bluuebunny/crossref_metadata_2025 huggingface dataset:
Comparison of Statistical Classification Methods Based on a Prostate Cancer Study
Authors: Maiti Tapabrata , Mukhopadhyay Pushpal
Published: August 2016

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 data set, at least from a predictive view point .
Symmetry and Bayesian Function Estimation1
Authors: Angers Jean-Francois , Kim Peter T.
Published: August 2016

Summary

This 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.
Estimation of Residual Effects in Repeated Measurements Designs
Authors: Bose Mausumi , Shah K.R.
Published: August 2016

Summary

Under 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.
A Perturbation Technique for Sample Moment Matching in Kernel Density Estimation
Authors: Maity Arnab , Sengupta Debapriya
Published: August 2016

Summary

The 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.
Latent Class Analysis of 1997 NSF Survey Data on Science PHDs
Authors: Larsen Michael D.
Published: August 2016

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.
Stimulant-Induced Spatial Temporal Patterns in Pet Data : Illustrations Using SPM, Manacova-CVA and PLS
Authors: Xu Lei , Mazumdar Sati , Greer Philip J. , Price Julie
Published: August 2016

Summary

Functional 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 mapping (SPM) providing a voxel-wise brain map of a selected statistic; (ii) multivariate analysis of covariance jointly with canonical variate analysis (MANCOVA-CVA) identifying regions of the brain that are most responsible for global statistical significance; and (iii) partial least squares (PLS) that uses a path modeling technique with latent variables for dimension reduction. The methods are illustrated using data from sequential [Formula: see text] PET studies in baboons to examine whether amphetamine affects relative cerebral blood flow (rCBF) differentially over time and over different regions of brain. The results are found to be consistent across the three methods.
Classification of Distributions Based on Reversed Hazard Rate
Authors: Chandra Nimai Kumar , Roy Dilip
Published: August 2016

Summary

Growing 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.
A Global Test for the Goodness of Fit of Generalized Linear Models : An Estimating Equation Approach
Authors: Rao R. Prabhakar , Sutradhar B.C.
Published: August 2016

Summary

Generalized 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.
Parametric Modelling Of Genomic Sequences Distance
Authors: Pinheiro A. , Sen P. K. , Pinheiro H. P.
Published: August 2016

Genomic data models relate to a large number of positions exhibiting categorical responses, and larger part of that provides no statistical information . For this reason, a reduction in complexity attained by focusing on the functional part of sequences (genes) is helpful for an appraisal of the statistical intersite dependence. The problem of homogeneity among groups of genomic sequences incorporating the available (heuristic) evidence of diversity in categorical data models is considered here. The proposed fully operational parametric statistical model is fortified with flexibility to withstand use in several organisms and adaptability to intersite dependence. Properties of the proposed inference procedures are studied and an illustrative real data example is thoroughly explored.
On the Bayes Estimation of the General Half-Normal Distribution
Authors: Farsipour N. Sanjari , Rasouli Abbas
Published: August 2016

In this article we consider Bayes estimation of the general half-normal distribution. The general half-normal distribution is defined in Pewsey (2002). The parameters estimation on the basis of symmetric Squared-error and asymmetric LINEX loss function under conjugate priors have been obtained. The admissibility of estimators with respect to risk efficiency of them are studied.
On the Exact Distribution for the Product and Ratio of Normal and t Random Variables
Authors: Nadarajah Saralees , Kibria B. M. Golam
Published: August 2016

This paper considers the exact distributions of the product | XY | and the ratio | X/ Y | when X and Y are normal and Student's t random variables distributed independently of each other. Apart from its intrinsic interest possible applications of these results include Bayesian wavelet shrinkage, project density derivations, calculations in the theoretical analysis of project indices and computation of certain moments. Several R programs are given for computing the associated pdfs, cdfs, percentile points and the random numbers. The use of the R programs is illustrated by tabulating the associated percentage points.
Inference on Ratio of two Medians
Authors: Paranjpe S. A. , Gore A. P.
Published: August 2016

