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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01 Jan 2008
TL;DR: A latent variable model for the e-PCA is introduced and a learning algorithm for those mixture models based on the variational Bayes method applying Laplace’s method to carry out clustering on an arbitrary subspace is derived.
Abstract: The e-PCA has been proposed to reduce the dimension of the parameters of probability distributions using Kullback information as a distance between two distributions. It also provides a framework for dealing with various data types such as binary and integer for which the Gaussian assumption on the data distribution is inappropriate. In this paper, we introduce a latent variable model for the e-PCA. Assuming the discrete distribution on the latent variable leads to mixture models whose parameters are constrained to the lower-dimensional subspace of exponentialfamily distributions. We derive a learning algorithm for those mixture models based on the variational Bayes method applying Laplace’s method to carry out clustering on an arbitrary subspace. Combined with the estimation of the subspace, the resulting algorithm performs simultaneous dimensionality reduction and clustering.
3 citations
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TL;DR: In this article, two characterization properties of the two-piece double exponential distribution are derived for the symmetric Laplace distribution and they reduce to well-known characterizations of the exponential distribution as special cases.
Abstract: SYNOPTIC ABSTRACTThe Two-Piece Double Exponential Distribution is known to be very useful in modeling currency rates, interest rates, share price indices, and so on. Two characterization properties of this distribution are derived in this article. These properties are also applicable to the symmetric Laplace distribution and they reduce to well-known characterizations of the exponential distribution as special cases.
3 citations
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21 Nov 2008TL;DR: In this article, a mixture distribution based on two different Weibull distributions is proposed, which includes a mixing parameter, which represents the proportion of mixing associated to the two component models.
Abstract: The aim of this paper is to introduce a method of combining two different Weibull distributions. This method illustrates on how to produce a mixture distribution based on two Weibull distributions by including a mixing parameter, say w, which represents the proportion of mixing associated to the two component models. Weibull distributions. The mixture distribution produced from the combination of two Weibull distributions has a number of parameters which include shape parameters, scale parameters and location parameters in addition to the mixing parameter. In this paper, we focus on the estimation of parameters of the proposed mixture Weibull distribution using maximum likelihood method. In addition, we illustrate the characteristics of this distribution in terms of the probability density function, cumulative distribution function, reliability function and failure rate for a particular value of w.
3 citations
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TL;DR: In this paper, the odd generalized ex ponential generalized linear exponential distribution (OGLED) was proposed, and the mathematical properties, including moments and order s tatistics, have been derived.
Abstract: In this article, a new generalization of the Generalized Lin ear Exponential distribution called the odd generalized ex ponential generalized linear exponential distribution is proposed. The mathematical properties, including moments and order s tatistics, have been derived. An application of the model to real data sets reveal d that the new model can be used to provide a better fit than its sub-models.
3 citations
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TL;DR: In this article, the authors derived the exact distributions of αX+βY when X and Y are correlated random variables and come from the same family, based on real-life examples in quality and reliability engineering.
Abstract: The distribution ofαX+βYhas been studied by several authors especially when X and Y are independent random variables and come from the same familyHowever,there is relatively little work of this kind when X and Y are correlated random variablesI haven't found related results in domestic so farBased on this consideration,in this paper,we takes bivariate exponential distribution which is widely applied in reliability as an example,derive the exact distributions ofαX+βYThe work is motivated by real-life examples in quality and reliability engineering
3 citations