Pub Date : 2016-06-30DOI: 10.6092/ISSN.1973-2201/5422
K. Das, Sahana Bhattacharjee
In the present study, we have developed new circular descriptive statistics for Censored circular sample and attempted to analyse the occurrence of seasonal diseases, both month-wise and season-wise. The Rayleigh Uniformity Test has also been proposed for the same, using which the presence of seasonal effect in both the cases. Finally, a regression model for predicting binary response from circular predictor has been proposed. The months being of unequal length, have been adjusted accordingly so as to make them of equal lengths. But since the seasons differ by a significant length and making them equal in length will mislead the analysis, we propose to group the cases in unequal intervals, the width of the intervals being proportional to the length of the seasons. That the season-wise analysis using circular statistical tools has not been attempted before is the main motivation behind our study. The data has been taken from the project entitled Statistical Modeling in Circular Statistics: An Application to Health Science, sponsored by the UGC, India, where diseases have been reported for the Kamrup (rural) district of Assam, India. It is revealed that the occurrence of seasonal diseases is highest in the months of March or equivalently, during the Pre-monsoon season. The distribution of occurrence of seasonal diseases both month-wise and season-wise is found to be marginally positively skewed and platykurtic. The regression analysis suggests that seasonal diseases is least likely to occur in April as compared to December and in Winter in comparison to Post-monsoon.
{"title":"Circular Statistical Approach to Study the Occurrence of Seasonal Diseases","authors":"K. Das, Sahana Bhattacharjee","doi":"10.6092/ISSN.1973-2201/5422","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/5422","url":null,"abstract":"In the present study, we have developed new circular descriptive statistics for Censored circular sample and attempted to analyse the occurrence of seasonal diseases, both month-wise and season-wise. The Rayleigh Uniformity Test has also been proposed for the same, using which the presence of seasonal effect in both the cases. Finally, a regression model for predicting binary response from circular predictor has been proposed. The months being of unequal length, have been adjusted accordingly so as to make them of equal lengths. But since the seasons differ by a significant length and making them equal in length will mislead the analysis, we propose to group the cases in unequal intervals, the width of the intervals being proportional to the length of the seasons. That the season-wise analysis using circular statistical tools has not been attempted before is the main motivation behind our study. The data has been taken from the project entitled Statistical Modeling in Circular Statistics: An Application to Health Science, sponsored by the UGC, India, where diseases have been reported for the Kamrup (rural) district of Assam, India. It is revealed that the occurrence of seasonal diseases is highest in the months of March or equivalently, during the Pre-monsoon season. The distribution of occurrence of seasonal diseases both month-wise and season-wise is found to be marginally positively skewed and platykurtic. The regression analysis suggests that seasonal diseases is least likely to occur in April as compared to December and in Winter in comparison to Post-monsoon.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2016-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-06-30DOI: 10.6092/ISSN.1973-2201/6159
N. Nair, Johny Scaria, Sithara Mohan.
The Cambanis family of bivariate distributions was introduced as a generalization of the Farlie-Gumbel-Morgenstern system. The present work is an attempt to investigate the distributional characteristics and applications of the family. We derive various coecients of association, dependence concepts and time-dependent measures. Bivariate reliability functions such as hazard rates and mean residual life functions are analysed. The application of the family as a model for bivariate lifetime data is also demonstrated.
{"title":"The Cambanis family of bivariate distributions: Properties and applications","authors":"N. Nair, Johny Scaria, Sithara Mohan.","doi":"10.6092/ISSN.1973-2201/6159","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6159","url":null,"abstract":"The Cambanis family of bivariate distributions was introduced as a generalization of the Farlie-Gumbel-Morgenstern system. The present work is an attempt to investigate the distributional characteristics and applications of the family. We derive various coecients of association, dependence concepts and time-dependent measures. Bivariate reliability functions such as hazard rates and mean residual life functions are analysed. The application of the family as a model for bivariate lifetime data is also demonstrated.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2016-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-06-30DOI: 10.6092/ISSN.1973-2201/5993
A. Yadav, S. Singh, U. Singh
In this paper, we proposed the estimation procedures to estimate the unknown parameters, reliability and hazard functions of Inverse Lomax distribution. The mathematical expressions for maximum likelihood and Bayes estimators are derived in presence of hybrid censoring scheme. In most of the cases, it has been seen that maximum likelihood and Bayes estimators of the parameters are not appear in explicit form. Hence, Newton-Raphson (N-R) method has been used to draw the maximum likelihood estimates of the parameters. The Bayes estimators are obtained under Jeffrey's non-informative prior for both shape and scale using Markov Chain Monte Carlo (MCMC) technique. Further, we have also constructed the 95% asymptotic confidence interval based on maximum likelihood estimates (MLEs) and highest posterior density (HPD) credible intervals based on MCMC samples. Finally, two data sets have been used to demonstrate the proposed methodology.
