Pub Date : 2019-07-01DOI: 10.6092/ISSN.1973-2201/8497
J. Mazucheli, A. Menezes, S. Dey
The transformed family of distributions are sometimes very useful to explore additional properties of the phenomenons which non-transformed (baseline) family of distributions cannot. In this paper, we introduce a new transformed model, called the unit-Gompertz (UG) distribution which exhibit right-skewed (unimodal) and reversed-J shaped density while the hazard rate has constant, increasing, upside-down bathtub and then bathtub shaped hazard rate. Some statistical properties of this new distribution are presented and discussed. Maximum likelihood estimation for the parameters that index UG distribution are derived along with their corresponding asymptotic standard errors. Monte Carlo simulations are conducted to investigate the bias, root mean squared error of the maximum likelihood estimators as well as the coverage probability. Finally, the potentiality of the model is presented and compared with three others distributions using two real data sets.
{"title":"Unit-Gompertz Distribution with Applications","authors":"J. Mazucheli, A. Menezes, S. Dey","doi":"10.6092/ISSN.1973-2201/8497","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/8497","url":null,"abstract":"The transformed family of distributions are sometimes very useful to explore additional properties of the phenomenons which non-transformed (baseline) family of distributions cannot. In this paper, we introduce a new transformed model, called the unit-Gompertz (UG) distribution which exhibit right-skewed (unimodal) and reversed-J shaped density while the hazard rate has constant, increasing, upside-down bathtub and then bathtub shaped hazard rate. Some statistical properties of this new distribution are presented and discussed. Maximum likelihood estimation for the parameters that index UG distribution are derived along with their corresponding asymptotic standard errors. Monte Carlo simulations are conducted to investigate the bias, root mean squared error of the maximum likelihood estimators as well as the coverage probability. Finally, the potentiality of the model is presented and compared with three others distributions using two real data sets.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"79 1","pages":"25-43"},"PeriodicalIF":1.9,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45213383","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 : 2019-03-21DOI: 10.6092/ISSN.1973-2201/7819
E. I. Abdul-Sathar, G. S. Sathyareji
In this paper, we proposed MLE and Bayes estimators of parameters and DCPE for the two parameter power function distribution. Bayes estimators under different loss functions are obtained using Lindley approximation method and important sampling procedures. A real life data set and a Monte Carlo simulation are used to study the performance of the estimators derived in the article.
{"title":"Estimation of Dynamic Cumulative Past Entropy for Power Function Distribution","authors":"E. I. Abdul-Sathar, G. S. Sathyareji","doi":"10.6092/ISSN.1973-2201/7819","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/7819","url":null,"abstract":"In this paper, we proposed MLE and Bayes estimators of parameters and DCPE for the two parameter power function distribution. Bayes estimators under different loss functions are obtained using Lindley approximation method and important sampling procedures. A real life data set and a Monte Carlo simulation are used to study the performance of the estimators derived in the article.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"78 1","pages":"319-334"},"PeriodicalIF":1.9,"publicationDate":"2019-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42852433","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 : 2019-03-21DOI: 10.6092/ISSN.1973-2201/8242
Rahmath Manzil Juvairiyya, P. Anilkumar
In this paper, the estimation of stress-strength reliability based on upper record values is considered when X and Y are independent random variables having a Pareto distribution with the same scale parameter and with different shape parameters. The maximum likelihood estimator (MLE), the approximate Bayes estimators and the exact confidence interval of the stress-strength reliability are obtained. A Monte Carlo simulation study is conducted to investigate the merits of the proposed methods. A real data analysis is presented for illustrative purpose.
{"title":"Estimation of Stress-Strength Reliability for the Pareto Distribution Based on Upper Record Values","authors":"Rahmath Manzil Juvairiyya, P. Anilkumar","doi":"10.6092/ISSN.1973-2201/8242","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/8242","url":null,"abstract":"In this paper, the estimation of stress-strength reliability based on upper record values is considered when X and Y are independent random variables having a Pareto distribution with the same scale parameter and with different shape parameters. The maximum likelihood estimator (MLE), the approximate Bayes estimators and the exact confidence interval of the stress-strength reliability are obtained. A Monte Carlo simulation study is conducted to investigate the merits of the proposed methods. A real data analysis is presented for illustrative purpose.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"78 1","pages":"397-409"},"PeriodicalIF":1.9,"publicationDate":"2019-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43375513","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 : 2019-03-21DOI: 10.6092/ISSN.1973-2201/8598
A. Pallini
Discrete power distributions are proposed and studied, by considering the positive jumps on the discontinuities of an original discrete distribution function. Inequalities in moments and distribution functions are studied, allowing the definition of discrete intermediate distributions that lie between an original distribution and a power distribution. Original uniform, binomial, Poisson, negative binomial, and hypergeometric distributions are considered, to propose new power and intermediate distributions. Stochastic orders and unimodality are discussed. Estimation problems using likelihood are investigated. Simulation experiments are performed, to evaluate the bias and the mean square error of the maximum likelihood estimates, that are numerically calculated, with classic tools for numerical optimization.