The problem of interest is confidence interval for ratio of two location parameters. The classical Fieller's theorem yields such a confidence interval for ratio of normal means. Resulting CI may sometimes be inadmissible. Also a median may be more appropriate location parameter if the parent distribution is skew. We explore the sampling distribution of ratio of two medians as an alternative to Fieller's theorem. Probability density function has been obtained for this statistic in case of Weibull parent populations. Use of this result to obtain confidence intervals becomes intractable for moderate sample sizes. A simulation based approach is therefore proposed. Results are applied to a study of two skin care products, based on dermatological assessment. Lastly we also explore the possibility of using the ‘proportional hazards’ approach for this purpose.
Cohen's Kappa Statistic: A Critical Appraisal and Some Modifications
Authors: Sinha Bikas K. , Yimprayoon Pornpis , Tiensuwan Montip
Published: August 2016

In this paper we consider the problem of assessing agreement between two raters while the ratings are given separately in 2 - point nominal scale and critically examine some features of Cohen's kappa statistic ( K C), widely and extensively used in this context. We point out some undesirahle features of K C and, in the process, propose two modified kappa statistics. Properties and features of these statistics are explained with illustrative examples.
Improving the Estimation of Eigenvectors Under Quadratic Loss
Authors: Ahmed S. E. , An L. , Nkurunziza S.
Published: August 2016

Improved estimation of eigenvectors of a covariance matrix is considered under uncertain prior information (UP!) regarding the parameter vector. Like statistical models underlying the statistical inferences to be made, the prior information will be susceptible to uncertainty and the practitioners may be reluctant to impose the additional information regarding parameters in the estimation process. A very large gain in precision may be achieved by judiciously exploiting the information about the parameters which in practice will be available in any realistic problem.

Several estimators based on preliminary test and the Stein-type shrinkage rules are constructed. The expressions for the bias and risk of the proposed estimators are derived and compared with the usual estimators. We demonstrate how the classical large sample theory of the conventional estimator can be extended to shrinkage and preliminary test estimators for the eigenvector of a covariance matrix. It is established that shrinkage estimators are asymptotically superior to the usual sample estimators. For illustration purposes, the method is applied to three data sets.
Study on R­Norm Residual Entropy
Authors: Nanda Asok K. , Das Samhita
Published: August 2016

In this paper a stochastic order and an aging property have been defined based on R-norm residual entropy, and their properties have been studied. A few useful parametric distributions have been characterized with the help of this entropy. A couple of results have been developed for discrete random variables.

AMS {2000} Subject Classification: 94AXX, 94A17.
A Natural Goodness­of­Fit Test for the Exponential Growth Curve Model Based on the Relative Growth Rate
Authors: Basu Ayanendranath , Bhattacharjee Amit
Published: August 2016

This paper develops a natural goodness-of-fit test for the exponential growth curve model (EGCM) based on the property of finite differences. The EGCM has wide applications in various scientific fields such as biology, ecology, demography, population dynamics, finance, econometrics etc. Hill (1968, Biometrics, 4, 192-196) proposed a test for the polynomial growth curve model (PGCM) based on finite differences of the size variable. However, the PGCM has limited practical use and does not have any biologically interpretable para.ffieters. In comparison, the exponential model is more realistic and biologically meaningful; a goodness-of-fit test for the EGCM has substantial practical value. Bhattacharya et. al. (2004) generalized Hill's approach to the case of the EGCM based on appropriate finite differences of functions of the size variable. In this paper we present an alternative test for the EGCM by directly modeling the relative growth rate (rather than the size variable itself) and hence avoid the assumptions necessary in Bhattacharya et al (2004). The performance of the theory developed is illustrated with several sets of real data and through simulation.

AMS {2000} Subject Classification: 62F03, 62P10.
Study on Diffusion of Rumours Through Epidemic Models Under Non Identical Set Up
Authors: Chattopadhyay Asis Kumar , Gupta Arindam
Published: August 2016

The spread of rumour can be modelled easily by using epidemic models because of the similarity in underlying processes. The present paper attempts to study diffusion of rumours through a simple epidemic model, taking into account two possible sources of rumour viz primary and secondary. Since the behavior of different persons involved under the process will be different and also the rate of spread will be time depe~dent the underlying variables will not be independent and identical. The process has been studied through simulation and the process average has been compared with the average obtained from an established theoretical result. The objective of the study is to predict the number of hearers at a particular time point by using the proposed model.

