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, a generalized Weibull-Rayleigh distribution was proposed and its properties like moment generation function, moments, cumulants, survival function, hazard function and Shannon entropy were investigated.
Abstract: In this paper we consider certain results characterizing the generalization of Weibull and Rayleigh distributions through their distribution functions and moment generating functions. Our work was motivated in part by a new method for generating families of continuous random variable developed in Alzaatreh et al (2013a). The resulting Weibull-Rayleigh distribution was defined and some of its properties like the moment generation function, moments, cumulants, survival function, hazard function and Shannon entropy were investigated. This distribution was found to generalize some known distributions. Simulated data were analyzed and density plots given. Results showed that the Weibull-Rayleigh distribution is highly peaked, skewed, unimodal with heavy tails. Consequently, the proposed generalized distribution can represent effectively, heavily tailed and slightly skewed and normal type distributions that are unimodal. Keywords: Weibull distribution, Rayleigh Distribution, Transformed-Transformer Family, Moments, unimodal..
7 citations
TL;DR: In this article, new characterizations for the exponential distribution are given in terms of record values and the probabilities of finite sums of independent and identically distributed nonnegative random variables provided that the underlying distribution is either new better than used or new worse than used.
Abstract: New characterizations for the exponential distribution are given in terms of record values and the probabilities of finite sums of independent and identically distributed nonnegative random variables provided that the underlying distribution is either new better than used or new worse than used.
7 citations
TL;DR: A fitting technique that fits trace data into a generalized Erlang distribution class using an EM method and comparative numerical simulation results of this approach and other methods are presented.
7 citations
TL;DR: In this paper, it was shown that the rate of exponential convergence for the maximum likelihood estimator attains the Bahadur bound if and only if the underlying distribution is a member of the exponential family of distributions.
7 citations
TL;DR: In this paper, the exponential family of models is defined in a general setting, not relying on probability theory, and some results of information geometry are shown to remain valid, while other less obvious applications are predicted.
Abstract: The exponential family of models is defined in a general setting, not relying on probability theory. Some results of information geometry are shown to remain valid. Exponential families both of classical and of quantum mechanical statistical physics fit into the new formalism. Other less obvious applications are predicted. For instance, quantum states can be modeled as points in a classical phase space and the resulting model belongs to the exponential family.
7 citations