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.

Characterizations of exponential distributions within the life distribution classes

Abstract: Within different life distribution classes, we discuss characterization of exponential distributions based on moment properties of order statistics or spacing.

Maximum Likelihood Analysis for Bivariate Exponential Distributions

Abstract: A generalization of Marshall-Olkin(1967) bivariate exponential model is proposed and the existence, uniqueness and asymptotic distributional properties of the maximum likelihood estimators are studied. The classical Marshall- Olkin model is a mixture of an absolutely continuous and a singular component, that concentrates its mass on the line x = y. In this paper, I generalize Marshall-Olkin s results considering a distribution with positive mass on the line x = \mu y, \mu > 0. Some simulation results to compare the two models are presented. I also derive an extension of Marshall-Olkin (1967) model for any function which is continuous and twice continuously differentiable in some open dense domain. This extension gives class of models some of it have exponential marginals. I derive its asymptotic normalities. I model the first mixed moments of bivariate exponential models whose marginals are also exponential using the method of generalized linear models.

The Generalized Distributions on the Unit Interval based on the T-Topp-Leone Family of Distributions

Abstract: The Topp-Leone (TL) distribution is introduced by Topp and Leone [1]. Its probability density function is a simple function with only one parameter. Even though the TL distribution has been discussed and applied in many research fields, but there is a limitation about its shape. In this article, we propose the T-TL family of distributions using quantile function of family of distributions to generate generalized TL distributions including the Weibull-TL{exponential}, the log-logistic-TL{exponential}, the logistic-TL{extreme value}, the exponential-TL{log-logistic} and the normal-TL{logistic} distributions. Some associated properties and inferences are discussed. Some graphical representations related to the probability density function are shown. Finally, 3 real datasets are applied to illustrate the generalized TL distributions. HIGHLIGHTS The Topp-Leone distribution is introduced in 1955. Its probability density function is a simple function with only one parameter. It has been discussed and applied in many research fields The T-Topp-Leone family of distributions using quantile function of family of distributions to generate generalized Topp-Leone distributions including the Weibull-Topp-Leone{exponential}, the log-logistic-Topp-Leone{exponential}, the logistic-Topp-Leone{extreme value}, the exponential-Topp-Leone{log-logistic} and the normal-Topp-Leone{logistic} distributions Some statistical properties, such as reliability function, hazard function, quantile function of T-Topp-Leone family, Shannon entropy, moments, mean deviation and median deviation are discussed All generalized Topp-Leone distributions are applied to three real datasets and the results indicated that five distributions obtained from the new family can be used as good alternatives to the Topp-Leone, beta and Kumaraswamy distributions GRAPHICAL ABSTRACT

Modeling Posterior Probabilities using the Linear Exponential Family

Abstract: A commonly used distribution on the probability simplex is the Dirichlet distribution In this paper we present the linear exponential family as an alternative The distribution is known in the statistics community, but we present in this paper a numerically stable method to compute its parameters Although the Dirichlet distribution is known to be a good Bayesian prior for probabilities we believe this paper shows that the linear exponential model offers a good alternative in other contexts, such as when we want to use posterior probabilities as features for automatic speech recognition We show how to incorporate posterior probabilities as additional features to an existing GMM, and show that the resulting model gives a 06% relative gain on a broadcast news speech recognition system Index Terms: Linear Exponential Family, Simplex, Divided Difference, Partition Function