PDF with skewness

  • Context: Graduate 
  • Thread starter Thread starter loloPF
  • Start date Start date
  • Tags Tags
    Gauss Pdf
Click For Summary
SUMMARY

The discussion centers on the need for a Probability Density Function (PDF) that exhibits Gaussian-like characteristics while incorporating skewness. The desired PDF must be defined on the real line, possess a non-null skewness controlled by a parameter, and degenerate to the Gaussian distribution. The user currently employs a beta function, which fails to meet the specified requirements. The Pearson system was also considered, but it only meets the degeneracy condition in its generating differential equation, not in its solution.

PREREQUISITES
  • Understanding of Probability Density Functions (PDFs)
  • Familiarity with Gaussian distributions
  • Knowledge of skewness in statistical distributions
  • Experience with the Pearson system of distributions
NEXT STEPS
  • Research alternative distributions that allow for skewness, such as the skew-normal distribution
  • Explore the mathematical properties of the Pearson system in greater detail
  • Investigate the construction of custom PDFs that meet specific skewness requirements
  • Learn about the implications of skewness on statistical analysis and modeling
USEFUL FOR

Statisticians, data scientists, and researchers involved in probability theory and statistical modeling who require advanced understanding of skewed distributions.

loloPF
Messages
15
Reaction score
0
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?
 
Physics news on Phys.org
I say, good luck to you. I don't think any of the commonly used distributions satisfy all of the 3 properties.
 

Similar threads

Graduate Skewed Generalized Gaussian Distribution
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Monte Carlo to compute uncertainties, why report the mean and SD?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Are components in a gaussian mixture independent?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How to implement proper error estimation using MC
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Do equipotential lines fall on the equiprobability contours?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate PDF of multimodal circular data
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Pdf of Difference of Random Variables
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Stable Distributions And Limit Theorems
  • · Replies 7 ·
Replies
7
Views
2K
Use Gauss' Law to find E-field, tricky problem
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad How does one time-evolve a quantum state with its kernel function?
  • · Replies 0 ·
Replies
0
Views
1K