Showing papers in "Calcutta Statistical Association Bulletin in 2005"
TL;DR: In this paper, the authors studied the properties of finite mixture of Pareto distributions, which arise as models of income and wealth in many practical problems, and they showed that finite mixtures of probability distributions arise as a model of wealth and income.
Abstract: Finite mixtures of probability distributions arise as models of income and wealth in many practical problems. In the present paper, we study the properties of finite mixture of Pareto distributions...
14 citations
TL;DR: In this article, the authors consider the dependence nature of the bivariate weighted models using the local dependence function introduced by Holland and Wang (1987) and examine its relationship in the context of reliability modelling.
Abstract: In this paper we consider the weighted conditional models and bivariate weighted models using different weight functions and examine its relationships in the context of reliability modelling. We also study the dependence nature of the bivariate weighted models using the local dependence function introduced by Holland and Wang (1987).
10 citations
TL;DR: In this article, the authors have made an attempt to define different classes of distributions and study their implicative relationships, and a probability bound has also been proposed for the increasing RHR class of distributions.
Abstract: SummaryGrowing importance of reversed hazard rate (RHR) and inactivity time, as measures of the life distributions, can be noticed from the recent literature on survival and reliability analysis. Keeping in mind tilis special role of RHR and the mean inactivity time, we have made an attempt to define different classes of distributions and study their implicative relationships. A probability bound has also been proposed for the increasing RHR class of distributions.
6 citations
TL;DR: In this paper, the estimation and testing of P(Y < X) when X and Y follow independent generalized uniform distributions with known shape parameters is considered, and it is shown that the distribution can be approximated by a generalized uniform distribution with known parameters.
Abstract: The paper considers estimation and testing of P(Y < X), when X and Y follow independent generalized uniform distributions with known shape parameters .
4 citations
TL;DR: In this paper, the authors consider a purchase inventory problem where both demand and supply have been taken to be random and consider several possible ways of deriving the optimum order quantity based on the distribution of total cost.
Abstract: We consider a purchase inventory problem where both demand and supply have been taken to be random. Several possible ways of deriving the optimum order quantity based on the distribution of total cost have been proposed. Expressions for the optimum order quantity that minimizes the mode or exceedance probability of this distribution have been worked out for some particular demand and supply distributions.
4 citations
TL;DR: In this paper, the Laplace-Beltrami operator on Riemannian manifolds is combined with Bayesian methods along with aspects of spectral geometry associated with the LBP operator.
Abstract: SummaryThis paper develops Bayesian function estimation on compact Riemannian manifolds. The approach is to combine Bayesian methods along with aspects of spectral geometry associated with the Laplace-Beltrami operator on Riemannian manifolds. Although frequentist nonparametric function estimation in Euclidean space abound, to date, no attempt has been made with respect to Bayesian function estimation on a general Riemannian manifold. The Bayesian approach to function estimation is very natural for manifolds because one can elicit very specific prior information on the possible symmetries in question . One can then establish Bayes estimators that possess built in symmetries. A detailed analysis for the 2–sphere is provided.
3 citations
TL;DR: In this article, an extended version of the LOMP is proposed to tie together the exponential and the Lomax distributions through characterization, and a stochastic version of this extended property with unique determination of the same life distributions.
Abstract: SummaryIn the reliability analysis the lack of memory property plays a pivotal role in conceptualizing some life distribution classes and in unique determination of the exponential distribution. On the other hand quite a few results like constancy of the coefficient of variation of the residual life, linearity of the mean residual life characterize the exponential distribution along with the Lomax distribution. Question that arises is - can there be an extended version of the lack of memory property to tie together the exponential and the Lomax distributions through characterization. The present paper presents an affirmative claim and extends the lack of memory property based on standardization technique. It also presents a stochastic version of this extended property with unique determination of the same life distributions. Attempts have also been made to define this extended lack of memory property in the bivariate set up and indicate the bivariate distributions that satisfy the same.
3 citations
TL;DR: In this paper, the authors give necessary and sufficient conditions for a repeated measurements design to be universally optimal for residual effects under the standard model and using an approximate design theory approach, and give examples of optimal designs which can be obtained from these conditions, together with new ones.
