Pub Date : 2018-10-02DOI: 10.6092/ISSN.1973-2201/7990
C. Kumar, S. Harisankar
A modified version of Yule distribution is introduced here and discuss some of its properties by deriving expressions for its probability generating function, raw moments, factorial moments etc. Certain recursion formulae for its probabilities, raw moments and factorial moments are also developed. Various methods of estimation are employed for estimating the parameters of the distribution and certain test procedures are suggested for testing the significance of the additional parameters of the distribution. The distribution has been fitted to certain real-life data sets for illustrating its usefulness, compared with certain existing models available in the literature. Further, a simulation study is conducted for assessing the performance of the maximum likelihood estimators.
{"title":"On a Modified Yule Distribution","authors":"C. Kumar, S. Harisankar","doi":"10.6092/ISSN.1973-2201/7990","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/7990","url":null,"abstract":"A modified version of Yule distribution is introduced here and discuss some of its properties by deriving expressions for its probability generating function, raw moments, factorial moments etc. Certain recursion formulae for its probabilities, raw moments and factorial moments are also developed. Various methods of estimation are employed for estimating the parameters of the distribution and certain test procedures are suggested for testing the significance of the additional parameters of the distribution. The distribution has been fitted to certain real-life data sets for illustrating its usefulness, compared with certain existing models available in the literature. Further, a simulation study is conducted for assessing the performance of the maximum likelihood estimators.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"78 1","pages":"169-181"},"PeriodicalIF":1.9,"publicationDate":"2018-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44148636","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 : 2018-10-02DOI: 10.6092/ISSN.1973-2201/7201
Vikas Kumar, Rekha Rani
In the present paper, we propose a quantile version of generalized entropy measure for residual and past lifetimes and study their properties. Lower and upper bounds of the proposed measures are derived. Some of the quantile lifetime distributions have been characterized. We also introduce quantile versions of the generalized divergence measure of Varma between two residual and two past lifetime random variables. Some properties of this measure are studied and a characterization of the proportional (reversed) hazards model is given.
{"title":"Quantile Approach of Dynamic Generalized Entropy (Divergence) Measure","authors":"Vikas Kumar, Rekha Rani","doi":"10.6092/ISSN.1973-2201/7201","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/7201","url":null,"abstract":"In the present paper, we propose a quantile version of generalized entropy measure for residual and past lifetimes and study their properties. Lower and upper bounds of the proposed measures are derived. Some of the quantile lifetime distributions have been characterized. We also introduce quantile versions of the generalized divergence measure of Varma between two residual and two past lifetime random variables. Some properties of this measure are studied and a characterization of the proportional (reversed) hazards model is given.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"78 1","pages":"105-126"},"PeriodicalIF":1.9,"publicationDate":"2018-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49186934","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 : 2018-10-02DOI: 10.6092/ISSN.1973-2201/8260
C. Chesneau
In this paper, a new general family of distributions using the hypoexponential distribution is introduced and studied. A special case of this family is explored in detail, corresponding to a new finite generalized mixture of generalized exponential distributions. Some of their mathematical properties are provided. We investigate maximum likelihood estimation of the model parameters. Two real data sets are used to prove the potential of this distribution among some recent extensions of the exponential distribution.
