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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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Journal ArticleDOI
TL;DR: In this paper , a new family of continuous distributions called the generalized odd linear exponential family is proposed, where the probability density and cumulative distribution function are expressed as infinite linear mixtures of exponentiated-F distribution.
Abstract: A new family of continuous distributions called the generalized odd linear exponential family is proposed. The probability density and cumulative distribution function are expressed as infinite linear mixtures of exponentiated-F distribution. Important statistical properties such as quantile function, moment generating function, distribution of order statistics, moments, mean deviations, asymptotes and the stress–strength model of the proposed family are investigated. The maximum likelihood estimation of the parameters is presented. Simulation is carried out for two of the mentioned sub-models to check the asymptotic behavior of the maximum likelihood estimates. Two real-life data sets are used to establish the credibility of the proposed model. This is achieved by conducting data fitting of two of its sub-models and then comparing the results with suitable competitive lifetime models to generate conclusive evidence.

4 citations

Journal ArticleDOI
TL;DR: In this article, the authors presented an optimal value to be used in the power transformation to transform the exponential to normality for statistical process control (SPC) applications, where the optimal value is found by minimizing the sum of absolute differences between two distinct cumulative probability functions.
Abstract: This work presents an optimal value to be used in the power transformation to transform the exponential to normality for statistical process control (SPC) applications. The optimal value is found by minimizing the sum of absolute differences between two distinct cumulative probability functions. Based on this criterion, a numerical search yields a proposed value of 3.5142, so the transformed distribution is well approximated by the normal distribution. Two examples are presented to demonstrate the effectiveness of using the transformation method and its applications in SPC. The transformed data are almost normally distributed and the performance of the individual charts is satisfactory. Compared to charts that use the original exponential data and probability control limits, the individual charts constructed using the transformed distribution are superior in appearance, ease of interpretation and implementation by practitioners.

4 citations

Journal ArticleDOI
TL;DR: In this paper, a large sample and exact significance tests are developed to test the relationship between survival and one covariate, and the standard unconditional likelihood approach is compared with two new tests based on the conditional distribution of the sufficient statistics.

4 citations

Journal Article
TL;DR: In this paper, the authors defined the skewed double exponential (SDE) distribution in terms of a mixture of double exponential distributions as well as a scaled product of a c.d.f.
Abstract: Definitions of the skewed double exponential (SDE) distribution in terms of a mixture of double exponential distributions as well as in terms of a scaled product of a c.d.f. and a p.d.f. of double exponential random variable are proposed. Its basic properties are studied. Multi-parameter versions of the skewed double exponential distribution are also given. Characterization of the SDE family of distributions and stochastic representation of the SDE distribution are derived.

4 citations

Journal ArticleDOI
01 Apr 1992
TL;DR: In this paper, the uniform asymptotic expansions of integrals are used to obtain an expansion for a function related to the exponential function, which is associated with Ramanujan, Watson, Copson, and Buckholtz.
Abstract: Some recent techniques in the uniform asymptotic expansions of integrals are used to obtain an expansion for a function related to the exponential function. This function is associated with Ramanujan, Watson, Copson, and Buckholtz. The results obtained complement those given by Buckholtz.

4 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202319
202262
202114
202010
20196
201823