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.

Results related to the bhattacharyya matrices

Abstract: SUMMARY. In this paper, we consider characterizations based on the Bhattacharyya matrices. We begin the paper by obtaining the structure of the r th moment of the random variable X about the origin for a natural exponential family when the variance is a polynomial of the mean such that the mean is a linear function of the parameter of the family. We also characterize, under certain constraints, distributions such as normal, compound Poisson and gamma via the diagonality of the 2 £ 2 Bhattacharyya matrix.

Reliability analysis of load-sharing m-out-of-n systems with arbitrary load and different probability distributions of time to failure

Abstract: The reliability analysis of load-sharing m-out-of-n systems where the workload is shared by the remaining working units when a unit fails is proposed in the paper. General expressions are provided for the m-out-of-n system reliability by arbitrary probability distributions of time to failure of units. Simplified methods are given for computing the survivor function in cases when the time to unit failure is governed by the Weibull and exponential probability distributions. The system survivor function and the mean time to failure in the explicit form are obtained for systems with arbitrary load (decreasing and increasing) by the exponential time to unit failure. Numerical examples illustrate the properties of load-sharing m-out-of-n systems.

Recursive characterization of a large family of discrete probability distributions showing extra-Poisson variation

Abstract: This article analyses the broad family of discrete probability distributions generated by relating Prob (y) to Prob (y−1), …, Prob (y−n), for some n≥1, through a recursive equation. This family contains the binomial, negative binomial and Poisson distributions as well as the Katz family of distributions. In addition, the suggested family contains some convolutions of Poisson distributions and other generalized distributions, which provide models for Poisson overdispersion or underdispersion.

Estimating exponential reliability function and exponential density

Abstract: The estimation problem of the reliability function and the density at a point of two-parameter exponential population is considered. The Bayes nature of the best unbiased estimator of the reliability is demonstrated. The nonexistence of the unbiased density estimates is noticed and the admissibility of related generalized Bayes estimators in the class of all scale-equivariant procedures is established. Asymptotical formulae for quadratic risk of these estimators and the maximum likelihood estimator are obtained.

Testing for a change point in a sequence of exponential random variables with repeated values

Abstract: Two test statistics are proposed for the change-point problem with repeated values when the data follow an exponential distribution. The properties of these two statistics have been studied and their asymptotic distributions under the alternative have been derived. The powers of the two test statistics are compared. Real-data examples are presented to illustrate the application of these tests.