On a preliminary test estimator for one of the parameters of the log-zero-poisson distribution

A discrete distribution called the log-zero-Poisson distribution has been recommended by Katti (c.f. Biometrics 1970) as an alternate to the negative binomial and other distributions usually called "contagious" distributions.A major problem in the use of this and all other contagious distributions has been the difficulty of obtaining the maximum likelihood esti-mates. A custom-made ad hoc estimator, λ, has been proposed for the parameter λ of this distribution in Katti and Khedr (1980). In this paper, its efficiency relative to Fisher information is studied, only to discover that λ can be 30 times better than the maximum likelihood estimate in some parts of the parameter space and much weaker in other parts.A preliminary test is recommended to choose between the estimates, and the efficiency of the procedure is tabulated. As it is to be expected, the resultant estimator equals the better of the two estimators with some error at the values of the parameters where the two estimators are equivalent.     

Computation of finite population parameters and approximate probability values for multi-response randomized block permutation procedures (mrbp)

An algorithm is presented for computing the finite population parameters and the approximate probability values associated with a recently-developed class of statistical inference techniques termed multi-response randomized block permutation procedures (MRBP).     

Small sample study on estimators of life distributions and of mean survival times using randomly censored data

Whereas large-sample properties of the estimators of survival distributions using censored data have been studied by many authors, exact results for small samples have been difficult to obtain. In this paper we obtain the exact expression for the ath moment (a > 0) of the Bayes estimator of survival distribution using the censored data under proportional hazard model. Using the exact expression we compute the exact mean, variance and MSE of the Bayes estimator. Also two estimators ofthe mean survival time based on the Kaplan-Meier estimator and the Bayes estimator are compared for small samples under proportional hazards.     

A multiparameter extension of two stage modified shrinkage estimator

A multiparameter extension is made to modified two stage shrinkage estimator proposed by Handa andKambo (1990), For aparticular class of shrinkage estimator, the local optimality of the extended modified estimator is shown over the two stage shrinkage estimator defined by Bhattacharya and Prakasa Rao(1990) in terms of quadratic loss.     

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.     

Robust williams trent test

To investigate the biological activities of a new compound or drug, experimenters usually compare a series of increasing doses to a control. Among other objectives, one may try to investigate any possible dose-response trend and to determine the minimum effective dose among all the experimental doses. Williams (1971, 1972) proposed a procedure to test the dose-response trend and also to identify the minimum effective dose based on the normally distributed data. In this paper, we propose a similar test procedure based on the robust estimate'of the average response to perform similar analysis. The proposed method is more resistant to the outliers and more powerful than the Williams procedure when the data distribution deviates from normality. We illustrate the use of this procedure with data arising from a recent study.     

Testing non-nested log-linear models with pseudo estimator

As the number of random variables for the categorical data increases, the possible number of log-linear models which can be fitted to the data increases rapidly, so that various model selection methods are developed. However, we often found that some models chosen by different selection criteria do not coincide. In this paper, we propose a comparison method to test the final models which are non-nested. The statistic of Cox (1961, 1962) is applied to log-linear models for testing non-nested models, and the Kullback-Leibler measure of closeness (Pesaran 1987) is explored. In log-linear models, pseudo estimators for the expectation and the variance of Cox's statistic are not only derived but also shown to be consistent estimators.     

Reliability estimation based on ranked set sampling

In this paper we consider the problem of estimating the reliability of an exponential component based on a Ranked Set Sample (RSS) of size n. Given the first r observations of that sample, 1≤r≤n, we construct an unbiased estimator for this reliability and we show that these n unbiased estimators are the only ones in a certain class of estimators. The variances of some of these estimators are compared. By viewing the observations of the RSS of size n as the lifetimes of n independent k-out-of-n systems, 1≤k≤n, we are able to utilize known properties of these systems in conjunction with the powerful tools of majorization and Schur functions to derive our results.     

Estimation of parameters of a pareto distribution by generalized order statistics

In this paper we address the problem of estimating the parameters of Pareto II distribution based on generalized order statistics. The estimators based on order statistics and record values are shown to be special cases of these estimators.