Abstract: SummaryUnder the standard model and using an approximate design theory approach, we give necessary and sufficient conditions for a repeated measurements design to be universally optimal for residual effects. In exact design theory, it is shown that symmetric optimal designs can be derived from a single linear equation. Examples of optimal designs, which can be obtained from these conditions, are given. Many of the existing optimal designs, together with new ones, can be obtained by this method. Bounds are given for computing the efficiencies of designs for estimating residual effects.
2 citations
TL;DR: In this paper, the bivariate Burr system of distributions is introduced, which generalizes the differential equation in the univariate case to the case of distributions in the Bivariate case.
Abstract: In the present paper we introduce the bivariate Burr system of distributions by generalizing the differential equation in the univariate case.
2 citations
TL;DR: In this paper, the problem of classification with multiple q-variate observations with time effect on each individual was studied, and the covariance matrices as well as mean vectors were mordelled respectively to accommodate the correlation between the successive repeated measures and to describe the time effects.
Abstract: In repeated measures studies how observations change over time is often of prime interest. Modelling this time effect in the context of discrimination, is the objective of this article. We study the problem of classification with multiple q-variate observations with time effect on each individual. The covariance matrices as well as mean vectors are mordelled respectively to accommodate the correlation between the successive repeated measures and to describe the time effects. Computation schemes for maximum likelihood estimation of required population parameters are provided.
2 citations
TL;DR: In this article, Latent class analysis was used to identify important subgroups of females and males based on clustering simultaneously on several categorical variables, such as desired work activities, job search resources, and adequacy of doctoral training.
Abstract: Summary The field of Information Technology (IT) has provided extraordinary job growth in the United States over the last two decades; however, women and some minority groups are severely underrepresented in IT occupations, especially in management positions. These groups also on average receive lower salaries than their counterparts. The U.S. National Science Foundation's SESTAT database is created from biennial nationally representative surveys of U.S. scientists and engineers. SESTAT provides detailed information, such as employment history, educational background, and demographic characteristics. These data are analyzed here using latent class analysis, which is an exploratory technique that can be used to cluster cases based on categorical variables. The data are from the 1997 Survey of Doctoral Recipients. The subset of respondents received Ph.D.'s between 1990 and 1996 in either than physical or biological sciences or in engineering and work at higher educational institutions. There are a few significant differences between men and women in desired work activities, job search resources, and adequacy of doctoral training. There are many large, significant differences in limitations when searching for a job, work activities, and family and career status. Latent class analysis helped identify important subgroups of females and males based on clustering simultaneously on several categorical variables.
TL;DR: In this article, a shrinkage preliminary test estimator (SPTE) of the coefficient vector in the multiple linear regression model based on the size corrected Wald (W), likelihood ratio (LR) and Lagrangian multiplier (LM) tests was proposed.
Abstract: In this paper we propose shrinkage preliminary test estimator (SPTE) of the coefficient vector in the multiple linear regression model based on the size corrected Wald (W), likelihood ratio (LR) and Lagrangian multiplier (LM) tests. The correction factors used are those obt,ained from degrees of freedom corrections to the estimate of the error variance and those obtained from the secondorder Edgeworth approximations to the exact distributions of the test statistics. The bias and weighted mean squared error (WMSE) fun ctions of the estimators are derived. With respect to WMSE, the relative efficiencies of the SPTEs relative to the maximum likelihood estimator are calculated. This study shows that the amount of conflict can be substantial when the three t ests are based on the same asymptotic chisquare critical value. The conflict among the SPTEs is due to the asymptotic tests not having the correct significance level. The Edgeworth size corrected W, LR and LM tests reduce the conflict remarkably.
TL;DR: This paper focuses on the application of multivariate statical techniques for making a cost effective decision in an industrial set up and an optimum classification rule has been established for making the decision.