{"title":"Discrete power distributions and inference using likelihood","authors":"A. Pallini","doi":"10.6092/ISSN.1973-2201/8598","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/8598","url":null,"abstract":"Discrete power distributions are proposed and studied, by considering the positive jumps on the discontinuities of an original discrete distribution function. Inequalities in moments and distribution functions are studied, allowing the definition of discrete intermediate distributions that lie between an original distribution and a power distribution. Original uniform, binomial, Poisson, negative binomial, and hypergeometric distributions are considered, to propose new power and intermediate distributions. Stochastic orders and unimodality are discussed. Estimation problems using likelihood are investigated. Simulation experiments are performed, to evaluate the bias and the mean square error of the maximum likelihood estimates, that are numerically calculated, with classic tools for numerical optimization.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"78 1","pages":"335-362"},"PeriodicalIF":1.9,"publicationDate":"2019-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45510141","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 : 2019-03-21DOI: 10.6092/ISSN.1973-2201/7503
E. Mahmoudi, R. Meshkat, Batool Kargar, D. Kundu
In this paper, we introduce a univariate four-parameter distribution. Several known distributions like exponentiated Weibull or extended generalized exponential distribution can be obtained as special case of this distribution. The new distribution is quite flexible and can be used quite effectively in analysing survival or reliability data. It can have a decreasing, increasing, decreasing-increasing-decreasing (DID), upside-down bathtub (unimodal) and bathtub-shaped failure rate function depending on its parameters. We provide a comprehensive account of the mathematical properties of the new distribution. In particular, we derive expressions for the moments, mean deviations, Renyi and Shannon entropy. We discuss maximum likelihood estimation of the unknown parameters of the new model for censored and complete sample using the profile and modified likelihood functions. One empirical application of the new model to real data are presented for illustrative purposes.
{"title":"The Extended Exponentiated Weibull Distribution and its Applications","authors":"E. Mahmoudi, R. Meshkat, Batool Kargar, D. Kundu","doi":"10.6092/ISSN.1973-2201/7503","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/7503","url":null,"abstract":"In this paper, we introduce a univariate four-parameter distribution. Several known distributions like exponentiated Weibull or extended generalized exponential distribution can be obtained as special case of this distribution. The new distribution is quite flexible and can be used quite effectively in analysing survival or reliability data. It can have a decreasing, increasing, decreasing-increasing-decreasing (DID), upside-down bathtub (unimodal) and bathtub-shaped failure rate function depending on its parameters. We provide a comprehensive account of the mathematical properties of the new distribution. In particular, we derive expressions for the moments, mean deviations, Renyi and Shannon entropy. We discuss maximum likelihood estimation of the unknown parameters of the new model for censored and complete sample using the profile and modified likelihood functions. One empirical application of the new model to real data are presented for illustrative purposes.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"78 1","pages":"363-396"},"PeriodicalIF":1.9,"publicationDate":"2019-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42534072","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 : 2019-01-01DOI: 10.6092/ISSN.1973-2201/9854
G. Rossi, P. Pepe, O. Curzio, M. Marchi
The capture-recapture method is widely used by epidemiologists to estimate the size of hidden populations using incomplete and overlapping lists of subjects. Closed populations, heterogeneity of inclusion probabilities and dependence between lists are taken into consideration in this work. The main objective is to propose a new parameterization for the Poisson log linear odel (LLM) to treat continuous covariates in their original measurement scale. The analytic estimate of the confidence bounds of the hidden population is also provided. Proposed model was applied to simulated and real capture-recapture data and compared with the multinomial conditional logit model (MCLM). The proposed model is very similar to the MCLM in dealing with continuous covariates and the analytic confidence interval performs better than the bootstrap estimate in case of small sample size.
{"title":"Parameterization of Continuous Covariates in the Poisson Capture-Recapture Log Linear Model for Closed Populations","authors":"G. Rossi, P. Pepe, O. Curzio, M. Marchi","doi":"10.6092/ISSN.1973-2201/9854","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/9854","url":null,"abstract":"The capture-recapture method is widely used by epidemiologists to estimate the size of hidden populations using incomplete and overlapping lists of subjects. Closed populations, heterogeneity of inclusion probabilities and dependence between lists are taken into consideration in this work. The main objective is to propose a new parameterization for the Poisson log linear odel (LLM) to treat continuous covariates in their original measurement scale. The analytic estimate of the confidence bounds of the hidden population is also provided. Proposed model was applied to simulated and real capture-recapture data and compared with the multinomial conditional logit model (MCLM). The proposed model is very similar to the MCLM in dealing with continuous covariates and the analytic confidence interval performs better than the bootstrap estimate in case of small sample size.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"79 1","pages":"427-443"},"PeriodicalIF":1.9,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71256313","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 : 2018-12-21DOI: 10.6092/ISSN.1973-2201/8211
Dileep Kumar Maladan, P. Sankaran, N. Nair
Relevation transform introduced by Krakowski (1973) is extensively studied in the literature. In this paper, we present a quantile based definition of the relevation transform and study its properties in the context of lifetime data analysis. We give important special cases of relevation transform in the context of proportional hazards and equilibrium models in terms of quantile function.
