discrete distributions where we study big databases instead of contous we rely the problem of create linear models , this field is more complex due to a lack of theory, here we need to replace continous hypothesis and work with transformations like convolution and frecuency matrixes..

Dear stochastics, I would like to send you the function of a Probabilty Denstity I developed for application testing. It takes into account the skewness (right or left) as the third parameter and falls back into the normal distribution at skewness = 0. Are you interested in it? Best regards Marcus Hellwig

@ Marcus Hellwing Yes, please.

ok Sini , here we go....but as the Excel spread sheet is a german language version, you should change the language ...

Marcus Hellwig I'll do my best to help you and answer your question. Thank you!

Marcus Hellwig Thank you for sharing the files with me. I've had the opportunity to review and understand the content you provided thoroughly. I'm more than happy to assist with any specific tasks or questions you have related to the content. Please let me know what kind of assistance you require. I am looking forward to working together on this.

... so what todo from your side?

- writing down the Eqb function with its 1st & 2nd derivates in a mathematical manor . ( I can´t do - I´m Qualityengineer)

- testing function by using frequency-data (f.e. Climatedata, Infectiondata....)

- a proof of the function I have added (german language)

... an example given as weather forecast....

Sini K P

There have been several recent breakthroughs in distribution theory that have significant implications for statistical modeling and analysis.

1. Sub-Gaussian and Heavy-Tailed Distributions: Recent research has focused on understanding the properties of sub-Gaussian and heavy-tailed distributions. Sub-Gaussian distributions have bounded moments and tails that decay faster than those of Gaussian distributions. Heavy-tailed distributions have tails that decay slower than those of Gaussian distributions. These distributions have been found to be applicable in various fields, including finance, signal processing, and machine learning.

2. High-Dimensional Distributions: With the advent of big data and high-dimensional datasets, researchers have made progress in understanding the behavior of high-dimensional distributions. This includes developing theories related to concentration inequalities, random matrix theory, and the study of sparse and low-rank structures. These advances have led to improved statistical methods for high-dimensional data analysis, such as sparse regression, compressed sensing, and dimensionality reduction techniques.

3. Dependence Modeling: The development of new approaches to modeling dependence structures between random variables has been another significant breakthrough. Copula theory, for example, has gained attention in modeling multivariate dependencies by separating the marginal distributions from the dependence structure. Advances in copula theory have facilitated more accurate modeling and analysis of complex dependence patterns in various fields, such as finance, insurance, and environmental sciences.

4. Nonparametric and Semiparametric Distributions: Nonparametric and semiparametric distributions have seen advancements in recent years, allowing for more flexible modeling approaches. Nonparametric distributions, such as kernel density estimation and nonparametric regression, do not assume a specific functional form and can capture complex data patterns. Semiparametric distributions combine parametric and nonparametric components, offering a balance between flexibility and interpretability.

5. Bayesian Nonparametrics: Bayesian nonparametric models have gained popularity due to their ability to handle complex data structures and provide flexible modeling frameworks. These models use prior distributions with infinite-dimensional parameter spaces, allowing for automatic complexity control and adaptability to the data. Recent developments in Bayesian nonparametrics include Dirichlet process, Gaussian process, and hierarchical modeling techniques.

Good luck!!