Abstract: This paper focuses on the application of multivariate statical techniques for making a cost effective decision in an industrial set up. The objective of this study is to take a decision with respect to several parameters whether a particular product can be sent to the customer or not. The techniques like MANOVA, discriminant and classification function analysis have been used to fulfil the objectives. An optimum classification rule has been established for making the decision. A cost benefit analysis has also been done after iniplementing the proposed optimum decisionmaking rule.
TL;DR: In this paper, convergence properties of deterministic Robbins-Monro recursion with singularities and multiple zeros are established for the output of a deterministic deterministic RMC.
Abstract: SummaryConvergence properties are established for the output of a deterministic Robbins- Monro recursion whose function can have singularities and multiple zeros. Our analysis is built largely on s...
TL;DR: A comparative analysis of three voxel-based methods for characterization of spatial-temporal patterns provided by PET images of cerebral blood flow using data from sequential H 2 15 O PET studies in baboons to examine whether amphetamine affects relative cerebralBlood flow differentially over time and over different regions of brain.
Abstract: SummaryFunctional brain images arc extraordinarily rich data sets that reflect brain function such as cerebral blood flow. These images are widely applied to study brain activity after drug administration or in response to perceptual and cognitive stimuli. Positron Emission Tomography (PET) constitutes one important modality that provides functional brain images. Spatial and temporal patterns in brain activities captured from these images have helped to better understand brain dysfunction in disease and aid in diagnosis and treatment of diseases including ncurogenerative disorders. As PET provides maps consisting of average levels of activity for cuboidal voxels of tissue, it is a substantial analytic challenge to integrate the temporal, spatial and statistical signals making up these data. This paper presents a comparative analysis of three voxel-based methods for characterization of spatial-temporal patterns provided by PET images of cerebral blood flow . The methods are: (i) statistical parametric mapp...
TL;DR: This article found that when a subject was asked to guess the length of an object such as a straight line or a ruler, one's answer routinely depended upon (i) presence or absence of landmarks or reference points, and (ii) what one had thought that was being shown rather than what the true item really was.
Abstract: SummaryAn eyewitness's description of a missing criminal, for example, is very crucial for apprehending the individual. But, some accounts may be unreliable if it turned out that the witness was ‘far away’ from a crime scene. Estimation of the perception of “distance” can be an important input in many situations including this one.We ran a number of designed experiments, collected data, and analyzed them in order to understand how individuals perceived “distance”. These experiments and associated data analyses have some clear messages: When a subject was asked to guess the length of an object such as a straight line or a ruler, we found time and again that one's answer routinely depended upon (i) presence or absence of landmarks or reference points, and (ii) what one had thought that was being shown rather than what the true item really was. More investigations in experimental psychology are deemed essential in one's thorough understauding of human perception of “distance”.
TL;DR: A technique based on two-parameter data perturbation is developed for sample moment matching in kernel density estimation and it is shown that the moments calculated from the resulting tuned kernel density estimate can be made arbitrarily close to the raw sample moments.
Abstract: SummaryThe fundamental idea of kernel smoothing technique can be recognized as one-parameter data perturbation with a smooth density. The usual kernel density estimates might not match arbitrary sample moments calculated from the unsmoothed data. A technique based on two-parameter data perturbation is developed for sample moment matching in kernel density estimation. It is shown that the moments calculated from the resulting tuned kernel density estimate can be made arbitrarily close to the raw sample moments. Moreover, the pointwise rate of MISE of the resulting density estimates remains optimal. Relevant simulation studies are carried out to demonstrate the usefulness and other features of this technique.
TL;DR: In this article, several distributional properties of the upper weak record from geometric distribution are presented, based on which some characterizations of the geometric distribution is given, and some distributions of upper weak records from geometric distributions are given.
Abstract: SummaryUpper weak record values from a sequence of independent identically distributed random variables are considered. Several distributional properties of the upper weak records from geometric distribution are presented. Based on these distributional properties some characterizations of the geometric distribution are given.
TL;DR: In this paper, a bivariate version of the randomized play the winner (RPvV) rule is proposed, and various properties of the rule through asymptotics and simulations are studied.