{"title":"On Hybrid Censored Inverse Lomax Distribution: Application to the Survival Data","authors":"A. Yadav, S. Singh, U. Singh","doi":"10.6092/ISSN.1973-2201/5993","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/5993","url":null,"abstract":"In this paper, we proposed the estimation procedures to estimate the unknown parameters, reliability and hazard functions of Inverse Lomax distribution. The mathematical expressions for maximum likelihood and Bayes estimators are derived in presence of hybrid censoring scheme. In most of the cases, it has been seen that maximum likelihood and Bayes estimators of the parameters are not appear in explicit form. Hence, Newton-Raphson (N-R) method has been used to draw the maximum likelihood estimates of the parameters. The Bayes estimators are obtained under Jeffrey's non-informative prior for both shape and scale using Markov Chain Monte Carlo (MCMC) technique. Further, we have also constructed the 95% asymptotic confidence interval based on maximum likelihood estimates (MLEs) and highest posterior density (HPD) credible intervals based on MCMC samples. Finally, two data sets have been used to demonstrate the proposed methodology.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2016-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-06-30DOI: 10.6092/ISSN.1973-2201/6348
F. Greco
Nowadays, traditional population censuses based on total enumeration of the population are being accompanied by sample surveys. Sampling within censuses allows to reduce costs and workload of authorities involved in censuses operations, along with the statistical burden for the people involved in the enumeration. In this paper, we deal with estimation of multi-way contingency tables involving variables measured both via census and sampling. In this framework, two main issues need to be addressed: first of all, sample size for estimating some of the entries of the contingency tables may be too small, delivering estimates prone to huge sampling variability. On the other hand, since estimates of the joint distribution need to be coherent with the marginal distribution of the variable collected via a census, estimation methods need to be coherent with the constraint imposed by marginal distribution of variables measured via census. The problem is tackled via a model-based approach that allows to comply with all coherence constraints following a fairly simple procedure. The merit of the proposed methodology is illustrated by means of a simulation study.
{"title":"ESTIMATION OF MULTI-WAY TABLES SUBJECT TO COHERENCE CONSTRAINTS","authors":"F. Greco","doi":"10.6092/ISSN.1973-2201/6348","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6348","url":null,"abstract":"Nowadays, traditional population censuses based on total enumeration of the population are being accompanied by sample surveys. Sampling within censuses allows to reduce costs and workload of authorities involved in censuses operations, along with the statistical burden for the people involved in the enumeration. In this paper, we deal with estimation of multi-way contingency tables involving variables measured both via census and sampling. In this framework, two main issues need to be addressed: first of all, sample size for estimating some of the entries of the contingency tables may be too small, delivering estimates prone to huge sampling variability. On the other hand, since estimates of the joint distribution need to be coherent with the marginal distribution of the variable collected via a census, estimation methods need to be coherent with the constraint imposed by marginal distribution of variables measured via census. The problem is tackled via a model-based approach that allows to comply with all coherence constraints following a fairly simple procedure. The merit of the proposed methodology is illustrated by means of a simulation study.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2016-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-03-31DOI: 10.6092/ISSN.1973-2201/5457
Manoj Kumar, S. Singh, U. Singh
In this paper, a poissoin-exponential distribution(PED) is considered as a lifetime model. Its statistical characteristics and important distributional properties are discussed by Louzada-Neto et al.[13]. The method of Maximum likelihood estimation and least square estimation of parameters involved along with reliability and failure rate functions is also studied here. In view of cost and time constraints, Progressive type-II censored data with binomial removals (PT-II CBRs) have been used. Finally, a real data example is given to show the practical applications of the paper.
