Showing papers in "Calcutta Statistical Association Bulletin in 2010"
TL;DR: In this paper, the definition of geometric vitality function is extended to the bivariate set up and the problem of characterizing some bivariate models using the functional form of the geometric vitality functions is investigated.
Abstract: AbtsrcatIn the present work we extends the definition of geometric vitality function, considered by Nair and Rajesh (2000) to the bivariate set up. We also look into the problem of characterizing some bivariate models using the functional form of the bivariate geometric vitality function.
13 citations
TL;DR: In this paper, Bayes estimators of trafic intensity and other measures of effectiveness are worked out under squared error loss function (SELF) and entropy loss function with Beta distribution as prior.
Abstract: AbtsrcatIn this paper, Bayes estimators of trafic intensity (ρ) and other measures of effectiveness are worked out under squared error loss function (SELF) and entropy loss function (ELF) with Beta distribution as prior. Number of customers present in each of n iid M/M/1 queueing systems are considered as data. A comprehensive simulation study has been carried out in the last section.
11 citations
TL;DR: In this article, the mean vector θ of a p-variate elliptically contoured distribution, Ep(θ,Σ,f) based on the sample Y1Y2,...,YN of size n of size N of size B, was estimated for a p× r known matrix B, where the hypothesis θ = Bη, η∈ Rr may hold.
Abstract: Abtsrcat This paper deals with the estimation of the mean vector θ of a p-variate elliptically contoured distribution, Ep(θ,Σ,f) based on the sample Y1Y2,...,YN of size N of size N when it is suspected that for a p× r known matrix B, the hypothesis θ = Bη, η∈ Rr may hold. We consider the following estimators, (i) the unrestricted estimator (UE), (ii) the restricted estimator (RE), (iii) the preliminary test estimator (PTE), (iv) the James—Stein estimator (JSE), and (v) the positive-rule Stein estimator (PRSE). The bias and the risk expressions under the squared loss function are obtained for the five estimators and compared. It is noted that the dominance properties of these estimators remain the same as under normal theory. Further, it is shown that the shrinkage factor of the Stein-type estimators is robust with respect to the mean and unknown mixing distributions.
6 citations
TL;DR: In this article, the authors deal with the approximation of distribution functions of complicated statistics using Beta distribution, and two methods are suggested to estimate the parameters of the Beta distribution and their error analysis is given.
Abstract: AbtsrcatThis paper deals with the approximation of distribution func- tions of complicated statistics using Beta distribution. The problem is motivated and the performance of our method is evaluated by several examples. Two methods are suggested to estimate the parameters of Beta distribution. We approximate distributions of cusum statistic and Hsu's G test statistic by this method. Error analysis is given. Fitting the mixture of Beta distributions are examined. Finally, a discussion Section is given.
6 citations
TL;DR: In this paper, the best linear unbiased estimators (BLUEs) for the location and scale parameters of the uniform distribution are derived using k-record values, and the eciency of BLUEs relative to maximum likelihood estimators is also determined.
Abstract: AbtsrcatThere are many situations where experimental outcomes are a sequence of record-breaking observations. In this paper, an extension of record models, well known as k-records, is considered. The best linear unbiased estimators (BLUEs) for the location and scale parameters of the uniform distribution are derived using k-record values. In addition, best linear invariant estimators of two parameter uniform distribution are obtained on the basis of k-record values. We have also determined the e�ciency of BLUEs relative to maximum likelihood estimators (adjusted for bias). The best linear unbiased predictor of future k-record values is also determined.
5 citations
TL;DR: In this article, simple expressions for single and product moments of lower generalized order statistics from power function distribution have been obtained, and some important deductions and computational works are carried out for dual GOS.
Abstract: AbtsrcatOrder statistics, record values and several other model of ordered random variables can be viewed as special case of generalized order statistics (gos) [Kamps, 1995]. Pawlas and Szynal (2001) introduced the con-cept of lower generalized order statistics (lgos) to enable a common approach to descending ordered rv's like reversed order statistics and lower record values. The work of Burkschat et al. (2003) may also be seen for dual (lower) generalized order statistics. In this paper simple expressions for single and product moments of lower generalized order statistics from power function distribution have been obtained. Further, some important deductions and computational works are carried out.
5 citations
TL;DR: In this paper, the authors apply ranked set sampling and its modi-fied version called Extreme Ranked Set Sampling (ESS) to estimate the parameters of the Morgenstern type bivariate logistic distribution (MTBLD).
Abstract: AbtsrcatIn this work we apply ranked set sampling and its modi-fied version called extreme ranked set sampling to estimate the parameters of Morgenstern type bivariate logistic distribution (MTBLD)...
5 citations
TL;DR: Bayesian approaches for modeling overdispersed Poisson data in the context of regression problem in presence of missing data are developed.
