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.
Papers published on a yearly basis
Papers
More filters
01 Jan 2013
TL;DR: In this article, double stage shrinkage estimator (DSSE) was used to reduce the mean squared error of classical estimator for the shape parameter of generalized exponential distribution in a region (R) around available prior knowledge (α0) about the actual value (α) as initial estimate in case when a scale parameter (λ) is known as well as reduce the cost of experimentations.
Abstract: This paper is concerned with double stage shrinkage estimator (DSSE) for lowering the mean squared error of classical estimator (MLE) for the shape parameter (α) of generalized Exponential (GE) distribution in a region (R) around available prior knowledge (α0) about the actual value (α) as initial estimate in case when a scale parameter (λ) is known as well as to reduce the cost of experimentations. In situation where the experimentations are time consuming or very costly, a double stage procedure can be used to reduce the expected sample size needed to obtain the estimator. This estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor ψ(⋅) and for acceptance mentioned region R. Expressions for Bias, Mean square error (MSE), Expected sample size [E(n/α,R)], Expected sample size proportion [E(n/α,R)/n], probability for avoiding the second sample 1̂ [p( R)] α∈ and percentage of overall sample saved 2 1 n ˆ [ p( R) 100] n α∈ ∗ for the proposed estimator are derived. Numerical results and conclusions are established when the consider estimator (DSSE) are estimator of level of significance Δ. Comparisons with the classical estimator and with the last studies shown the usefulness of the proposed estimator
TL;DR: In this article, several characterizations of the RGCGE distribution are presented, which are based on conditional expectation of certain functions of the random variable, a single function, and the hazard function of a random variable.
Abstract: Abstract The problem of characterizing a distribution is an important problem which has recently attracted the attention of many researchers. Thus, various characterizations have been established in many different directions. An investigator will be vitally interested to know if their model fits the requirements of a particular distribution. To this end, one will depend on the characterizations of this distribution which provide conditions under which the underlying distribution is indeed that particular distribution. In this work, several characterizations of Randomly Censored Generalized Exponential (RCGE) distribution are presented. These characterizations are based on: ( i) conditional expectation of certain functions of the random variable , (ii ) a single function of the random variable, ( iii) the hazard function of the random variable.
01 Jan 1998
TL;DR: In this article, the problem of testing independence in a multivariate exponential distribution with identical marginals is considered, and the conditional test for the transformed hypothesis proposed here is the likelihood ratio test.
Abstract: In this article the problem of testing independence in a multivariate exponential distribution with identical marginals is considered. Following Bhattacharyya and Johnson (1973) the null hypothesis of independence is transformed into a hypothesis concerning the equality of scale parameters of several exponential distributions. The conditional test for the transformed hypothesis proposed here is the likelihood ratio test. The powers of this test are estimated for selected values of the parameters, using Monte Carlo simulation and non-central chi-square approximation. The powers of the overall test are estimated using a simple formula involving the power function of the conditional test. Application to reliability problems is also discussed in some detail.
15 Feb 2011
TL;DR: In this paper, a number of classical nonparametric and parametric procedures for estimating the survival probability (often called the reliability function) of nonrepairable units are discussed and some graphical methods are briefly presented.
Abstract: This article illustrates a number of classical nonparametric and parametric procedures for estimating the survival probability (often called the reliability function) of nonrepairable units. Both point and interval estimation procedures are discussed and some graphical methods are briefly presented. A specific attention is devoted to two frequently used distribution functions: the standard exponential and two-parameter Weibull distributions. Finally, a number of examples are given to illustrate the estimation procedures.
Keywords:
survival probability;
singly censored;
multiply censored;
likelihood function;
two-parameter Weibull distribution;
exponential distribution;
probability plots
TL;DR: In this paper , a new statistical distribution based on power series is proposed, which is constructed based on a latent complementary risk problem and is obtained by compounding Beta Exponential (BE) and Power Series distributions.
Abstract: In this paper, we investigate to propose a new statistical distribution based on power series. We introduce a new family of distributions which are constructed based on a latent complementary risk problem and are obtained by compounding Beta Exponential (BE) and Power Series distributions. The new distribution contains, as special sub-models, several important distributions which are discussed in the literature, such as Beta Exponential Poisson (BEP) distribution, Beta Exponential Geometric (BEG) distribution, Beta Exponential Logarithmic (BEL) distribution, Beta Exponential Binomial (BEB) distribution as special cases. The hazard function of the BEPS distributions can be increasing, decreasing or bathtub shaped among others. The comprehensive mathematical properties of the new distribution is provided such as closed-form expressions for the density, cumulative distribution, survival function, failure rate function, the r-th raw moment, maximum likelihood estimation and also the moments of order statistics. The proposed type of distributions is used to modeling simulated and real datasets.