Analysis of discrete lifetime data under middle-censoring and in the presence of covariates

‘Middle censoring’ is a very general censoring scheme where the actual value of an observation in the data becomes unobservable if it falls inside a random interval (L, R) and includes both left and right censoring. In this paper, we consider discrete lifetime data that follow a geometric distribution that is subject to middle censoring. Two major innovations in this paper, compared to the earlier work of Davarzani and Parsian [3 N. Davarzani and A. Parsian, Statistical inference for discrete middle-censored data, J. Statist. Plan. Inference 141 (2011), pp. 1455–1462. doi: 10.1016/j.jspi.2010.10.012[Crossref], [Web of Science ®] , [Google Scholar]], include (i) an extension and generalization to the case where covariates are present along with the data and (ii) an alternate approach and proofs which exploit the simple relationship between the geometric and the exponential distributions, so that the theory is more in line with the work of Iyer et al. [6 S.K. Iyer, S.R. Jammalamadaka, and D. Kundu, Analysis of middle censored data with exponential lifetime distributions, J. Statist. Plan. Inference 138 (2008), pp. 3550–3560. doi: 10.1016/j.jspi.2007.03.062[Crossref], [Web of Science ®] , [Google Scholar]]. It is also demonstrated that this kind of discretization of life times gives results that are close to the original data involving exponential life times. Maximum likelihood estimation of the parameters is studied for this middle-censoring scheme with covariates and their large sample distributions discussed. Simulation results indicate how well the proposed estimation methods work and an illustrative example using time-to-pregnancy data from Baird and Wilcox [1 D.D. Baird and A.J. Wilcox, Cigarette smoking associated with delayed conception, J, Am. Med. Assoc. 253 (1985), pp. 2979–2983. doi: 10.1001/jama.1985.03350440057031[Crossref], [Web of Science ®] , [Google Scholar]] is included.     

分数型几何亚式-再装股票期权的保险精算定价公式及其仿真

文章讨论了再装股票期权在再装日按B-S定价模型执行所产生的经理激励缺陷,提出了将有效期内股价的几何平均值作为再装期权结算价格的思想,建立了几何亚式-再装股票期权的定价模型。并利用保险精算方法,从评估实际损失和相应概率分布的角度,研究了几何亚式-再装股票期权的价值构成,获得了基于分数布朗运动下几何亚式-再装股票期权的保险精算定价公式。还通过数值模拟分析比较了传统再装期权与几何亚式-再装股票期权在经理激励中的作用。     

几何分布产品不完全数据场合下的统计分析

几何分布是离散型寿命分布中最为重要的分布之一,许多产品的寿命（比如开关等）都可以用几何分布来描述。由于几何分布的无记忆性,它在可靠性理论与应用概率模型中有着非常重要的地位。目前,对关于几何分布在全样本场合、截尾样本场合以及加速寿命试验场合下参数的统计分析已经有了广泛的研究。并且有着重要的理论与应用价值。因此将不完全数据场合下的几何分布问题转化为指数分布问题,再利用指数分布的已有结果首次得到了几何分布在缺失数据场合和分组数据场合下参数的近似点估计,Monte—Carlo模拟算例结果令人满意,说明该方法是可行的。     

高空卷云冰晶粒子的散射特性研究

高空卷云是一种大范围发生的高空大气现象。文中对卷云冰晶粒子的物理特性进行了概要总结,用几何射线近似求解冰晶粒子的散射特性,计算了冰晶粒子对１ ．３１５ μｍ 光波的散射相矩阵、散射截面、吸收截面,并进行了讨论     

The exponentiated G geometric family of distributions

We propose a new class of distributions called the exponentiated G geometric family motivated mainly by lifetime issues which can generate several lifetime models discussed in the literature. Some mathematical properties of the new family including asymptotes and shapes, moments, quantile and generating functions, extreme values and order statistics are fully investigated. We propose the log-exponentiated Weibull geometric and log-exponentiated log-logistic geometric regression models to cope with censored data. The model parameters are estimated by maximum likelihood. Three examples with real data expose quite well the new family.     

Recursive computation of the single and product moments of order statistics from the complementary exponential–geometric distribution

The complementary exponential–geometric distribution has been proposed recently as a simple and useful reliability model for analysing lifetime data. For this distribution, some recurrence relations are established for the single and product moments of order statistics. These recurrence relations enable the computation of the means, variances and covariances of all order statistics for all sample sizes in a simple and efficient recursive manner. By using these relations, we have tabulated the means, variances and covariances of order statistics from samples of sizes up to 10 for various values of the shape parameter θ. These values are in turn used to determine the best linear unbiased estimator of the scale parameter β based on complete and Type-II right-censored samples.     

Uniform-Geometric distribution

In this paper, a new discrete distribution called Uniform-Geometric distribution is proposed. Several distributional properties including survival function, moments, skewness, kurtosis, entropy and hazard rate function are discussed. Estimation of distribution parameter is studied by methods of moments, proportions and maximum likelihood. A simulation study is performed to compare the performance of the different estimates in terms of bias and mean square error. Two real data applications are also presented to see that new distribution is useful in modelling data.     

On the functional relationship between entropy and variance with related applications

The functional relationship between entropy and variance is investigated for some well-known distributions. The distributions considered here are the reparameterized versions of the original forms. Such a reparameterization is necessary as in each case we have a common variance. The related graphs of entropy as a function of variance are used for certain comparisons. Further, within the class of distributions having a common variance, a measure of affinity between these distributions is proposed using entropy. A few aspects of the sampling distributions of an estimator of entropy, when the samples are either from the normal or from the exponential distributions, are discussed with a view to possible applications in the testing of hypotheses for related parameters     

On the fisher β-sufficient partition

This paper shows that the Fisher information in a partition of the space of a random variable X is less than or equal to the Fisher information of X about the unknown parameter. It also provides tables to construct β-sufficient partitions if X has an exponential distribution or a geometric distribution. Simulation study was conducted to show the advantage of using these tables over the usual methods used to construct histograms.