Abstract: AbtsrcatIn this paper, we consider the diurnal (day time) activities of peracarisdis in Baltic sea. The peracaridis is a large group of malacostracan crustaceans, having members in marine, freshwater, and terrestrial habitats. They are defined by the possession of a single pair of maxillipeds (rarely 2-3), of mandibles with an articulated accessory process between the molar and incisor teeth in the adults (called the lacinia mobilis), and of a carapace which is often reduced in size and is not fused with the posterior thoracic somites. The experimental data is given in Janson and Kallander (1968). In this study, the animals are caught by sweeping a net over a known distance and fixed time intervals. The total number of caught along with various covariates are recoded. The data is missing some responses and some covariates. In view of that we develop Bayesian approaches for modeling overdispersed Poisson data in the context of regression problem in presence of missing data. We handle the missing data probl...
3 citations
TL;DR: In this article, the authors investigated the spread of H1N1 in Pune, India and investigated the role of temperature and humidity in spreading the disease, and the efficacy of the government strategy in arresting the further growth of the disease in the city.
Abstract: AbtsrcatWe consider data on the daily numbers of Swine flu (H1N1) cases during July 15, 2009 to October 9, 2009 in Pune, India. Fearing a major epidemic, the government closed educational institutes, malls and theaters for the period August 17, 2009 to August 23, 2009. We investigate the rate of spread of disease, efficacy of the government strategy in arresting the further growth of the disease in the city and the role of temperature and humidity in the spread of the disease.
3 citations
TL;DR: In this paper, the correlation between the pooled sample mean and certain linear functions of order statistics of independent non-identically distributed random variables is obtained for pooled sample from pop- ulations with common location parameter μ and common scale parameter σ.
Abstract: AbtsrcatIn this paper the correlation between the pooled sample mean and certain linear functions of order statistics of independent non-identically distributed(inid) random variables are obtained for pooled sample from pop- ulations with common location parameter μ and common scale parameter σ and the results if the parent distributions are symmetric about the common location parameter μ are derived therefrom.
1 citations
TL;DR: In this article, a set of test statistics for all perennial notions of aging are given for testing exponentiality against either the class of increasing failure rate (IFR) or the class that is better than used in expectation (NBUE) life distributions.
Abstract: AbtsrcatIn this investigation, classes of test statistics are given for testing exponentiality against either the class of increasing failure rate (IFR) or the class of new is better than used in expectation (NBUE) life distributions. Our development complete the set of classes of test statistics for all perennial notions of aging. The major advantage of having a class of test statistics for any testing situation is that we can choose the member of that class that enjoys the highest power or efficiency for an alternative at hand and work with it, cf Klar (2000).
TL;DR: In this paper, the authors developed a model to determine an optimal ordering policy for deteriorating items under permissible delay of payment and allowable shortage for future supply uncertainty by suppliers using Spectral theory.
Abstract: Abtsrcat This paper develops a model to determine an optimal ordering policy for deteriorating items under permissible delay of payment and allowable shortage for future supply uncertainty by suppliers. Spectral theory is used to derive explicit expression for the transition probabilities of a four state continuous time markov chain representing the state of the system. These probabilities are used to compute the average cost. Optimal solution is obtained using Newton Raphson method in R programming.
TL;DR: In this article, a parametric regression model using Hankin and Lee distribution is introduced and the properties of the model are studied using maximum likelihood method. And the proposed model is applied to a real life data.
Abstract: Abtsrcat In this paper, we introduce a parametric regression model using Hankin and Lee distribution. The properties of the models are studied. We estimate the parameters of the model using maximum likelihood method. Asymptotic properties of the estimators are discussed. Finally, we apply the proposed model to a real life data.
TL;DR: In this paper, the authors derived regression planes using three variables including observed measuremental errors in all the variables and found that in most situations the variances of the regression coefficients are reduced by inclusion of measuremental error.
Abstract: AbtsrcatRegression planes using three variables have been derived including observed measuremental errors in all the variables. It is found that in most situations the variances of the regression coefficients are reduced by inclusion of measuremental errors. To get rid of the confusion of dependent and independent variables a symmetric regression plane is also suggested as a representative one, though the choice is never unique in case of three variables. The model is tested in case of fundamental planes (FP) for some early type galaxies.
TL;DR: In this paper, the authors consider the case when the errors have non-identical Gumbel distributions and derive explicit expressions for distributional properties of the resulting model, consider estimation issues and illustrate an application to some real data.
Abstract: AbtsrcatThe common assumption with binary choice models is that the errors arise from identical Gumbel distributions. This gives rise to the well known logistic model. In this note, we consider the case when the errors have non—identical Gumbel distributions. We derive explicit expressions for distributional properties of the resulting model, consider estimation issues and illustrate an application to some real data.