AMS {2000} Subject Classification: 62P25.
On Measurement of Export Instability: An Innovative Index
Authors: Chakrabarty Ranajit , Nath Swaraj Kumar
Published: August 2016

Instability in export performances may be caused by a variety of market forces both short-term and long-term. Fluctuations may be caused by upward or downward turn of export performances or may be due to their combined effect. When such fluctuations upset the export target, it may become a serious concern of the export-planners. But, unfortunately, the present methodologies fail to segregate the downward or negative pulling effect of export performance. The present paper aims at developing a quantitative tool for measuring exportinstability based on upward and downward turn of export performance and which is capable of quantifying instability on a year-to-year basis.

AMS {2000) Subject Classification : 91B82
Models Characterized by the Reversed Lack of Memory Property
Authors: Asha G. , John Rejeesh C.
Published: August 2016

Block et.al (1998) studied the properties of the reversed hazard rate (rhr) and characterized a class of distributions having constant rhr in its interval of support. In this paper we study another equivalent characterization of this class along with its bivariate extensions.
The Exponentiated Gamma Distribution with Application to Drought Data
Authors: Nadarajah Saralees , Gupta Arjun K.
Published: August 2016

Gamma distributions are some of the most popular models for hydrological processes. In this paper, a very flexible family which contains the gamma distrihution as a particular case is introduced. This distribution generalizes the standard gamma distribution in the same way the exponentiated exponential distribution (Gupta et al., 1998; Roy, 1998) generalizes the standard exponential distribution. We refer to this new distribution as the exponentiated gamma distribution. A comprehensive treatment of the math­ ematical properties is provided by deriving expressions for various particular cases and bounds, analytical shapes of the corresponding probability density function and the hazard rate function, moment generating function, the nth moment, skewness, kurtosis, mean deviation , Shannon entropy, and the asymptotic distribution of the extreme order statistics. Estimation procedure by the method of maximum likelihood and an expression for the Fisher information matrix are also provided. Finally, an application to drought data from the State of Nebraska is illustrated.
Step­Stress Accelerated Life Testing for Pareto Distribution with Type I Censoring
Authors: Rahman Md. Monsur , Dharmadhikari A. D.
Published: August 2016

This paper presents step­stress accelerated life test for the Pareto distribution with type I censoring. It is assumed that Pareto scale parameter depends on the stress variable and the shape parameter remains constant. It is also assumed that failures occur according to a cumulative exposure modcl(CEM) by Nelson (1990). On the basis of this model we describe maximum likelihood estimation proceuure and expression of the Fisher information matrix has been derived in closed form. A simulation study has been done to obtain the maximum likelihood estimates(MLE), Fisher information matrix and hence the variance­covariance matrix of the parameters. For selected values of the rlesign parameters the optimum low stress as well as the stress change time are obtained which minimize the asymptotic variance of the MLE of a stated percentile.
Statistics at Cross-Road : CSA Bulletin Perspectives and Prospectives
Authors: Sen Pranab Kumar
Published: August 2016

As we approach to bring out the 60th Volume of (CSA) Bulletin, we look back into our (modest) accomplishment, and look forward to our continuing progress, in a much wider and more challenging field, with our commitments and assessment of prospectives. The basic challenge comes from the ever-changing discipline, its integration into more interdisciplinary fields, its genuine dependence on rapidly faster computing facility along with diverse computational algorithms, and above all, the necessity to go beyond the so-called Neyman-Pearson paradigm in the 21st century. Even the Bayes perspectives have pointed out the limitations of conventional Bayes methods. These perspectives and prospectives are appraised thoroughly.
A Natural Goodness-of-Fit Testing Procedure for the Logistic Growth Curve Model
Authors: Chakraborty Bratati , Basu Ayanendranath
Published: August 2016

