Fisher Information in Type II Progressive Censored Samples

Recently, progressively Type II censored samples have attracted attention in the study and analysis of life-testing data. Here we propose an indirect approach for computing the Fisher information (FI) in progressively Type II censored samples that simplifies the calculations. Some recurrence relations for the FI in progressively Type II censored samples are derived that facilitate the FI computation using the proposed decomposition. This paper presents a standard recurrence relation that simplifies computation of the FI in progressively Type II censored samples to a sum; FI in collections order statistics (OS). We compute the FI in a collections of progressively Type II censored samples for some known distributions.     

Clustering Discrete Data Through the Multinomial Mixture Model

In this work, the multinomial mixture model is studied, through a maximum likelihood approach. The convergence of the maximum likelihood estimator to a set with characteristics of interest is shown. A method to select the number of mixture components is developed based on the form of the maximum likelihood estimator. A simulation study is then carried out to verify its behavior. Finally, two applications on real data of multinomial mixtures are presented.     

Is the Selected Population the Best?—Location and Scale Parameter Cases

We observe X ₁,…,X _k , where X _i has density f(x,θ _i ) possessing monotone likelihood ratio. The best population corresponds to the largest θ _i . We select the population corresponding to the largest X _i . The goal is to attach the best possible p-value to the inference: the selected population has the uniquely largest θ _i . Gutmann and Maymin (1987 Gutmann , S. , Maymin , Z. ( 1987 ). Is the selected population the best? Ann. Statist . 15 : 456 – 461 .[Crossref], [Web of Science ®] , [Google Scholar]) considered the location parameter case and derived the supremum of the error probability by conditioning on S, the index of the largest X _i . Using this conditioning approach, Kannan and Panchapakesan (2009 Kannan , N. , Panchapakesan , S. ( 2009 ). Does the selected normal population have the smallest variance? Amer. J. Math. Management Sci . 29 : To appear . [Google Scholar]) considered the problem for the gamma family. We consider here a unified approach to both the location and scale parameter cases, and obtain the supremum of the error probability without using conditioning.     

The poisson-inverse gaussian disiribuiion as a model for species abundance

An inverse Gaussian mixture of Poisson distributions(the P-IG distribution) is considered as a model for species abundance data,, Minimum chi-square and maximum likelihood methods of estimation for the zero-truncated P-IG distribution are developed, Ihe performance of the P-IG distribution is illustrated and discussed for several well-known sets of insect abundance data.     

Improved deviance goodness of fit statistics for a gamma regression model

A gamma regression model with an exponential link function for the means Is considered. Moment properties of the deviance statistics based on maximum likelihood and weighted least squares fits are used to define modified deviance statistics which provide alternative global goodness of fit tests. The null distribution properties of the deviances and modified deviances are compared with those of the approximating chi-square distribution and It is shown that the use of the modified deviances gives much better control over the significance levels of the tests.     

Umvu estimation for the cumulative hazard function in a pareto distribution of the first kind

The uniformly minimum variance unbiased estimator of the cumulative hazard function in the Pareto distribution of the first kind is derived. The variance of the estimator is also obtained in an analytic form, and for some cases its values are compared numerically with mean square errors of the maximum likelihood estimator.     

A stepwise approach for the purely periodic interaction spline model

The basic idea of an interaction spline model was presented in Barry (1983). The general interaction spline models were proposed by Wahba (1986). The purely periodic spline model, a special case of the general interaction spline models, is considered in this paper. A stepwise approach using generalized cross validation (GCV) for fitting the model is proposed. Based on the nice orthogonality properties of the purely periodic functions, the stepwise approach is a promising method for the interaction spline model. The approach can also be generalized to the non-purely-periodic spline models. But this is no done here.     

A Measure of partial association between disease and genotype for the two-parent problem

The two-parent disease-genotype association problem is studied from the point of view of a coefficient of association between the disease phenotype of the child and the disease phenotypes of the parents, in the presence of some genotypic information about the parents. This coefficient of partial association is derived, and certain tests of hypotheses are constructed. The results are shown to be useful in estimation of recurrence risks, and in understanding the nature of the association between child and parental disease phenotypes.