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.

On sequential and fixed designs for estimation with comparisons and applications

Abstract: A fully sequential approach to the estimation of the difference of two population means for distributions belonging to the exponential family of distributions is adopted and compared with the best fixed design. Results on the lower bound for the Bayes risk due to estimation and expected cost are presented and shown to be of first order efficiency. Applications involving the Poisson and exponential distributions with gamma priors as well as the Bernoulli distribution with beta priors are given. Finally, some numerical results are presented. MSC: 62L12

A New Member of T-X Family with Applications in Different Sectors

Abstract: This paper proposes a member of the T-X family that incorporates heavy-tailed distributions, known as “a new exponential-X family of distribution.” As a special case, the paper studies a submodel of the proposed class named a “new exponential Weibull (NEx-Wei) distribution.” Some mathematical properties including hazard rate function, ordinary moments, moment generating function, and order statistics are discussed. Furthermore, we adopt the method of MLE (maximum likelihood estimation) for estimating its model parameters. A brief Monte Carlo simulation study is conducted to evaluate the performances of the MLEs based on biases and mean square error. Finally, we provide a comprehensive study to illustrate the introduced approach by analyzing three real data sets from different disciplines. The analytical goodness of fit measure of the proposed distribution is compared with other well-known distributions. We hope that the proposed class may produce many more new distributions for fitting monotonic and nonmonotonic data in the field of reliability analysis and survival analysis as well.

Prediction Intervals of an Ordered Observation from One-Parameter Exponential Distribution Based on Multiple Type II Censored Samples

Abstract: This paper provides a suitable pivotal quantity to present the prediction interval of the j(superscript th) future ordered-observation in a sample of size n from one-parameter exponential distribution in case of a multiple type II censored sample. In addition, we also discuss the approximate prediction interval, the best linear unbiased estimate and approximate maximum likelihood estimate of X(subscript j) based on the censored sample. As in application, the total duration time in a life test and the failure time of a j-out-of-n system may be predicated. Finally, a simulated study and three illustrative examples are included.

A Generalized Gamma-Weibull Distribution: Model, Properties and Applications

Abstract: We propose a new method to generate family of distributions. Then, a family of univariate distributions generated by the Gamma random variable is defined. The generalized Gamma-Weibull (GGW) distribution is studied as a special case of this family. Results for moments are provided. To estimate the model parameters, the maximum likelihood estimators and the asymptotic distributions of the estimators are discussed. Certain characterizations of GGW distribution are presented. Finally, the usefulness of the new distribution is shown via an application.