Growth curve models are frequently used in a wide range of disciplines such as biology, ecology, demography, population dynamics etc. Living organisms exhibit different types of growth patterns. To analyze these curves investigators need adequate parametric models. A proper identification of the growth model is very important for the appropriateness of the subsequent analysis. In this paper we develop a natural goodness of fit test for the logistic growth curve model. Bhattacharya et al. (2004, 2008) have provided some interesting approaches based on Hill's method of finite differences (Hill 1968) in case of the exponential and exponential polynomial growth curve models. But in case of the logistic model their approach leads to very complicated and cumbersome mathematics. Basu and Bhattacharj6ee (2006) have presented an alternative method to test the goodness of fit for the exponential growth curve model by directly modeling the relative growth rate rather than the size variable itself. In this paper we extend that approach for testing goodness of fit in case of the logistic growth curve model.
Convergence Rates of Two Sample U-Statistics in Non IID Case
Authors: Dasgupta Ratan
Published: August 2016

An estimate of the remainder of two sample U-statistics where each sample consists of independent observations, from its linear projection is obtained. A Berry-Esseen theorem with random index is established. A normal approximation zone for the tail probability of a standardized U-statistic is obtained. Application of this statistic to a real data set related to burr formation in production processes is investigated as a nonparametric tool, instead of a model based approach.
Adjusted Non-Linear Unbiased Estimation of the Location Parameter of a Symmetric Distribution
Authors: Thomas P. Yageen , Samuel Philip
Published: August 2016

In this paper we consider a location family of distributions which are symmetric about the location parameter μ and propose a nonlinear function of order statistics as an estimator of μ. We call this estimator as the adjusted non-linear unbiased estimator of μ. For the U-shaped distribution with location parameter μ, we have illustrated that our estimator is a competitor of [Formula: see text], the best linear unbiased estimator of μ based on order statistics. We have also identified the region of the parameter space in which the proposed estimator is more efficient than [Formula: see text].
Possibilistic Linear Regression Analysis with Fuzzy Response Variable for Crop YIELD Estimation
Authors: Ghosh Himadri , Singh Rama Krishna , Prajneshu
Published: August 2016

Reliable estimates of crop yields at small area level, say blocks, are of great importance for policy planning at micro-level. To this end, application of present methodology of Crop-cutting experiments is not practicable, as it would require total number of such experiments to increase many folds. Additional information about farmers' estimates of crop yields at block level, which are crisp values, may be used provided these can explain the actual crop yields, which are fuzzy. Accordingly, in this paper, theory of fuzzy sets and possibilistic regression analysis is discussed. Three methods, viz . Minimization, Maximization, and Conjunction are considered. The methodology is applied for modelling cotton crop yields at block levels of Sirsa district, Haryana. It is found that Conjunction method performed the best. Further, farmers' estimates are able to explain the actual crop yields with fitness level as high as 0.6.
Two-Stage Selection of the Best Signal-To-Noise Ratio with Related Approximations
Authors: Aoshima Makoto , Mukhopadhyay Nitis , Yata Kazuyoshi
Published: August 2016

We consider the problem of calibrating k (≥ 2) channels or signal processors and select the best one, that is the one having the largest signal-to-noise ratio (SNR). Assuming a Gaussian distribution for the back-ground white noise or clutter, the problem reduces to selecting from k (≥ 2) normal populations the one with the largest value of the absolute mean. Assuming unknown means and a common unknown variance, we proceed under Bechhofer's 1954 indifference-zone formulation. Since the common variance is unknown, a single-stage procedure guaranteeing a preassigned level of the minimum probability of correct selection (PCS) would not exist. We propose a two-stage selection methodology whose minimum PCS meets the minimum PCS requirement up to the second-order term with respect to the difference of the absolute means. The roles of the proposed approximation are examined both via exact computations and simulations. A realistic example on passive acoustic sonar detection of marine mammals (Abraham 2004) is included with data analyses.
A Zero-Inflated Bivariate Poisson Regression Model and Application to Some Dental Epidemiological Data
Authors: Jiang Xing , Paul Sudhir R.
Published: August 2016

