Bayesian estimation and prediction for Weibull model with progressive censoring

This article presents the statistical inferences on Weibull parameters with the data that are progressively type II censored. The maximum likelihood estimators are derived. For incorporation of previous information with current data, the Bayesian approach is considered. We obtain the Bayes estimators under squared error loss with a bivariate prior distribution, and derive the credible intervals for the parameters of Weibull distribution. Also, the Bayes prediction intervals for future observations are obtained in the one- and two-sample cases. The method is shown to be practical, although a computer program is required for its implementation. A numerical example is presented for illustration and some simulation study are performed.     

众数测算的一种新方法及其应用

针对传统众数估计值会因为组距的改变而不稳定,在已有的半极差(样本)众数估计方法上,提出多比例极差(样本)众数估计新方法。模拟研究显示,相对于半极差(样本)众数估计方法,该方法估计结果更稳定、准确。在实证分析中,基于2014、2015年国家一体化住户调查数据,使用新方法计算了新疆兵团居民人均可支配收入众数。结果表明,众数可以作为居民人均可支配收入平均数、中位数的有益补充,众数在政府统计中的推广及应用具有一定的可行性与必要性。     

Multiple comparisons of exponential location parameters with a control based on doubly censored sample under heteroscedasticity

In this article, a one-sample procedure for multiple comparisons of exponential location parameters with a control under heteroscedasticity is proposed. The observations are obtained by doubly censored samples. A one-sided and two-sided confidence intervals are used to perform such multiple comparisons. Statistical tables of critical values and an example of comparing four drugs in treating leukemia are provided.     

The economic design of multivariate binomial EWMA VSSI control charts

Since multi-attribute control charts have received little attention compared with multivariate variable control charts, this research is concerned with developing a new methodology to employ the multivariate exponentially weighted moving average (MEWMA) charts for m-attribute binomial processes; the attributes being the number of nonconforming items. Moreover, since the variable sample size and sampling interval (VSSI) MEWMA charts detect small process mean shifts faster than the traditional MEWMA, an economic design of the VSSI MEWMA chart is proposed to obtain the optimum design parameters of the chart. The sample size, the sampling interval, and the warning/action limit coefficients are obtained using a genetic algorithm such that the expected total cost per hour is minimized. At the end, a sensitivity analysis has been carried out to investigate the effects of the cost and the model parameters on the solution of the economic design of the VSSI MEWMA chart.     

A generalization of the compound rayleigh distribution: using a bayesian method on cancer survival times

In this paper the generalized compound Rayleigh model, exhibiting flexible hazard rate, is high¬lighted. This makes it attractive for modelling survival times of patients showing characteristics of a random hazard rate. The Bayes estimators are derived for the parameters of this model and some survival time parameters from a right censored sample. This is done with respect to conjugate and discrete priors on the parameters of this model, under the squared error loss function, Varian's asymmetric linear-exponential (linex) loss function and a weighted linex loss function. The future survival time of a patient is estimated under these loss functions. A Monte Carlo simu¬lation procedure is used where closed form expressions of the estimators cannot be obtained. An example illustrates the proposed estimators for this model.     

A SADDLEPOINT APPROXIMATION TO THE DISTRIBUTION FUNCTION OF THE ANDERSON-DARLING TEST STATISTIC

The Anderson-Darling goodness-of-fit test has a highly skewed and non-standard limit distribution. Various attempts have been made to tabulate the associated critical points, using both theoretical approximations and simulation methods. We show that a standard saddlepoint approximation performs well in both tails of the distribution. It is markedly superior to other theoretical approximations in the lower tail of the distribution.     

The effect of non-normality on estimating the variance of the combined ratio estimate in complex surveys

The performance of the balanced half-sample, jackknife and linearization methods for estimating the variance of the combined ratio estimate is studied by means of a computer simulation using artificially generated non-normally distributed populations.

The results of this investigation demonstrate that the variance estimates for the combined ratio estimate may be highly biased and unstable when the underlying distributions are non-normal. This is particularly true when the number of observations available from each stratum is small. The jack-     

Information in Tender Offers With a Large Shareholder

We study takeovers of firms whose ownership structure is a mixture of minority block‐holders and small shareholders. We show that the combination of dispersed private information on the side of small shareholders and the presence of a large shareholder can facilitate profitable takeovers. Furthermore, our analysis implies that even if some model of takeovers predicts a profit for the raider, for example, due to private benefits, the profit will be underestimated unless the large shareholder and the dispersion of information among the small shareholders are modeled.     

A strong law of large numbers for independent random variables under non-additive probabilities

Abstract

Under non‐additive probabilities, cluster points of the empirical average have been proved to quasi-surely fall into the interval constructed by either the lower and upper expectations or the lower and upper Choquet expectations. In this paper, based on the initiated notion of independence, we obtain a different Marcinkiewicz-Zygmund type strong law of large numbers. Then the Kolmogorov type strong law of large numbers can be derived from it directly, stating that the closed interval between the lower and upper expectations is the smallest one that covers cluster points of the empirical average quasi-surely.     

发电成本垂直差异电力市场概率发电——基于大用户电量偏好视角

针对碳减排后普遍存在的发电成本垂直差异电力市场及其显著的大用户电量偏好差异,本文提出概率性电量供给以及与之对应的概率发电,并利用价格杠杆调控发电商低碳发电尤其高发电成本发电机会与供给效能不足.先后构建发电成本内、外生选择下的概率发电模型,求解发电商的电量供给均衡并分析概率发电策略的最优性.最后,将发电成本内生选择模型拓展到分解市场需求不确定性的概率发电模型.研究发现:相比基准发电,概率发电可以作为一种有利可图的发电容量过剩的解决方法,即使在发电成本内生选择时也是可行的;当发电商采用“强”成本差异的发电策略时,引入折中的概率发电会让产品线上成本水平相互更接近,且大用户的消费者剩余得到提高;与此相反,在市场中实施“弱”成本差异发电,发电商利用概率发电则增大成本分离并降低大用户的消费者剩余;在不确定性市场需求下,当偏好低发电成本电量的大用户对单位发电成本的估价相对于偏好高发电成本电量的大用户对单位发电成本的估价足够高时,概率发电可以以一种管理不利需求状况工具的身份出现.