Topic
Natural exponential family
About: Natural exponential family is a research topic. Over the lifetime, 1973 publications have been published within this topic receiving 60189 citations. The topic is also known as: NEF.
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TL;DR: In this paper, it was shown that stochastic independence of the random variables SN and N-SN characterizes the Poisson and Bernoulli distributions simultaneously with the help of the result that exponential-type families are determined by their mean value functions.
Abstract: With the help of the result that exponential-type families are determined by their mean value functions it is shown that stochastic independence of the random variables SN and N-SN characterizes the Poisson and Bernoulli distributions simultaneously.
1 citations
Journal Article•
TL;DR: In this article, the p-order moment exponential stability and the almost sure exponential stability for stochastic large-scale systems with variable multi-delay were established, and the algebraic criteria of the delay-independent mean square exponential stability were derived.
Abstract: We establish a new criteria of p-order moment exponential stability and the almost sure exponential stability for stochastic functional differential equation. Applying the derived criteria to nonlinear stochastic large-systems with variable multi-delay, we get the algebraic criteria of the delay-independent mean square exponential stability and the almost sure exponential stability for this type of stochastic large-scale systems.
1 citations
1 citations
TL;DR: In this paper, the authors discuss the T.O.M (Term Omission Method) to estimate the distribution parameters that have not single exponential family of exponential family with one single distribution parameter.
Abstract: We discuss the T.O.M (Term Omission Method) to estimate the distribution parameters that have not single exponential family of exponential family with one single distribution parameter, and compare it with different methods using Mean Square Method (MSE).
1 citations