Likelihood inference based on EM algorithm for the destructive length-biased Poisson cure rate model with Weibull lifetime

In this article, we consider the destructive length-biased Poisson cure rate model, proposed by Rodrigues et al., that presents a realistic and interesting interpretation of the biological mechanism for the recurrence of tumor in a competing causes scenario. Assuming the lifetime to follow the Weibull distribution and censoring mechanism to be non-informative, the necessary steps of the EM algorithm for the determination of the MLEs of the model parameters are developed here based on right censored data. The standard errors of the MLEs are obtained by inverting the observed information matrix. A simulation study is then carried out to examine the method of inference developed here. Finally, the proposed methodology is illustrated with a real melanoma dataset.     

Zero-inflated models and estimation in zero-inflated Poisson distribution

In this paper, we briefly overview different zero-inflated probability distributions. We compare the performance of the estimates of Poisson, Generalized Poisson, ZIP, ZIGP and ZINB models through Mean square error (MSE), bias and Standard error (SE) when the samples are generated from ZIP distribution. We propose a new estimator referred to as probability estimator (PE) of inflation parameter of ZIP distribution based on moment estimator (ME) of the mean parameter and compare its performance with ME and maximum likelihood estimator (MLE) through a simulation study. We use the PE along with ME and MLE to fit ZIP distribution to various zero-inflated datasets and observe that the results do not differ significantly. We recommend using PE in place of MLE since it is easy to calculate and the simulation study in this paper demonstrates that the PE performs as good as MLE irrespective of the sample size.     

The conditional maximum of Poisson random variables

The conditional maxima of independent Poisson random variables are studied. A triangular array of row-wise independent Poisson random variables is considered. If condition is given for the row-wise sums, then the limiting distribution of the row-wise maxima is concentrated onto two points. The result is in accordance with the classical result of Anderson. The case of general power series distributions is also covered. The model studied in Theorems 2.1 and 2.2 is an analogue of the generalized allocation scheme. It can be considered as a non homogeneous generalized scheme of allocations of at most n balls into N boxes. Then the maximal value of the contents of the boxes is studied.     

地震死亡人数预测与巨灾保险基金测算

巨灾保险制度在很大程度上依赖于巨灾损失的建模分析。由于巨灾损失通常存在极端值,一般的统计分布很难对其进行有效拟合。本文以我国大陆地区1950-2015年期间的地震灾害为研究样本,基于二维泊松过程建立了地震灾害死亡人数的预测模型。根据地震死亡人数的分布特征,将地震灾害分为非巨灾事件和巨灾事件,分别用右截断的负二项分布和右截断的广义帕累托分布拟合死亡人数;用齐次泊松过程描述地震灾害在给定期间的发生次数;用Panjer迭代法和快速傅里叶变换计算地震死亡人数在特定时期的分布以及风险度量值;用蒙特卡罗模拟法测算我国地震死亡保险基金的规模和纯保费水平。与传统的巨灾模型相比,本文提出的方法同时考虑了地震灾害发生的时间和地震死亡人数两个维度,并用贝叶斯方法估计模型参数,对地震死亡人数的拟合更加合理,为完善我国地震死亡保险提供了一种新的思路。     

Efficient regression modeling for correlated and overdispersed count data

Abstract

The objective of this paper is to propose an efficient estimation procedure in a marginal mean regression model for longitudinal count data and to develop a hypothesis test for detecting the presence of overdispersion. We extend the matrix expansion idea of quadratic inference functions to the negative binomial regression framework that entails accommodating both the within-subject correlation and overdispersion issue. Theoretical and numerical results show that the proposed procedure yields a more efficient estimator asymptotically than the one ignoring either the within-subject correlation or overdispersion. When the overdispersion is absent in data, the proposed method might hinder the estimation efficiency in practice, yet the Poisson regression based regression model is fitted to the data sufficiently well. Therefore, we construct the hypothesis test that recommends an appropriate model for the analysis of the correlated count data. Extensive simulation studies indicate that the proposed test can identify the effective model consistently. The proposed procedure is also applied to a transportation safety study and recommends the proposed negative binomial regression model.     

On Some Applications of Poisson Point Processes

Poisson point processes play important role in various domains of Probability Theory and Mathematical Statistics. In this article, we investigate only two applications of Poisson point processes: a generated white noise problem and parameters estimation problem. This work continues the investigations started in paper Egorov and Kondybaev (2009 Egorov , V. A. , Kondybaev , N. S. ( 2009 ). On the estimation of a signal covered by background om Poisson noise . Methods and programs of data processing 4 : 75 – 81 . [Google Scholar]).     

Zero-inflated Poisson and negative binomial integer-valued GARCH models

Zero inflation means that the proportion of 0's of a model is greater than the proportion of 0's of the corresponding Poisson model, which is a common phenomenon in count data. To model the zero-inflated characteristic of time series of counts, we propose zero-inflated Poisson and negative binomial INGARCH models, which are useful and flexible generalizations of the Poisson and negative binomial INGARCH models, respectively. The stationarity conditions and the autocorrelation function are given. Based on the EM algorithm, the estimating procedure is simple and easy to be implemented. A simulation study shows that the estimation method is accurate and reliable as long as the sample size is reasonably large. A real data example leads to superior performance of the proposed models compared with other competitive models in the literature.     

Prediction of accrual closure date in multi-center clinical trials with discrete-time Poisson process models

In a phase III multi‐center cancer clinical trial or a large public health study, sample size is predetermined to achieve desired power, and study participants are enrolled from tens or hundreds of participating institutions. As the accrual is closing to the target size, the coordinating data center needs to project the accrual closure date on the basis of the observed accrual pattern and notify the participating sites several weeks in advance. In the past, projections were simply based on some crude assessment, and conservative measures were incorporated in order to achieve the target accrual size. This approach often resulted in excessive accrual size and subsequently unnecessary financial burden on the study sponsors. Here we proposed a discrete‐time Poisson process‐based method to estimate the accrual rate at time of projection and subsequently the trial closure date. To ensure that target size would be reached with high confidence, we also proposed a conservative method for the closure date projection. The proposed method was illustrated through the analysis of the accrual data of the National Surgical Adjuvant Breast and Bowel Project trial B‐38. The results showed that application of the proposed method could help to save considerable amount of expenditure in patient management without compromising the accrual goal in multi‐center clinical trials. Copyright © 2012 John Wiley & Sons, Ltd.