{"title":"Reliability Estimation for poisson-exponential model under Progressive type-II censoring data with binomial removal data","authors":"Manoj Kumar, S. Singh, U. Singh","doi":"10.6092/ISSN.1973-2201/5457","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/5457","url":null,"abstract":"In this paper, a poissoin-exponential distribution(PED) is considered as a lifetime model. Its statistical characteristics and important distributional properties are discussed by Louzada-Neto et al.[13]. The method of Maximum likelihood estimation and least square estimation of parameters involved along with reliability and failure rate functions is also studied here. In view of cost and time constraints, Progressive type-II censored data with binomial removals (PT-II CBRs) have been used. Finally, a real data example is given to show the practical applications of the paper.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2016-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-03-31DOI: 10.6092/ISSN.1973-2201/6090
K. Jayakumar, K. K. Sankaran
Nadarajah et al.(2013) introduced a family life time models using truncated negative binomial distribution and derived some properties of the family of distributions. It is a generalization of Marshall-Olkin family of distributions. In this paper, we introduce Generalized Uniform Distribution (GUD) using the approach of Nadarajah et al.(2013). The shape properties of density function and hazard function are discussed. The expression for moments, order statistics, entropies are obtained. Estimation procedure is also discussed.The GDU introduced here is a generalization of the Marshall-Olkin extended uniform distribution studied in Jose and Krishna(2011).
Nadarajah et al.(2013)引入了使用截断负二项分布的家庭寿命时间模型，并推导了家庭分布的一些性质。它是Marshall-Olkin分布族的推广。在本文中，我们使用Nadarajah等人(2013)的方法引入广义均匀分布(GUD)。讨论了密度函数和危险函数的形状性质。得到了矩量、阶统计量、熵的表达式。并对估计过程进行了讨论。这里介绍的GDU是对Jose和Krishna(2011)研究的Marshall-Olkin扩展均匀分布的推广。
{"title":"On a Generalisation of Uniform Distribution and its Properties","authors":"K. Jayakumar, K. K. Sankaran","doi":"10.6092/ISSN.1973-2201/6090","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6090","url":null,"abstract":"Nadarajah et al.(2013) introduced a family life time models using truncated negative binomial distribution and derived some properties of the family of distributions. It is a generalization of Marshall-Olkin family of distributions. In this paper, we introduce Generalized Uniform Distribution (GUD) using the approach of Nadarajah et al.(2013). The shape properties of density function and hazard function are discussed. The expression for moments, order statistics, entropies are obtained. Estimation procedure is also discussed.The GDU introduced here is a generalization of the Marshall-Olkin extended uniform distribution studied in Jose and Krishna(2011).","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2016-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-03-31DOI: 10.6092/ISSN.1973-2201/6319
E. Fabrizi, F. Greco, C. Trivisano
In this paper, we consider the problem of specifying priors for the variance components in the Bayesian analysis of the Besag-York-Mollie model, a model that is popular among epidemiologists for disease mapping. The model encompasses two sets of random effects: one spatially structured to model spatial autocorrelation and the other spatially unstructured to describe residual heterogeneity. In this model, prior specification for variance components is an important problem because these priors maintain their influence on the posterior distributions of relative risks when mapping rare diseases. We propose using generalised inverse Gaussian priors, a broad class of distributions that includes many distributions commonly used as priors in this context, such as inverse gammas. We discuss the prior parameter choice with the aim of balancing the prior weight of the two sets of random effects on total variation and controlling the amount of shrinkage. The suggested prior specification strategy is compared to popular alternatives using a simulation exercise and applications to real data sets.