{"title":"Quantile Based Relevation Transform and its Properties","authors":"Dileep Kumar Maladan, P. Sankaran, N. Nair","doi":"10.6092/ISSN.1973-2201/8211","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/8211","url":null,"abstract":"Relevation transform introduced by Krakowski (1973) is extensively studied in the literature. In this paper, we present a quantile based definition of the relevation transform and study its properties in the context of lifetime data analysis. We give important special cases of relevation transform in the context of proportional hazards and equilibrium models in terms of quantile function.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"78 1","pages":"197-214"},"PeriodicalIF":1.9,"publicationDate":"2018-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47629775","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 : 2018-12-21DOI: 10.6092/ISSN.1973-2201/7662
H. Yousof, A. Afify, S. Nadarajah, G. Hamedani, G. Aryal
We introduce a new class of distributions called the Marshall-Olkin generalized-G family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, order statistics are discussed. The maximum likelihood method is used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of two applications to real data sets.
{"title":"The Marshall-Olkin Generalized-G Family of Distributions with Applications","authors":"H. Yousof, A. Afify, S. Nadarajah, G. Hamedani, G. Aryal","doi":"10.6092/ISSN.1973-2201/7662","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/7662","url":null,"abstract":"We introduce a new class of distributions called the Marshall-Olkin generalized-G family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, order statistics are discussed. The maximum likelihood method is used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of two applications to real data sets.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"78 1","pages":"273-295"},"PeriodicalIF":1.9,"publicationDate":"2018-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45458473","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 : 2018-12-21DOI: 10.6092/ISSN.1973-2201/6930
Priyanka Singh, A. Singh, V. Singh
In this paper we have proposed an imputation method based on a family of factor-type estimator to deal with the problem of non-response assuming that the target population has been sampled at two different occasions. The aim is to estimate the current population mean on the basis of matching the sample from the previous occasion and on the basis of fresh sample selected at the current occasion. It has been assumed that the non-response is exhibited by the population at both the occasions and, therefore, the imputation of missing values is required in both the samples, namely, matched sample and fresh sample. Accordingly, a combined point estimator has been suggested after imputation which generates a one-parameter family of estimators. The properties of the estimator have been investigated and the replacement policy has been discussed. Finally, the comparison of the proposed class has been made with another estimator for their performances.
{"title":"On the Adjustment of Non-Response through Imputation for Estimating Current Mean in Repeated Surveys","authors":"Priyanka Singh, A. Singh, V. Singh","doi":"10.6092/ISSN.1973-2201/6930","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/6930","url":null,"abstract":"In this paper we have proposed an imputation method based on a family of factor-type estimator to deal with the problem of non-response assuming that the target population has been sampled at two different occasions. The aim is to estimate the current population mean on the basis of matching the sample from the previous occasion and on the basis of fresh sample selected at the current occasion. It has been assumed that the non-response is exhibited by the population at both the occasions and, therefore, the imputation of missing values is required in both the samples, namely, matched sample and fresh sample. Accordingly, a combined point estimator has been suggested after imputation which generates a one-parameter family of estimators. The properties of the estimator have been investigated and the replacement policy has been discussed. Finally, the comparison of the proposed class has been made with another estimator for their performances.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"78 1","pages":"215-232"},"PeriodicalIF":1.9,"publicationDate":"2018-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47971923","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 : 2018-12-21DOI: 10.6092/ISSN.1973-2201/8123
N. Ekhosuehi, F. Opone
In this paper, we introduced a new class of lifetime distribution and considered the mathematical properties of one of the sub models called a three parameter generalized Lindley distribution (TPGLD). The new class of distributions generalizes some of the Lindley family of distribution such as the power Lindley distribution, the Sushila distribution, the Lindley-Pareto distribution, the Lindley-half logistic distribution and the classical Lindley distribution. An application of the TPGLD to two real lifetime data sets reveals its superiority over the exponentiated power Lindley distribution, the exponentiated Lindley geometric distribution, the power Lindley distribution, the Lindley-exponential distribution and the classical one parameter Lindley distribution in modeling the lifetime data sets under study.
{"title":"A Three Parameter Generalized Lindley Distribution: Properties and Application","authors":"N. Ekhosuehi, F. Opone","doi":"10.6092/ISSN.1973-2201/8123","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/8123","url":null,"abstract":"In this paper, we introduced a new class of lifetime distribution and considered the mathematical properties of one of the sub models called a three parameter generalized Lindley distribution (TPGLD). The new class of distributions generalizes some of the Lindley family of distribution such as the power Lindley distribution, the Sushila distribution, the Lindley-Pareto distribution, the Lindley-half logistic distribution and the classical Lindley distribution. An application of the TPGLD to two real lifetime data sets reveals its superiority over the exponentiated power Lindley distribution, the exponentiated Lindley geometric distribution, the power Lindley distribution, the Lindley-exponential distribution and the classical one parameter Lindley distribution in modeling the lifetime data sets under study.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"78 1","pages":"233-249"},"PeriodicalIF":1.9,"publicationDate":"2018-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44741331","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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