Abstract: In the present work , we frame an adaptive allocation rule in matching pairs of experimental units. The proposed rule is a bivariate version of the randomized play the winner (RPvV) rule. We study various properties of the rule through asymptotics and simulations. Related inferential problem is also considered.
TL;DR: In this article, the Latin square type association scheme has been generalized and on the basis of this association scheme, a class of designs having orthogonal factorial structure and partial bala...
Abstract: SummaryIn this paper Latin Square type association scheme has been generalized and on the basis of this association scheme, a class of designs having orthogonal factorial structure and partial bala...
TL;DR: In this article, a unit is classified into one of two correlated homoscedastic normal populations by W classification statistic, where observations made on the same unit in the two populations are correlated.
Abstract: SummaryA unit is to be classified into one of two correlated homoscedastic normal populations by W classification statistic. The two populations are like two different states of a disease. A sample unit can be observed in both the states (populations) . The observations made on the same unit in the two populations are correlated. W is based on an unmatched training sample where N sample units are observed in both the populations and Ni- N units are observed in population i, i = 1, 2. The exact density of W in such set up is derived for unknown means and common dispersion matrix where the correlation linking the populations is known or unknown. Simulated density of W is plotted and probability of correct classification (PCC) is evaluated using simulation.
TL;DR: Identification of the of crossreactive pollen allergens by using an empirical approach proposed in this paper may help the doctors in the allergy clinic to decide on the doses and number of pollen extracts to be used for immunotherapy in considerable savings of time and cost.
Abstract: Twenty airborne pollen grains and fungal spores prevalent in the air during February to June in and around Kolkata, India were found to have caused most of the allergy related respiratory illness among 100 atopic paients who visited the allergy clinic of the Institute of Child Health, Kolkata. They were subjected to the skin prick tests(SPT) using extracts from the allergens selected in accordance with the patient's history.Strongly crossreactive allergens are expected to show similar reactions with respect to wheal diameters when applied to a given patient. An exploratory data analysis of wheal diameters is proposed to discover the groups of cross reactive allergens.Cluster analysis of wheal diameters is carried out to identify the groups of cross reactive allergens. It is well known that the same data set may produce altogether different clusters if different clustering methods are applied or different measures of dissimilarities are used. As such the clusters produceed by a single method and a single ...
TL;DR: In this article, the authors provided a general method of constructing such arrays and their applications to obtain several asymmetric compound orthogonal arrays for mixed level dispersion experiments, which are universally optimal even if the model includes some more parameters.
Abstract: Summary Rosenbaum (1996) and Hedayat and Stufken (1999) considered the construction of compound orthogonal arrays for the two-level factors which are useful in the study of dispersion experiments, pioneered by Taguchi (1986). This paper provides a general method of constructing such arrays and their applications to obtain several asymmetric compound orthogonal arrays for mixed level dispersion experiments. Such arrays are also found to be universally optimal even if the model includes some more parameters.
TL;DR: In this article, some strategies for selecting a single minimally incompatible joint distribution are surveyed, where the marginals and conditionals of a bivariate distribution are shown to be incompatible.
Abstract: Summary Full or partial information about the marginals and conditionals of a bivariate distribution is likely to be incompatible. Additionally, information may come from heterogenous sources with limited agreement between sources. Some strategies for selecting a single “minimally incompatible” joint distribution are surveyed.
TL;DR: In this article, explicit algebraic expressions for computing the means, variances and covariances of the record values from a beta distribution were derived using a representation theorem due to Bairamov and Ahsanullah (2000).
Abstract: Explicit algebraic expressions are derived for computing the means, variances and the covariances of the record values from a beta distribution. The derivation uses a representation theorem due to Bairamov and Ahsanullah (2000) and a series expansion for the inverse function of the standard beta cdf. The results generalize those presented in Nadarajah and Ahsanullah (2004) for the arc-sine distribution.
TL;DR: In this paper, the authors compared Gaussian mixture transition distribution (GMTD) and mixture autoregressive (MAR) models by considering weekly wholesale onion price data during April, 1998 to November, 2001.