For the analysis of Data in the form of paired (pre-treatment, post-treatment) counts we propose a zero-inflated bivariate Poisson regression (ZIBPR) model. We develop EM algorithm to obtain maximum likelihood estimates of the parameters of the ZIBPR model. Further, we obtain exact Fisher information matrix of the maximum likelihood estimates of the parameters of the ZIBPR model which can be used in a procedure for testing treatment effects. The Procedure to detect treatment effects based on the ZIBPR model is compared, in terms of size, by simulations, with an earlier procedure using a zero-inflated Poisson regression (ZIPR) model of the post- treatment count with the pre-treatment count treated as a covariate. The procedure based on the ZIBPR model holds level most effectively. A further simulation study indicates good power property of the procedure based on the ZIBPR model. We then analyze the DMFT index data based on the ZIBPR model and compare with the analysis using the ZIPR model.
Estimation for Stochastic Differential Equations Driven by Mixed Fractional Brownian Motions
Authors: Rao B. L. S. Prakasa
Published: August 2016

A linear stochastic differential equation driven by a mixture of two independent fractional Brownian motions possibly with different Hurst indices is considered and an estimator for the trend parameter is obtained based on the observation of the process up to time T. Distributional properties of this estimator are investigated.

AMS (2000) Subject Classification : 62M09.
On Generalized Stochastic Orders of Dispersion-Type
Authors: Nanda Asok K. , Kundu Amarjit
Published: August 2016

In the study of probabilistic orders iterated integrals of survival functions have been used by many authors. Recently, dispersion-typestochastic orders have been defined by Belzunce, Hu and Khaledi (2003) [ Probability in the Engineering and Informational Sciences, Vol. 17, pp. 305–334]. The purpose of this paper is to generalize the dispersion-type stochastic orders using generalized iterated survival functions. The relationships between generalized stochastic orders and the stochastic orders of dispersion-type have been studied. It is shown that under certain condition, generalized down stochastic orders imply generalized stochastic orders of dispersion-type which, in turn, imply generalized stochastic orders. Generalized stochastic orders of dispersion-type of residual random variables are discussed. Some characterizations of generalized stochastic orders of dispersion-type have also been studied. Some results regarding generalized orders are also discussed when the residual time is random.

AMS (2000) Subject Classification : 60E15, 60K10.
A New Skew­Normal Distribution and Its Properties
Authors: Sahu Sujit K. , Chai High S.
Published: August 2016

This article generalizes a multivariate skew-normal distribution and describes its many interesting properties. The univariate version of the new distribution is compared with two other currently used distributions. The use of the new distribution is illustrated with a real data example suitable for regression modeling. The new model provides a better model than its two rivals as evaluated by some suitable Bayesian model selection criteria.

AMS (2000) Subject Classification : 62F15, 62J05.
Rao­Hartley­Cochran Sampling with Competitive Estimators
Authors: Bose Arijit Chaudhuri Mausumi , Dihidar Kajal
Published: August 2016

We study the possibility of using the Horvitz-Thompson (HT) estimator from a sample collected by the Rao-Hartley-Cochran (RHC) scheme. We derive expressions for several alternative unbiased variance estimators of the estimators given by RHC and HT for estimating a population total. For a real life problem, on finding well correlated auxiliary variate values, we consider selecting the first stage units by the RHC scheme and the second stage units by equal probabilities without replacement. Using real data, we compare the relative accuracies in estimation by dint of simulation, using the classical and the new variance estimators. Our criteria for comparison are the actual coverage percentage (ACP) and the average coefficient of variation (ACV). We demonstrate that as against the RHC estimator, the HT estimator is a viable contender in estimation from an RHC sample.

AMS (2000) Subject Classification : 62D05.
Extremes, Extreme Spacings and Tail Lengths : An Investigation for Some Important Distributions
Authors: Mudholkar Govind S. , Chaubey Yogendra P. , Tian Lili
Published: August 2016

