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大样本随机删失下若干极大似然估计量的性质AI 解读

In the case the survival distribution of a life length X is of the form ln[1 - Fx (x)] = -αQ(βx) for x > 0, where the hazard function Q is known but α or β or both are unknown, the asymptotic distribution of the maximum likelihood estimators of the shape and scale parameters is found for large randomly censored samples. The covariance matrix of is expressed in terms of the distribution of the random variable that can be observed, namely, Y = min(X, T); here T is the random…

删失数据下双参数递减风险率分布的最大似然估计AI 解读

Problems of maximum likelihood estimation are discussed for shape and scale parameters from certain decreasing hazard rate distributions, typically either mixed-exponential or “work-hardened.” Sufficient conditions on the mixing distribution are given that guarantee regular behavior of the hazard rate and that ensure, even with highly censored data, that the MLE's exist from such DHR distributions whenever the sample satisfies a certain condition; otherwise a constant hazard…

删失数据下双参数递减风险率分布的极大似然估计AI 解读

Problems of maximum likelihood estimation are discussed for shape and scale parameters from certain decreasing hazard rate distributions, typically either mixed-exponential or “work-hardened.” Sufficient conditions on the mixing distribution are given that guarantee regular behavior of the hazard rate and that ensure, even with highly censored data, that the MLE's exist from such DHR distributions whenever the sample satisfies a certain condition; otherwise a constant hazard…

对取倒数封闭的一类随机变量AI 解读

Some of the known properties of a particular family of distributions derived as a model for fatigue failure by Birnbaum and Saunders [3] are shown to hold for a class of families. These results stem from the fact that each variate in the class suitably scaled has the same distribution as its reciprocal. This clarifies the utility of certain distributions proposed for fatigue life, e.g., lognormal. This property also influences the estimation of the scale parameter and makes…