{"title":"A New Family of Distributions Based on the Hypoexponential Distribution with Fitting Reliability Data","authors":"C. Chesneau","doi":"10.6092/ISSN.1973-2201/8260","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/8260","url":null,"abstract":"In this paper, a new general family of distributions using the hypoexponential distribution is introduced and studied. A special case of this family is explored in detail, corresponding to a new finite generalized mixture of generalized exponential distributions. Some of their mathematical properties are provided. We investigate maximum likelihood estimation of the model parameters. Two real data sets are used to prove the potential of this distribution among some recent extensions of the exponential distribution.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"78 1","pages":"127-147"},"PeriodicalIF":1.9,"publicationDate":"2018-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46621924","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 : 2018-10-02DOI: 10.6092/ISSN.1973-2201/8170
F. Opone, N. Ekhosuehi
In this paper, we review the quasi Lindley distribution and established its quantile function. A simulation study is conducted to examine the bias and mean square error of the parameter estimates of the distribution through the method of moment estimation and the maximum likelihood estimation. Result obtained shows that the method of maximum likelihood is a better choice of estimation method for the parameters of the quasi Lindley distribution. Finally, an applicability of the quasi Lindley disttribution to a waiting time data set suggests that the distribution demonstrates superiority over the power Lindley distribution, Sushila distribution and the classical oneparameter Lindley distribution in terms of the maximized loglikelihood, the Akaike information criterion, the Kolmogorov-Smirnov and Cramer von Mises test statistic.
本文综述了拟林德利分布，并建立了其分位数函数。通过矩估计法和极大似然估计法对分布参数估计的偏差和均方误差进行了仿真研究。结果表明，极大似然法是拟林德利分布参数估计的较好选择。最后，拟林德利分布对等待时间数据集的适用性表明，该分布在最大对数似然、Akaike信息准则、Kolmogorov-Smirnov和Cramer von Mises检验统计量方面优于幂林德利分布、Sushila分布和经典单参数林德利分布。
{"title":"Methods of Estimating the Parameters of the Quasi Lindley Distribution","authors":"F. Opone, N. Ekhosuehi","doi":"10.6092/ISSN.1973-2201/8170","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/8170","url":null,"abstract":"In this paper, we review the quasi Lindley distribution and established its quantile function. A simulation study is conducted to examine the bias and mean square error of the parameter estimates of the distribution through the method of moment estimation and the maximum likelihood estimation. Result obtained shows that the method of maximum likelihood is a better choice of estimation method for the parameters of the quasi Lindley distribution. Finally, an applicability of the quasi Lindley disttribution to a waiting time data set suggests that the distribution demonstrates superiority over the power Lindley distribution, Sushila distribution and the classical oneparameter Lindley distribution in terms of the maximized loglikelihood, the Akaike information criterion, the Kolmogorov-Smirnov and Cramer von Mises test statistic.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"78 1","pages":"183-193"},"PeriodicalIF":1.9,"publicationDate":"2018-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48741979","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 : 2018-10-02DOI: 10.6092/ISSN.1973-2201/7249
Ajit Chaturvedi, Ananya Malhotra
A positive exponential family of distributions is taken into consideration. Two measures of reliability are discussed. Uniformly minimum variance unbiased estimators (UMVUES) and maximum likelihood estimators (MLES) are developed for the reliability functions. In addition to the UMVUES and MLES, we derive the method of moment estimators (MOME). The performances of two types of estimators are compared through Monte Carlo simulation.
{"title":"Estimation of P(X>Y) for the Positive Exponential Family of Distributions","authors":"Ajit Chaturvedi, Ananya Malhotra","doi":"10.6092/ISSN.1973-2201/7249","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/7249","url":null,"abstract":"A positive exponential family of distributions is taken into consideration. Two measures of reliability are discussed. Uniformly minimum variance unbiased estimators (UMVUES) and maximum likelihood estimators (MLES) are developed for the reliability functions. In addition to the UMVUES and MLES, we derive the method of moment estimators (MOME). The performances of two types of estimators are compared through Monte Carlo simulation.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"78 1","pages":"149-167"},"PeriodicalIF":1.9,"publicationDate":"2018-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42439064","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 : 2018-07-12DOI: 10.6092/ISSN.1973-2201/7187
P. Y. Thomas, A. Philip
The method of ranked set sampling when units are to be inducted from several bivariate populations is introduced in this work. The best linear unbiased estimation of a common parameter of two bivariate Pareto distributions is discussed based on the n ranked set observations, when a sample of size n 1 is drawn from a bivariate Pareto population with shape parameter a 1 and a sample of size n 2 is drawn from another bivariate Pareto with shape parameter a 2 such that n = n 1 + n 2 . The application of the results of this paper is illustrated with a real life data.