Extreme value and extreme spacing distributions are elegant and important artifacts of statistical theory and practice. However, in statistical education, due to the highly technical nature of the subject, they are generally treated as special topics. But, as demonstrated by Freimer et al. (1989), the asymptotic distributions of the extremes and extreme spacings of random samples, and the related theory can be derived and developed by applying elementary methods to the population quantile functions when they are available in closed forms. However, their work excluded the pedagogically important Gaussian and gamma populations. In this paper, using the closed form expression for the quantile function of the Pareto family first, we show how this approach works. We then proceed to demonstrate its use by simple Taylor expansion for the normal and gamma populations, cases where the closed form expressions for the quantile functions are unavailable. In the process, we relate the geometric notion of tail length to the extreme value distribution. We also examine the case of inverse Gaussian (IG) family, which is well known to be strikingly and intriguingly analogous to the Gaussian family. Actually, in the present context we consider not only the IG but the related reciprocal IG (RIG) and the root reciprocal IG (RRIG) families. The extreme value theory for these three families is derived, again using the elementary methods, even though their quantile functions also lack closed form expressions. Interestingly, it is seen that the extreme value theory for the RRIG population, and not of the IG population, is somewhat analogous to the Gaussian distribution.

AMS (2000) Subject Classification : 62E20.
Improving the Hansen­Hurwitz Estimator in PPSWR Sampling
Authors: Adhikary Arun Kumar
Published: August 2016

An attempt has been made to improve upon the Hansen-Hurwitz (1943) estimator based on PPSWR sampling scheme through Rao-Blackwellisation. In order to derive the sampling variance of the improved estimator obtained by Rao-Blackwellisation, it is of interest to derive the probability distribution of the number of distinct units in the sample drawn according to PPSWR sampling scheme, as the improved estimator is based solely on the distinct units in the sample. It has been possible to write down the exact distribution of the number of distinct units in the sample drawn by PPSWR sampling scheme in a closed form. Assuming a super-population model, the model-expected design-variance of the improved estimator is worked out and it is compared with that of the Hansen-Hurwitz estimator under the same super-population model. The percentage gain in efficiency in using the improved estimator over the Hansen-Hurwitz estimator is worked out for certain selected values of the model parameters.

AMS (2000) Subject Classification : 62D05.
Classes of Statistics for Testing Exponentiality Versus IFR or NBUE Alternatives
Authors: Mugdadi A.R. , Ahmad Ibrahim A.
Published: August 2016

Abtsrcat

In 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).
Exact Moments of Lower Generalized Order Statistics from Power Function Distribution
Authors: Athar Haseeb , Khan R.U. , Anwar Zaki
Published: August 2016

Abtsrcat

Order 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.
A Parametric Quantile Regression Model Useful in Reliability Analysis
Authors: Sankaran P.G. , V. Preetha Kumari P.
Published: August 2016

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.
Bivariate Geometric Vitality Function and Some Characterization Results
Authors: Abdul-Sathar E.I. , Rajesh G. , Nair K.R. Muraleedharan
Published: August 2016

Abtsrcat

In 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.
A Note on Approximating Continuous Distribution Functions
Authors: Habibi Reza
Published: August 2016

Abtsrcat

This 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.
Fundamental Planes for Galaxy Data with Measuremental Errors
Authors: Mondal Saptarshi , Warule Bharat , Chattopadhyay Tanuka
Published: August 2016

Abtsrcat

Regression 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.
The Theil-Sen Estimator in Genomic High Dimensional Mearsurement Error Models Perspectives
Authors: Sen Pranab K.
Published: August 2016

In a simple multivariate measurement error regression model, the classical least squares estimator does not consistently estimate the vector of the slope parameters. Under multinormality, linear regression stands valid, although with some discount factor. The situation is entirely different when the multinormality assumption is dispensed with. In genomics studies. data models relate to excessively high dimensions where the multinormality assumption may rarely be tenable, and in addition, measurement errors in the regressor is universally anticipated. As such, robustness perspectives call for other estimators which may require less stringent distributional regularity assumptions. The Theil-Sen estimator in high-dimentional measurement error setups is studied here with due emphasis on genomics studies.
Plug-In Sequential Normal Density Estimation Under Unknown Variance: Mise Loss
Authors: Mukhopadhyay Nitis , Pepe William
Published: August 2016

