Inference on a progressive type I interval-censored truncated normal distribution

In this paper, we consider the problem of making statistical inference for a truncated normal distribution under progressive type I interval censoring. We obtain maximum likelihood estimators of unknown parameters using the expectation-maximization algorithm and in sequel, we also compute corresponding midpoint estimates of parameters. Estimation based on the probability plot method is also considered. Asymptotic confidence intervals of unknown parameters are constructed based on the observed Fisher information matrix. We obtain Bayes estimators of parameters with respect to informative and non-informative prior distributions under squared error and linex loss functions. We compute these estimates using the importance sampling procedure. The highest posterior density intervals of unknown parameters are constructed as well. We present a Monte Carlo simulation study to compare the performance of proposed point and interval estimators. Analysis of a real data set is also performed for illustration purposes. Finally, inspection times and optimal censoring plans based on the expected Fisher information matrix are discussed.     

Double and group acceptance sampling plan for truncated life test based on inverse log-logistic distribution

This paper introduces a double and group acceptance sampling plans based on time truncated lifetimes when the lifetime of an item follows the inverse log-logistic (ILL) distribution with known shape parameter. The operating characteristic function and average sample number (ASN) values of the double acceptance sampling inspection plan are provided. The values of the minimum number of groups and operating characteristic function for various quality levels are obtained for a group acceptance sampling inspection plan. A comparative study between single acceptance sampling inspection plan and double acceptance sampling inspection plan is carried out in terms of sample size. One simulated example and four real-life examples are discussed to show the applicability of the proposed double and group acceptance sampling inspection plans for ILL distributed quality parameters.     

A two phases queueing system with Bernoulli vacation schedule under multiple vacation policy

This paper deals with a single server Poisson arrival queue with two phases of heterogeneous service along with a Bernoulli schedule vacation model, where after two successive phases service the server either goes for a vacation with probability p (0≤p≤1) or may continue to serve the next unit, if any, with probability q(=1−p). Further the concept of multiple vacation policy is also introduced here. We obtained the queue size distributions at a departure epoch and at a random epoch, Laplace Stieltjes Transform of the waiting time distribution and busy period distribution along with some mean performance measures. Finally we discuss some statistical inference related issues.     

Estimation of mean using double sampling for stratification and multivariate auxiliary information

Several estimators for estimating the mean of a principal variable are proposed based on double sampling for stratification (DSS) and multivariate auxiliary information. The general properties of the proposed estimators are studied, search for optimum estimators is made and the proposed estimators are compared with the corresponding estimators based on unstratified double sampling (USDS).     

Combined sample scores versus two-sample scores under censoring

For testing the equality of K-populations against ordered alternatives a quadratic form based on two-sample scores of (K-l) pairs of adjacent samples has been suggested as an alternative to the statistic proposed by Beslow(1970). The Pitman asymptotic efficiency of the proposed statistic relative to the Breslow's statistic is found to be one or very close to one in all cases considered. The Bahadur asymptotic efficiency has also been studied and found to be at least one for the situations taken up in this paper.     

Inference on unknown parameters of a Burr distribution under hybrid censoring

Based on hybrid censored data, the problem of making statistical inference on parameters of a two parameter Burr Type XII distribution is taken up. The maximum likelihood estimates are developed for the unknown parameters using the EM algorithm. Fisher information matrix is obtained by applying missing value principle and is further utilized for constructing the approximate confidence intervals. Some Bayes estimates and the corresponding highest posterior density intervals of the unknown parameters are also obtained. Lindley’s approximation method and a Markov Chain Monte Carlo (MCMC) technique have been applied to evaluate these Bayes estimates. Further, MCMC samples are utilized to construct the highest posterior density intervals as well. A numerical comparison is made between proposed estimates in terms of their mean square error values and comments are given. Finally, two data sets are analyzed using proposed methods.     

A REGRESSION- TYPE ESTIMATOR IN SAMPLING WITH PPS AND WITH REPLACEMENT

A regression-type estimator is proposed for the population total of a character y , when sample-units are selected with probability proportional to some measure of size z (pps) and with replacement; and the information on yet another variate x is used. The proposed estimator is shown to be superior to the well-known estimator (pps with replacement), and the ratio estimator (pps with replacement). It is also shown to be superior to the simple random estimator under some general conditions.     

A unified approach to estimating parameters in some generalized poission distributions

A family of distributions labelled as Poisson v Katz is formulated, which includes, as particular or limiting cases, the Negative Binomial, Neyman Type A, Poisson v Pascal, and Poisson v Binomial. Thus, while analyzing data, estimating the parameters in the Poisson v Katz family obviates the necessity of having to choose from among the particular or limiting cases. In this article minimum chi-square estimators are presented and their asymptotic relative efficiency obtained. An example is presented to illustrate the procedure     

Improved estimation of a finite population mean based on paired observations

This paper considers an improvement of the customary estimator of a finite population mean under a single stage sampling design when paired data, are available on each unit of the sample. Guided by the well known problem of “corninon mean”, a mixture i.e. a weighted combination of the mean of the principal characteristic and that of the auxiliary (possibly transformed) characteristic is proposed. It is shown that, under some conditions, improveinent (with respect to MSE) over the traditional estimator is possible for a broad range of the values of the mixing constant. An estimator of the MSE of the proposed estimator is also provided.     

Inflated modified power series distributions with applications

In certain applications involving discrete data, it is sometimes found that X = 0 is observed with a frequency significantly higher than predicted by the assumed model. Zero inflated Poisson, binomial and negative binomial models have been employed in some clinical trials and in some regression analysis problems.

In this paper, we study the zero inflated modified power series distributions (IMPSD) which include among others the generalized Poisson and the generalized negative binomial distributions and hence the Poisson, binomial and negative binomial distributions. The structural properties along with the distribution of the sum of independent IMPSD variables are studied. The maximum likelihood estimation of the parameters of the model is examined and the variance-covariance matrix of the estimators is obtained. Finally, examples are presented for the generalized Poisson distribution to illustrate the results.