For chance-constrained programming (CCP) with non-Gaussian uncertainty, the optimization is generally intractable owing to the complicated probability density function (PDF). Using a simple fitted distribution with Kullback-Leibler (KL) divergence to represent the PDF mismatch is a systematic way to tackle CCP with non-Gaussian uncertainty. However, the essential difficulty of this methodology ...

One of the key problems in non-parametric data analysis is to create a good model of a generating probability distribution, assuming we are given as data a finite sample from that distribution. Obviously this problem is ill-posed for continuous distributions: with finite data, there is no way to distinguish between (or exclude) distributions that are not restricted to be smooth. The question th...

In this work, we study the asymptotic distribution of the normalized sum of independent, identically distributed random variables under the finite mixture models. In the Theorem we give necessary conditions for a distribution function of a mixed population with k components to belong to the domain of attraction of an α-stable distribution, by assuming that each component of the mixture also per...

We propose a class of Bayesian nonparametric mixture models with a Beta distribution providing the mixture kernel and a Dirichlet process prior assigned to the mixing distribution. Motivating applications include density estimation on bounded domains, and inference for non-homogeneous Poisson processes over time. We present the mixture model formulation, discuss prior specification, and develop...

We investigate existence and properties of discrete mixture representations $P_{\theta }=\sum _{i\in E}w_{\theta }(i)\,Q_{i}$ for a given family }$, $\theta \in \Theta $, probability measures. The noncentral chi-squared distributions provide classical example. obtain results about geometric statistical aspects the problem, latter including loss Fisher information, Rao-Blackwellization, asymptot...

A generalization of a distribution increases the flexibility particularly in studying phenomenon and its properties. Many generalizations continuous univariate distributions are available literature. In this study, an investigation is conducted on generalization. Several reviewed recent trends construction generalized classes with mixing parameter discussed. To check suitability comparability, ...

We develop a mixture model for transition density approximation, together with soft selection, in the presence of noisy and heterogeneous nonlinear dynamics. Our builds on Gaussian distribution (MTD) continuous state spaces, extending component means functions that are modeled using process (GP) priors. The resulting flexibly captures lag dependence when several components active, identifies lo...