Consider independent observations X1, X2,… having a common normal probability density function [Formula: see text] and unknown variance σ2(> 0). We propose estimating f( x; σ2) with a purely sequential methodology under the mean integrated squared error (MISE) loss function. Our goal is to make the associated risk not to exceed a preassigned positive number c, referred to as the risk-bound. Since no fixed-sample-size methodology would be able to handle this estimation problem, Mukhopadhyay and Pepe (2009) first gave a two-stage sampling method. We show that our purely sequential density estimation methodology satisfies asymptotic (i) first-order efficiency property (Theorem 2.1) and (ii) first-order risk-efficiency property (Theorem 2.2) just like the Mukhopadhyay and Pepe two-stage methodology did. But, the present purely sequential density estimation methodology has better second-order efficiency property (Theorems 2.3 and 3.1) than those associated with the Mukhopadhyay and Pepe two-stage methodology. Small, moderate, and large sample performances are investigated with the help of simulations. Illustrations are included with the help of a real dataset.
Testing Homogeneity of Mean Directions for Circular Dispersion Models
Authors: Sengupta Ashis , Roy Rishideep
Published: August 2016

Tests for equality of mean directions in independent circular populations is an important practical problem in many areas of applied research, for which results are yet to be obtained. Dispersion model approach with analysis of deviance is an appealing approach for testing equality of parameters under non-normal setups. In view of its wide applicability, the present endeavour is to examine whether standard circular models for describing directional data can be viewed as special cases of dispersion model. The answer is affirmative and this leads us to explore whether analysis of deviance can be employed for circular observations. Special emphasis is given on circular normal and wrapped Cauchy distributions for carrying out deviance analysis. Interestingly, we demonstrate that the Watson-Williams ad-hoc test (1956) proposed for independent von Mises distributions is equivalent to the analysis of deviance test. We thereby also exhibit the rare property possessed by von Mises distributions with high concentrations, that the nuisance concentration parameter can be ignored for this test in such a case.
Estimating Common Mean of a Bivariate Normal Population with Order Restricted Variances
Authors: Tripathy Manas Ranjan , Kumar Somesh
Published: August 2016

Let ( X1, Y1), ( X2, Y2),…,( X n, Y n) be a random sample of size n from a bivariate normal population with a common mean μ variances [Formula: see text] and [Formula: see text] and correlation coefficient ρ The estimation of the common mean μ has been considered when it is known a priori that the variances are ordered, that is, [Formula: see text] A new estimator has been proposed which dominates the maximum likelihood estimator (without restrictions) stochastically and also in terms of Pitman measure of closeness. Further an inadmissibility condition has been obtained for affine equivariant estimators when the variances are ordered. A numerical comparison of various estimators has been carried out.
On Improvement and Deterioration of A Repairable System Under Generalized Stochastic Orders
Authors: Nanda Asok K. , Kundu Amarjit
Published: August 2016

Improvement (deterioration) of a repairable system in the sense of several generalized stochastic orders has been discussed in this paper. We have also proved some general results for minimal repairable systems.
On P(X < Y) for Extended Family of Distributions
Authors: Maiti Sudhansu S. , Murmu Sudhir
Published: August 2016

The article considers the problem of R = P( X < Y ), when X and Y belong to independently distributed extended family of distributions proposed by Marshall and Olkin (1997). Maximum likelihood estimate of R have been found out and the estimates assuming different baseline distributions have been compared for complete samples. Lower confidence limits of R have been found out by Delta method and bootstrap method. The Bayes estimate of R have also been calculated using MCMC approach and one data analysis has been performed for illustrative purposes.
Estimation of Median Household Income for Small Areas : A Bayesian Semiparametric Approach
Authors: Bhadra Dhiman , Ghosh Malay , Kim Dalho
Published: August 2016

Abtsrcat

Estimation of median income of small areas is one of the prin- cipal targets of inference of the U.S Bureau of Census. These estimates play an important role in the formulation of various governmental decisions and policies. Since these estimates are collected over time, they often possess an inherent longitudinal pattern. Taking proper account of this time varying pattern may result in better estimates for the current or future median house-hold incomes for a particular state or county. In this study, we put forward a semiparametric modeling procedure for estimating the median household income for all the U.S states. Our models include a nonparametric functional part for accommodating any unspecified time varying income pattern and also a state specific random effect to account for the within-state correlation of the income observations. Model fitting and parameter estimation is carried out in a hierarchical Bayesian framework using Markov chain Monte Carlo (MCMC) methodology. It is seen that the semiparametric model esti- mates can be superior to both the direct estimates and the Census Bureau estimates. Overall, our study indicates that proper modeling of the underly- ing longitudinal income profiles can improve the performance of model based estimates of household median income of small areas.
On the Foundations of Dependency Models and Parameters for Random Variables on Cylinder R3
Authors: Seal Babulal , Sengupta Ashis
Published: August 2016