Abstract: Gaussian mixture transition distribution (GMTD) models and mixture autoregressive (MAR) models are generally employed to describe those data sets that depict sudden bursts, outliers and flat stretches at irregular time epochs. In this paper , these two approaches are compared by considering weekly wholesale onion price data during April, 1998 to November, 2001. After eliminating trend, seasonal fluctuations are studied by fitting BoxJenkins airline model to residual series. To this end, null hypothesis of presence of nonseasonal and seasonal stochastic trends is tested by using OsboruChuiSmithBirchenhall (OCSB) auxiliary regression. Subsequently, appropriate filters in airline model for seasonal fluctuations are selected. Presence of autoregressive co nditional heteroscedasticity (ARCH) is tested by Naive Lagrange multiplier (Nave LM) test. Estimation of parameters is carric~d out using ExpectationMaximization (EM) algorithm and the best model is selected on the basis of Bayesian information criterion (BIC). Outofsample forecasting is performed for onestep and twostep ahead prediction by uaive approach, proposed by Wong and Li (2000). It is concluded that, for data under consideration, a threecomponent MAR model performs the best.
TL;DR: In this paper, a global goodness of fit test for the general exponential family of distributions which may or may not contain overdispersion is proposed, which has asymptotically standard Gaussian distribution and is easy to implement.
Abstract: SummaryGeneralized linear models are used to analyze a wide variety of discrete and continuous data with possible overdispersion under the assumption that the data follow an exponential family of distributions. The violation of this assumption may have adverse effects on the statistical inferences. The existing goodness of fit tests for checking this assumption are valid only for a standard exponential family of distributions with no overdispersion. In this paper, we develop a global goodness of fit test for the general exponential family of distributions which may or may not contain overdispersion. The proposed statistic has asymptotically standard Gaussian distribution which should be easy to implement.
TL;DR: The study shows linear discriminant analysis and support vector machine perform better than other methods for this data set, at least from a predictive view point.
Abstract: Prostate cancer is one of the most common cancers in American men. Management of prostate cancer depends on its stage, because only cancers that are confined to the organ of origin are potentially curable by radical prostatectomy. In this article we have considered different statistical methods to predict the probabilities of nonorgan confined prostate cancer based on its clinical stage. Modern computer intensive methods such as bagging, neural networks and support vector machines are compared to more classical methods such as linear, quadratic and logistic discrimination and less computer intensive nonparametric methods such as smoothing splines and classification trees . All these methods are allied to a dataset from a recent prostate cancer study. We have presented sensitivity, specificity, positive predictive value, negative predictive value, and overall accuracy for each of the methods. The study shows linear discriminant analysis and support vector machine perform better than other methods for this...
TL;DR: In this paper, a new method for estimating multiplicative interactions between genetic and environmental factors on the risk of a dbease using projected score approach was proposed. But the method is not suitable for the case of lung cancer.
Abstract: The present article proposes a new method for estimating multiplicative interactions between genetic and environmental factor on the risk of a dbease using projected score approach (Waterman and Lindsay {1996a, b)). First we review the existing methods for determining geneenvironment interactions through casecontrol study and caseonly study design. Then we discuss the proposed method based on projection theory. We derive an unbiased estimating equation for estimating the parameter of interest and then derive its asymptotic standard error. In addition, we derive a score statistic based on the derived estimating equation. The advantage of using the proposed method are : 1. Gain in efficiency of the parameter estimate and 2. Robustness to the other model parameters and geneenvironment independence assumption. We apply the proposed method to a real casecontrol data on lung cancer. Finally, we compare the existing methods with the proposed method through a small simulation study which shows that the propo...
TL;DR: In this paper, it was shown that the waiting time for a stationary renewal process generated by a random variable has the form W = X+Y, with Y nonnegative independent of X if and only if X is a geometrically infinitely divisible random variable.
Abstract: It is shown that the waiting time W in a stationary renewal process generated by X has the form W = X+ Y, with Y nonnegative independent of X if and only if X is a geometrically infinitely divisible random variable. This is an improvement over Van Harn and Steutel (1995) where the converse is left unproved .