Bayesian inference for ammunition demand based on Gompertz distribution

Aiming at the problem that the consumption data of new ammunition is less and the demand is difficult to predict,combined with the law of ammunition consumption under different damage grades,a Bayesian inference method for ammunition demand based on Gompertz distribution is proposed.The Bayesian inference model based on Gompertz distribution is constructed,and the system contribution degree is introduced to determine the weight of the multi-source information.In the case where the prior distribution is known and the distribution of the field data is unknown,the consistency test is performed on the prior information,and the consistency test problem is transformed into the goodness of the fit test problem.Then the Bayesian inference is solved by the Markov chain-Monte Carlo(MCMC)method,and the ammunition demand under different damage grades is gained.The example verifies the accuracy of this method and solves the problem of ammunition demand prediction in the case of insufficient samples.

On the Application of Nadarajah Haghighi Gompertz Distribution as a Life Time Distribution

The convolution of Nadarajah-Haghighi-G family of distributions will result into a more flexible distribution (Nadarajah-Haghighi Gompertz distribution) than each of them individually in terms of the estimate of the characteristics in there parameters. The combination was done using Nadarajah-Haghighi (NH) generator. We investigated in the newly developed distribution some basic properties including moment, moment generating function, survival rate function, hazard rate function asymptotic behaviour and estimation of parameters. The proposed model is much more flexible and has a better representation of data than Gompertz distribution and some other model considered. A real data set was used to illustrate the applicability of the new model.

Parametric Regression Approach for Gompertz Survival Times with Competing Risks

Regression models play a vital role in the study of data regarding survival of subjects.The Cox proportional hazards model for regression analysis has been frequently used in sur-vival modelling.In survival studies,it is also possible that survival time may occur with multiple occurrences of event or competing risks.The situation of competing risks arises when there are more than one mutually exclusive causes of death(or failure)for the person(or subject).In this paper,we developed a parametric regression model using Gompertz distribution via the Cox proportional hazards model with competing risks.We discussed point and interval estimation of unknown parameters and cumulative cause-specific hazard function with maximum-likelihood method and Bayesian method of estimation.The Bayes estimates are obtained based on non-informative priors and symmetric as well as asym-metric loss functions.To observe the finite sample behaviour of the proposed model under both estimation procedures,we carried out a Monte Carlo simulation analysis.To demon-strate our methodology,we also included real data analysis.

E-Bayesian estimation for competing risk model under progressively hybrid censoring

This paper considers the Bayesian and expected Bayesian（E-Bayesian） estimations of the parameter and reliability function for competing risk model from Gompertz distribution under Type-I progressively hybrid censoring scheme（PHCS）. The estimations are obtained based on Gamma conjugate prior for the parameter under squared error（SE） and Linex loss functions. The simulation results are provided for the comparison purpose and one data set is analyzed.