本文介绍了从多个二元总体中引入单元的排序集抽样方法。当从一个形状参数为a 1的二元Pareto总体中抽取一个大小为n 1的样本，并从另一个形状参数为a 2的二元Pareto总体中抽取一个大小为n 2的样本，使得n = n 1 + n 2时，讨论了基于n个排序集观测值的两个二元Pareto分布的一个公共参数的最佳线性无偏估计。并以实际数据说明了本文结果的应用。
{"title":"Induced Ranked Set Sampling when Units are Inducted from Several Populations","authors":"P. Y. Thomas, A. Philip","doi":"10.6092/ISSN.1973-2201/7187","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/7187","url":null,"abstract":"The method of ranked set sampling when units are to be inducted from several bivariate populations is introduced in this work. The best linear unbiased estimation of a common parameter of two bivariate Pareto distributions is discussed based on the n ranked set observations, when a sample of size n 1 is drawn from a bivariate Pareto population with shape parameter a 1 and a sample of size n 2 is drawn from another bivariate Pareto with shape parameter a 2 such that n = n 1 + n 2 . The application of the results of this paper is illustrated with a real life data.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"78 1","pages":"57-79"},"PeriodicalIF":1.9,"publicationDate":"2018-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43524450","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 : 2018-07-12DOI: 10.6092/ISSN.1973-2201/7494
Ajit Chaturvedi, Narendra Kumar, Kapil Kumar
In this article, a general family of lifetime distributions is considered under progressive type II right censoring. The classical point estimation and testing procedures are developed for reliability function and stress-strength reliability. The uniformly minimum variance unbiased, maximum likelihood and invariantly optimal estimators are considered. Testing procedures are developed for the hypotheses related to scale parameter, reliability and stress-strength reliability functions. A Monte Carlo simulation study is performed for comparison of various estimators developed. Finally, the use of proposed estimators is shown in an illustrative example.
{"title":"Statistical Inference for the Reliability Functions of a Family of Lifetime Distributions based on Progressive Type II Right Censoring","authors":"Ajit Chaturvedi, Narendra Kumar, Kapil Kumar","doi":"10.6092/ISSN.1973-2201/7494","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/7494","url":null,"abstract":"In this article, a general family of lifetime distributions is considered under progressive type II right censoring. The classical point estimation and testing procedures are developed for reliability function and stress-strength reliability. The uniformly minimum variance unbiased, maximum likelihood and invariantly optimal estimators are considered. Testing procedures are developed for the hypotheses related to scale parameter, reliability and stress-strength reliability functions. A Monte Carlo simulation study is performed for comparison of various estimators developed. Finally, the use of proposed estimators is shown in an illustrative example.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"78 1","pages":"81-101"},"PeriodicalIF":1.9,"publicationDate":"2018-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42508467","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 : 2018-07-12DOI: 10.6092/ISSN.1973-2201/7301
A. Asgharzadeh, R. Valiollahi, A. Fallah, S. Nadarajah
Based on record data, the estimation and prediction problems for normal distribution have been investigated by several authors in the frequentist set up. However, these problems have not been discussed in the literature in the Bayesian context. The aim of this paper is to consider a Bayesian analysis in the context of record data from a normal distribution. We obtain Bayes estimators based on squared error and linear-exponential (Linex) loss functions. It is observed that the Bayes estimators can not be obtained in closed forms. We propose using an importance sampling method to obtain Bayes estimators. Further, the importance sampling method is also used to compute Bayesian predictors of future records. Finally, a real data analysis is presented for illustrative purposes and Monte Carlo simulations are performed to compare the performances of the proposed methods. It is shown that Bayes estimators and predictors are superior than frequentist estimators and predictors.