Abtsrcat

Directional data often deal with observations on circles, spheres, cylinders, torus, etc. The notion of dependency between the variables involved and the development of related models and dependency parameters are of fundamental importance in this area. Here we develop a method of obtaining regression curves on manifold (cylinder) on R3 based on a differential geometric approach. With an aim to develop statistical inference procedures, we propose useful distribution on the cylinder for which the dependency parameter can be elegantly elucidated, and demonstrate how this parameter can be estimated in practice.
Empirical Bayes Prediction in Random Effects Models with Covariates Subject to Measurement Error
Authors: Guao Meixi , Ghosh Malay
Published: August 2016

Abtsrcat

The paper considers a nested error linear regression model with multiple covariates subject to measurement error. An efficient empirical Bayes (EB) predictor is obtained using the information on both the observed response variables and the observed covariates. We derive a correct second- order unbiased approximation to the mean squared error (MSE) of the EB predictor.
On Sequential Point Estimation in a Uniform Distribution with Adjusted Non-Sufficient Estimators : A Comparative Study and Real Data Illustration
Authors: Bhattacharjee Debanjan , Mukhopadhyay Nitis
Published: August 2016

Abtsrcat

The purely sequential minimum risk point estimation procedure for the unknown parameter θ (> 0) in a Uniform (0; θ) population has been discussed in this article. This is developed under a squared error loss plus a linear cost function of sampling. The unknown parameter θ is estimated by means of four different estimators in the stopping rule, where as in the loss function two different unbiased estimators of θ are proposed. The unbiased estimators are randomly stopped versions of Χ n: n and X¯ n in either loss function. Performances of such estimators are compared. Clearly, using a randomly stopped version of X¯ n would amount to some loss of in- formation when compared with a corresponding randomly stopped largest sample order statistic under both loss functions and the stopping rules. In this paper, we explore a novel approach to recover any loss of information by fine-tuning the loss function and then properly tailoring the associated sequential methodologies. We examine how the sequential risks of our newly proposed methodologies would compare with those associated with the ex- isting sequential estimators and illustrate our methodologies with the help of a real dataset.
Stability of the Characterization Results in Terms of Hazard and Reverse Hazard Rates Under Matusita Distance
Authors: Roy Dilip
Published: August 2016

Abtsrcat

The classical approach of stochastic modeling is to first guess a model and then to validate the same using observed data and some test for goodness of fit. Unfortunately, this is not a very rational approach. The initial choice of model becomes a subjective one, some goodness of fit test may demand for large number of observations and difierent models may fit well for the same data set. Given these limitations of the classical approach, one may, as an alternative, make use of characterization results. At the same time, to take care of the difficulties in verification of characterizing properties one needs stability properties as well.

Stability results have been mostly studied for the exponential distribution. So far as non-exponential distributions are concerned, one may refer to only few works. The present study deals with stability properties in terms of Matusita distance for characterization results involving reliability measures. These results are generic in nature and can be used for the distribution cor- responding to any non-negative random variable.
On Generalized Quality Capability Index
Authors: Maiti Sudhansu S. , Saha Mahendra
Published: August 2016

Abtsrcat

A Generalized Process Capability Index, defined as the ratio of proportion of specification conformance (or, process yield) to proportion of desired (or, natural) conformance, has been developed by Maiti et al.(2010). Almost all the process capabilities defined in the literature are directly or indirectly associated with this generalized index. In this article, a loss function has been attached to the product quality characteristic for deviation from its target to define the index named as generalized quality capability index. Symmetric as well as asymmetric loss functions have been considered. We deal with the index in case of normal, non-normal and discrete processes. An algorithm for determining optimum process center for an off-centered process has been prescribed. A process data set has been analyzed.