جستجوی مقالات مرتبط با کلیدواژه « توزیع پواسن » در نشریات گروه « علوم پایه »

Gompertz-Poisson distribution is a three-parameter lifetime distribution with increasing, decreasing, increasing-decreasing and unimodal shape failure rate function and a composition of Gompertz and Poisson distributions cut at zero point that in this paper estimated the parameters of the distribution by maximum likelihood method and in order to confirm the calculated estimates, based on random sample with volumes of 100, 200, 300, 400 and 500 of Gompertz-Poisson distribution simulation study was conducted. Also with the help of two real data sets and comparing Gompertz-Poisson distribution with several other distributions of lifetime we show this distribution is a good model for data fitness related to lifetime.

ýA Poisson distribution is well used as a standard model for analyzing count dataý. ýSo the Poisson distribution parameter estimation is widely applied in practiceý. ýProviding accurate confidence intervals for the discrete distribution parameters is very difficultý. ýSo farý, ýmany asymptotic confidence intervals for the mean of Poisson distribution is providedý. ýIt is known that the coverage probability of the confidence interval (L(X),U(X)) is a function of distribution parameterý. ýSince Poisson distribution is discreteý, ýcoverage probability of confidence intervals for Poisson mean has no closed form and the exact calculation of confidence coefficientý, ýaverage coverage probability and maximum coverage probabilities for this intervalsý, ýis very difficultý. ýMethodologies for computing the exact average coverage probabilities as well as the exact confidence coefficients of confidence intervals for one-parameter discrete distributions with increasing bounds are proposed by Wang (2009)ý. ýIn this paperý, ýwe consider a situation that the both lower and upper bounds of the confidence interval is increasingý. ýIn such situationsý, ýwe explore the problem of finding an exact maximum coverage probabilities for confidence intervals of Poisson meaný. ýDecision about confidence intervals optimalityý, ýbased on simultaneous evaluation of confidence coefficientý, ýaverage coverage probability and maximum coverage probabilitiesý, ýwill be more reliableý.

In this Paper, We propose a new three-parameter lifetime of Power Series distributions of the Family Gampertz with decreasing, increasing, increasing-decreasing and unimodal Shape failure rate. The distribution is a Compound version of of the Gampertz and Zero-truncated Possion distributions, called the Gampertz-Possion distribution (GPD). The density function, the hazard rate function, a general expansion for moments, the density of the order statistic, and the maen and median deviations of the GPD are derived and studied in detail. The maximum likelihood estimation procedure is discussed and an algorithm EM is provided for estimating the parameters. The asymptotic confidence Intervals for the parameters are also obtained based on asymptotic variance covariance matrix.