{"title":"Bayesian Inference and Prediction for Normal Distribution Based on Records","authors":"A. Asgharzadeh, R. Valiollahi, A. Fallah, S. Nadarajah","doi":"10.6092/ISSN.1973-2201/7301","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/7301","url":null,"abstract":"Based on record data, the estimation and prediction problems for normal distribution have been investigated by several authors in the frequentist set up. However, these problems have not been discussed in the literature in the Bayesian context. The aim of this paper is to consider a Bayesian analysis in the context of record data from a normal distribution. We obtain Bayes estimators based on squared error and linear-exponential (Linex) loss functions. It is observed that the Bayes estimators can not be obtained in closed forms. We propose using an importance sampling method to obtain Bayes estimators. Further, the importance sampling method is also used to compute Bayesian predictors of future records. Finally, a real data analysis is presented for illustrative purposes and Monte Carlo simulations are performed to compare the performances of the proposed methods. It is shown that Bayes estimators and predictors are superior than frequentist estimators and predictors.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"78 1","pages":"15-36"},"PeriodicalIF":1.9,"publicationDate":"2018-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49473174","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 : 2018-07-12DOI: 10.6092/ISSN.1973-2201/7818
Sahana Bhattacharjee
This paper introduces a new counting process which is based on Generalized Exponentially distributed inter-arrival times. The advantage of this new count model over the existing Poisson count model is that the hazard function of the inter arrival time distribution is non-constant, so that the distribution is duration dependent and hence, is able to model both under dispersed and over dispersed count data, as opposed to the exponentially distributed inter arrival time of the Poisson count model, which is not duration dependent and the corresponding count model is able to model only equidispersed data. Further, some properties of this model are explored. Simulation from this new model is performed to study the behavior of count probabilities, mean and variance of the model for different values of the parameter. Use of the proposed model is illustrated with the help of real life data sets on arrival times of patients at a clinic and on arrival times of customers at a departmental store.
{"title":"A Counting Process with Generalized Exponential Inter-Arrival Times","authors":"Sahana Bhattacharjee","doi":"10.6092/ISSN.1973-2201/7818","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/7818","url":null,"abstract":"This paper introduces a new counting process which is based on Generalized Exponentially distributed inter-arrival times. The advantage of this new count model over the existing Poisson count model is that the hazard function of the inter arrival time distribution is non-constant, so that the distribution is duration dependent and hence, is able to model both under dispersed and over dispersed count data, as opposed to the exponentially distributed inter arrival time of the Poisson count model, which is not duration dependent and the corresponding count model is able to model only equidispersed data. Further, some properties of this model are explored. Simulation from this new model is performed to study the behavior of count probabilities, mean and variance of the model for different values of the parameter. Use of the proposed model is illustrated with the help of real life data sets on arrival times of patients at a clinic and on arrival times of customers at a departmental store.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"78 1","pages":"3-14"},"PeriodicalIF":1.9,"publicationDate":"2018-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45781702","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 : 2018-07-12DOI: 10.6092/ISSN.1973-2201/7495
Manoj Chacko, Laji Muraleedharan
In this paper, the lower k-record values arising from a two parameter generalized exponential distribution is considered. The maximum likelihood estimators for the shape parameter and scale parameter are obtained. The Bayes estimates of the parameters are also developed by using Markov chain Monte Carlo method under symmetric and asymmetric loss functions. Finally, a simulation study is performed to find the performance of different estimators developed in this paper.
{"title":"Inference Based on k-Record Values from Generalized Exponential Distribution","authors":"Manoj Chacko, Laji Muraleedharan","doi":"10.6092/ISSN.1973-2201/7495","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/7495","url":null,"abstract":"In this paper, the lower k-record values arising from a two parameter generalized exponential distribution is considered. The maximum likelihood estimators for the shape parameter and scale parameter are obtained. The Bayes estimates of the parameters are also developed by using Markov chain Monte Carlo method under symmetric and asymmetric loss functions. Finally, a simulation study is performed to find the performance of different estimators developed in this paper.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"78 1","pages":"37-56"},"PeriodicalIF":1.9,"publicationDate":"2018-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46338525","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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