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通过共同边际正态变量的依赖性比较统计实验AI 解读

In this note we study comparison of experiments via the positive dependence of normal variables with a common univariate marginal distribution. We show that positive dependence has an adverse effect on the information concerning the common mean $\theta$, and give a partial ordering of the information via a majorization ordering of the correlation matrices. In the special case when the random variables are equally correlated, the main theorem yields a result for the…

混合样本的参数估计AI 解读

Assume that a sample is a mixture of two samples from two different populations with distributions Fθ1 and Fθ2 . Given the form of Fθ , estimators of θ1 and θ2 are introduced. It is shown that the estimators are consistent and their asymptotic joint distribution is derived. The suggested estimators are compared with the maximum likelihood estimators and the method of moments estimators. For small sample sizes the comparison is done by a Monte Carlo study. For large sample…

混合样本中的参数估计AI 解读

Assume that a sample is a mixture of two samples from two different populations with distributions Fθ1 and Fθ2 . Given the form of Fθ , estimators of θ1 and θ2 are introduced. It is shown that the estimators are consistent and their asymptotic joint distribution is derived. The suggested estimators are compared with the maximum likelihood estimators and the method of moments estimators. For small sample sizes the comparison is done by a Monte Carlo study. For large sample…

加速寿命试验的非参数方法AI 解读

A nonparametric model of acceleration is introduced. Based on this model, a procedure is suggested for estimating the nonaccelerated life distribution from accelerated observations. Unlike previous nonparametric estimation procedures, our method does not require nonaccelerated observations. A relationship between the accelerated and the nonaccelerated distributions is assumed but there is variety in that choice. A comparison of our method with the power rule method under the…

泊松与正态均值的星形序列估计AI 解读

A vector $\mu = (\mu_1, \cdots, \mu_n)$ is said to be upper [lower] starshaped if $\mu_{m + 1} \geqslant 0 \lbrack \leqslant \mu_{m + 1} \leqslant \bar{\mu}_m\rbrack m = 1, \cdots, n - 1$, where $\bar{\mu}_m$ is a weighted average of $\mu_1, \cdots, \mu_m$. Obtained is the maximum likelihood estimate of $\mu$ when the $\mu_i$'s are the means of $n$ Poisson or normal populations and $\mu$ is known to be starshaped. The method is applied to obtain estimators of IHRA…

二元分布的一族依赖性概念AI 解读

A family of concepts of stochastic dependence for bivariate distribution functions is introduced. Each concept gives rise to a family of bivariate distribution functions. We show the equivalence of some of these families with families of positively dependent distribution functions, which are known in the literature, and characterize some of them by notions from reliability theory. Interrelations among the various families are studied, and some moment inequalities are…

可交换随机变量的一种正依赖概念AI 解读

An $n$-variate distribution function is said to be positive dependent by mixture (PDM) if it is a mixture of independent $n$-variate distributions with equal marginals. PDM distributions arise in various contexts of reliability and other areas of statistics. We give a necessary and sufficient condition, by means of independent random variables, for an $n$-variate distribution function to be PDM. The distributions and the expectations of the order statistics of PDM and of…