A new generalized exponentiated Weibull model called Gumbel-exponentiated </span><span style="font-family:Verdana;">Weibull</span><span style="font-family:""> </span...A new generalized exponentiated Weibull model called Gumbel-exponentiated </span><span style="font-family:Verdana;">Weibull</span><span style="font-family:""> </span><span style="font-family:Verdana;">{Logistic} distribution is introduced and studied. The new distribution extends the exponentiated Weibull distribution with additional parameters and bimodal densities. Some new and earlier distributions formed the sub-models of the proposed distribution. The mathematical properties of the new distribution including expressions for the hazard function, survival function, moments, order statistics, mean deviation and absolute mean deviation from the mean, and entropy were derived. Monte Carlo simulation study was carried out to assess the finite sample behavior of the parameter estimates by maximum likelihood estimation approach. The superiority of the new generalized exponentiated Weibull distribution over some competing distributions was proved empirically using the fitted results from </span><span style="font-family:Verdana;">three</span><span style="font-family:Verdana;"> real life datasets.展开更多
Bayesian predictive probability density function is obtained when the underlying pop-ulation distribution is exponentiated and subjective prior is used. The corresponding predictive survival function is then obtained ...Bayesian predictive probability density function is obtained when the underlying pop-ulation distribution is exponentiated and subjective prior is used. The corresponding predictive survival function is then obtained and used in constructing 100(1 – ?)% predictive interval, using one- and two- sample schemes when the size of the future sample is fixed and random. In the random case, the size of the future sample is assumed to follow the truncated Poisson distribution with parameter λ. Special attention is paid to the exponentiated Burr type XII population, from which the data are drawn. Two illustrative examples are given, one of which uses simulated data and the other uses data that represent the breaking strength of 64 single carbon fibers of length 10, found in Lawless [40].展开更多
文摘A new generalized exponentiated Weibull model called Gumbel-exponentiated </span><span style="font-family:Verdana;">Weibull</span><span style="font-family:""> </span><span style="font-family:Verdana;">{Logistic} distribution is introduced and studied. The new distribution extends the exponentiated Weibull distribution with additional parameters and bimodal densities. Some new and earlier distributions formed the sub-models of the proposed distribution. The mathematical properties of the new distribution including expressions for the hazard function, survival function, moments, order statistics, mean deviation and absolute mean deviation from the mean, and entropy were derived. Monte Carlo simulation study was carried out to assess the finite sample behavior of the parameter estimates by maximum likelihood estimation approach. The superiority of the new generalized exponentiated Weibull distribution over some competing distributions was proved empirically using the fitted results from </span><span style="font-family:Verdana;">three</span><span style="font-family:Verdana;"> real life datasets.
文摘Bayesian predictive probability density function is obtained when the underlying pop-ulation distribution is exponentiated and subjective prior is used. The corresponding predictive survival function is then obtained and used in constructing 100(1 – ?)% predictive interval, using one- and two- sample schemes when the size of the future sample is fixed and random. In the random case, the size of the future sample is assumed to follow the truncated Poisson distribution with parameter λ. Special attention is paid to the exponentiated Burr type XII population, from which the data are drawn. Two illustrative examples are given, one of which uses simulated data and the other uses data that represent the breaking strength of 64 single carbon fibers of length 10, found in Lawless [40].
