Florian Angeletti

This matlab library provides a set of estimator for the critical moment order for log-normal distribution and other log-power exponential distributions. These random variable can be decomposed as X= exp(Y), where the probability density function of Y, p_Y, is such that p_Y'(y) / p_Y(y) converges towards a finite constant ρ. For a finite number of samples, the empirical estimator of moments is faithful only up to a critical order q_c. For ρ>1, this critical moment order grow extremely slowly with the number of samples n: q_c(n) = L(ln n) (ln n)^{1-1/ρ}. It is therefore very useful to have a estimator for ρ and the critical order q_c.

The source code and supplementary information are available on the github repository.

This matlab library gathers a set of functions and procedure dedicated to the synthesis and estimation of matrix-correlated random variables. In brief, these random variables are characterized by joint probability density function which can be written as a matrix product: p(x_1, ..., x_n) = L (R_n(x_1 ).. R_n(x_n) ) / Z where R_k is positive matrix function and L a linear form. These random variables have some interesting statistical properties.. This library aims to provide a clear API in order to help interested practitioner to explore the potentiality of these laws. This objective is still far away. Critics and comments are welcome.

The source code and supplementary information are available on the github repository.

Thys python library gathers tools and scripts aimed toward the synthesis and analysis of random variables with a matrix representation. Compared to the "Matrixalea" matlab library, this library focuses more on the theoretical analysis of statistical property rather than the random variable synthesis aspect. In particular, this library contains the tools needed to compute limit distributions for the sum of such random variable. A first set of scripts can compute the reduced model associate with any matrix representation model. Then the limit distribution for the generalized law of number or the central limit theorem are computed using respectively simplices decomposition of polytopes and Markovian integration. This library try to use exact computation as often as possible. In order to test the result of the previous computation, a synthesis module, able to compute realization of a given model, is also available. A limited number of test is provided within the library. To complete the library, a random model generator is also included, with the aim to automate the tests in the future.

The source code and supplementary information are available on the github repository.