A new test for the extreme value distribution

In this paper a test statistic which is a modification of the W statistic for testing the goodness of fit for the two paremeter extreme value (smallest element) distribution is proposed. The test statistic Is obtained as the ratio of two linear estimates of the scale parameter. It Is shown that the suggested statistic is computationally simple and has good power properties. Percentage points of the statistic are obtained by performing Monte Carlo experiments. An example is given to illustrate the test procedure.     

Optimal testing in a three way anova model

We consider likelihood ratio, score and Wald tests for a three-way random effects ANOVA model. Competitor tests are compared using criteria such as small sample power, asymptotic relative efficiency, and convenient null distribution. The final choice is between a new test and two tests long used in practice.     

Elliptically contoured model and factorization of wllks1 A

In a series of papers, Kshirsagar (1964, 1971) and McHenry and Kshirsagar (1977), factorize Wilks' A into a number of factors and find the independent null multivariate beta densities of these factors. These factors are the likelihood ratio test criteria for testing the goodness of fit of certain assigned discriminant functions or canonical variables either in the space of independent or dependent variables. Essentially the factors of Wilks' A are the factors of certain multivariate beta distributed matrix or its determinant. The Bartlett decomposition of the underlying multivariate beta distribution into independent factors determines the distribution of these factors. The present paper generalizes Kshirsagar's (1971) normal theory to the elliptically contoured model, and shows that his results are null robust for the elliptically contoured model.     

Efficient estimators for the good family

We consider the problem of estimating the two parameters of the discrete Good distribution. We first show that the sufficient statistics for the parameters are the arithmetic and the geometric means. The maximum likelihood estimators (MLE's) of the parameters are obtained by solving numerically a system of equations involving the Lerch zeta function and the sufficient statistics. We find an expression for the asymptotic variance-covariance matrix of the MLE's, which can be evaluated numerically. We show that the probability mass function satisfies a simple recurrence equation linear in the two parameters, and propose the quadratic distance estimator (QDE) which can be computed with an ineratively reweighted least-squares algorithm. the QDE is easy to calculate and admits a simple expression for its asymptotic variance-covariance matrix. We compute this matrix for the MLE's and the QDE for various values of the parameters and see that the QDE has very high asymptotic efficiency. Finally, we present a numerical example.     

Posterior analysis,prediction and reliability in three-parameter weibull distributions

The paper develops Bayesian analysis in the context of samples from three-parameter Weibull distributions and shows how to tackle the problems of prediction and estimation of reliability curves. As Johnson, Kotz and Balakrishnan ( 1994 ) mentioned, the prediction problems for the three-parameter Weibull model seem to be unresolved and is certainly worth looking into (p.671). Posterior analysis organized around Gibbs sampling is shown to perform well. An application to stock returns is used to illustrate the potential of the approach.     

General location transform of the order statistics from the exponential,pareto and weibull,with application to maximum likelihood estimation

Based one some common distribution properties of the order statistics and the transformation theory by Efron(1982), we determine unified explicit general location transformations, which map the distributions of the order statistics from the Exponential, Pareto and Weibull to a standard normal distribution. This result is used to derive analytical formulas for the maximum likelihood estimators of the shape parameter of these distributions of order statistics. The presented exact method is applied to catastrophe earthquake life reinsurance.     

A model with long-term survivors: negative binomial Birnbaum-Saunders

Abstract

We propose a cure rate survival model by assuming that the number of competing causes of the event of interest follows the negative binomial distribution and the time to the event of interest has the Birnbaum-Saunders distribution. Further, the new model includes as special cases some well-known cure rate models published recently. We consider a frequentist analysis for parameter estimation of the negative binomial Birnbaum-Saunders model with cure rate. Then, we derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We illustrate the usefulness of the proposed model in the analysis of a real data set from the medical area.     

Some estimation procedures using a linear model in successive sampling

ABSTRACT

In successive sampling some recent works depict the use of super-population models where information on stable auxiliary variable over occasions has been utilized. Stability character of auxiliary variable may not sustain, if the duration between occasions is large. To cope with such situations, the present work is an attempt to develop some estimation procedures by utilizing the information on two independent auxiliary variables through a linear super-population model. Some estimators are proposed to estimate the current population mean in two occasions successive (rotation) sampling. Optimum replacement strategies are formulated and performances of the proposed estimators have been discussed. Results are interpreted through empirical studies.     

The Poisson-conjugate Lindley mixture distribution

ABSTRACT

A new discrete distribution that depends on two parameters is introduced in this article. From this new distribution the geometric distribution is obtained as a special case. After analyzing some of its properties such as moments and unimodality, recurrences for the probability mass function and differential equations for its probability generating function are derived. In addition to this, parameters are estimated by maximum likelihood estimation numerically maximizing the log-likelihood function. Expected frequencies are calculated for different sets of data to prove the versatility of this discrete model.     

A proportional hazards model for the analysis of doubly censored competing risks data

ABSTRACT

Competing risks data are common in medical research in which lifetime of individuals can be classified in terms of causes of failure. In survival or reliability studies, it is common that the patients (objects) are subjected to both left censoring and right censoring, which is refereed as double censoring. The analysis of doubly censored competing risks data in presence of covariates is the objective of this study. We propose a proportional hazards model for the analysis of doubly censored competing risks data, using the hazard rate functions of Gray (1988 Gray, R.J. (1988). A class of k-sample tests for comparing the cumulative incidence of a competing risk. Ann. Statist. 16:1141–1154.[Crossref], [Web of Science ®] , [Google Scholar]), while focusing upon one major cause of failure. We derive estimators for regression parameter vector and cumulative baseline cause specific hazard rate function. Asymptotic properties of the estimators are discussed. A simulation study is conducted to assess the finite sample behavior of the proposed estimators. We illustrate the method using a real life doubly censored competing risks data.