{"title":"On the specification of prior distributions for variance components in disease mapping models","authors":"E. Fabrizi, F. Greco, C. Trivisano","doi":"10.6092/ISSN.1973-2201/6319","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6319","url":null,"abstract":"In this paper, we consider the problem of specifying priors for the variance components in the Bayesian analysis of the Besag-York-Mollie model, a model that is popular among epidemiologists for disease mapping. The model encompasses two sets of random effects: one spatially structured to model spatial autocorrelation and the other spatially unstructured to describe residual heterogeneity. In this model, prior specification for variance components is an important problem because these priors maintain their influence on the posterior distributions of relative risks when mapping rare diseases. We propose using generalised inverse Gaussian priors, a broad class of distributions that includes many distributions commonly used as priors in this context, such as inverse gammas. We discuss the prior parameter choice with the aim of balancing the prior weight of the two sets of random effects on total variation and controlling the amount of shrinkage. The suggested prior specification strategy is compared to popular alternatives using a simulation exercise and applications to real data sets.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2016-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-03-31DOI: 10.6092/ISSN.1973-2201/6281
S. Jammalamadaka, S. Prasad, P. G. Sankaran
Middle censoring introduced by Jammalamadaka and Mangalam (2003), refers to data arising in situations where the exact lifetime becomes unobservable if it falls within a random censoring interval, otherwise it is observable. In the present paper we propose a semi-parametric regression model for such lifetime data, arising from an unknown population and subject to middle censoring. We provide an algorithm to find the nonparametric maximum likelihood estimator (NPMLE) for regression parameters and the survival function. The consistency of the estimators are established. We report simulation studies to assess the finite sample properties of the estimators. We then analyze a real life data on survival times for diabetic patients studied by Lee et al. (1988).
{"title":"A SEMI-PARAMETRIC REGRESSION MODEL FOR ANALYSIS OF MIDDLE CENSORED LIFETIME DATA","authors":"S. Jammalamadaka, S. Prasad, P. G. Sankaran","doi":"10.6092/ISSN.1973-2201/6281","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6281","url":null,"abstract":"Middle censoring introduced by Jammalamadaka and Mangalam (2003), refers to data arising in situations where the exact lifetime becomes unobservable if it falls within a random censoring interval, otherwise it is observable. In the present paper we propose a semi-parametric regression model for such lifetime data, arising from an unknown population and subject to middle censoring. We provide an algorithm to find the nonparametric maximum likelihood estimator (NPMLE) for regression parameters and the survival function. The consistency of the estimators are established. We report simulation studies to assess the finite sample properties of the estimators. We then analyze a real life data on survival times for diabetic patients studied by Lee et al. (1988).","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2016-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-03-31DOI: 10.6092/ISSN.1973-2201/6282
D. Shibu, M. Irshad
In this paper, we consider an extended version of new generalized Lindley distribution (NGLD). We refer to this new generalization as the extended new generalized Lindley distribution (ENGLD). A comprehensive account of the mathematical properties of the new distribution including estimation is presented. A real life data set is considered here to illustrate the relevance of the new model and compared it with other forms of Lindley models using method of moment estimation and method of maximum likelihood estimation.
{"title":"Extended New Generalized Lindley Distribution","authors":"D. Shibu, M. Irshad","doi":"10.6092/ISSN.1973-2201/6282","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6282","url":null,"abstract":"In this paper, we consider an extended version of new generalized Lindley distribution (NGLD). We refer to this new generalization as the extended new generalized Lindley distribution (ENGLD). A comprehensive account of the mathematical properties of the new distribution including estimation is presented. A real life data set is considered here to illustrate the relevance of the new model and compared it with other forms of Lindley models using method of moment estimation and method of maximum likelihood estimation.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2016-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-12-30DOI: 10.6092/ISSN.1973-2201/5607
M. Pal, M. Tiensuwan
Based on standard probability distributions, new families of univariate distributions have been introduced and their properties studied by many authors. The present paper investigates some general properties of a family of Gamma generated distributions proposed by Zografos and Balakrishnan (2009).
{"title":"Some Properties of Gamma Generated Distributions","authors":"M. Pal, M. Tiensuwan","doi":"10.6092/ISSN.1973-2201/5607","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/5607","url":null,"abstract":"Based on standard probability distributions, new families of univariate distributions have been introduced and their properties studied by many authors. The present paper investigates some general properties of a family of Gamma generated distributions proposed by Zografos and Balakrishnan (2009).","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2015-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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