Pub Date : 2020-03-12DOI: 10.6092/ISSN.1973-2201/8054
Shashi Bhushan, A. Pandey
This paper introduces an efficient estimation procedure for the population mean in the presence of non-response. The proposed estimators of population mean provides an improvement over the corresponding conventional estimators proposed by Cochran (1977), Rao (1983, 1986) and Singh and Kumar (2008, 2010) under the deterministic non-response in terms of efficiency. A comparative study has been performed and it has been shown that the proposed estimators perform better in comparison to the conventional estimators. The theoretical findings are supported by an empirical study.
{"title":"An Efficient Estimation Procedure for the Population Mean under Non-Response","authors":"Shashi Bhushan, A. Pandey","doi":"10.6092/ISSN.1973-2201/8054","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/8054","url":null,"abstract":"This paper introduces an efficient estimation procedure for the population mean in the presence of non-response. The proposed estimators of population mean provides an improvement over the corresponding conventional estimators proposed by Cochran (1977), Rao (1983, 1986) and Singh and Kumar (2008, 2010) under the deterministic non-response in terms of efficiency. A comparative study has been performed and it has been shown that the proposed estimators perform better in comparison to the conventional estimators. The theoretical findings are supported by an empirical study.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2020-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42724162","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 : 2020-03-12DOI: 10.6092/ISSN.1973-2201/8442
S. Dey, M. Nassar, D. Kumar, A. Alzaatreh, Muhammad Mohsin Tahir
We introduce a new lifetime distribution, called the alpha-power transformed Lomax (APTL) distribution which generalizes the Lomax distribution to provide better fits than the Lomax distribution and some of its known generalizations. Various properties of the proposed distribution, including explicit expressions for the quantiles, mode, moments, conditional moments, mean residual lifetime, stochastic ordering, Bonferroni and Lorenz curve, stress-strength reliability and order statistics are derived. The new distribution can have a decreasing and upside-down bathtub failure rate function depending on its parameters. The maximum likelihood estimators of the three unknown parameters of APTL are obtained. A simulation study is carried out to examine the performances of the maximum likelihood estimates in terms of their mean squared error using simulated samples. Finally, the potentiality of the distribution is analyzed by means of two real data sets. For the real data sets, this distribution is found to be superior in its ability to sufficiently model both the data sets as compared to the Lomax (L) distribution, exponentiated-Lomax (EL) distribution, gamma-Lomax (GL) distribution, beta-Lomax (BL) distribution and Kumaraswamy-Lomax (KuL) distribution.
{"title":"A New Lifetime Distribution with Decreasing and Upside-Down Bathtub-Shaped Hazard Rate Function","authors":"S. Dey, M. Nassar, D. Kumar, A. Alzaatreh, Muhammad Mohsin Tahir","doi":"10.6092/ISSN.1973-2201/8442","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/8442","url":null,"abstract":"We introduce a new lifetime distribution, called the alpha-power transformed Lomax (APTL) distribution which generalizes the Lomax distribution to provide better fits than the Lomax distribution and some of its known generalizations. Various properties of the proposed distribution, including explicit expressions for the quantiles, mode, moments, conditional moments, mean residual lifetime, stochastic ordering, Bonferroni and Lorenz curve, stress-strength reliability and order statistics are derived. The new distribution can have a decreasing and upside-down bathtub failure rate function depending on its parameters. The maximum likelihood estimators of the three unknown parameters of APTL are obtained. A simulation study is carried out to examine the performances of the maximum likelihood estimates in terms of their mean squared error using simulated samples. Finally, the potentiality of the distribution is analyzed by means of two real data sets. For the real data sets, this distribution is found to be superior in its ability to sufficiently model both the data sets as compared to the Lomax (L) distribution, exponentiated-Lomax (EL) distribution, gamma-Lomax (GL) distribution, beta-Lomax (BL) distribution and Kumaraswamy-Lomax (KuL) distribution.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2020-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45384342","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 : 2020-03-12DOI: 10.6092/ISSN.1973-2201/9764
Moumita Chatterjee, S. S. Roy
In this paper, we study the pattern of inclusion and exclusion of players from a team in any team sport. Usually these inclusions and exclusions are related to the player’s performance in the matches previously played. Also the inclusion and exclusion at any particular cycle depends on the player’s history as observed through the number of times he has been included or excluded previously. The focus of this paper is to study this pattern for cricketers who have represented their respective countries in One Day Internationals (ODIs). As observed in the study, there is a distinct difference in the inclusion and exclusion patterns of bowlers and batsmen, and hence the two groups have been studied separately. Respective survival functions over the cycles of inclusion and exclusion have been constructed for both groups. These reveal several interesting features regarding the chances of an ODI cricketer being retained or dropped from the team.
{"title":"A Study on the Selection Pattern of Players in any Team Sport","authors":"Moumita Chatterjee, S. S. Roy","doi":"10.6092/ISSN.1973-2201/9764","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/9764","url":null,"abstract":"In this paper, we study the pattern of inclusion and exclusion of players from a team in any team sport. Usually these inclusions and exclusions are related to the player’s performance in the matches previously played. Also the inclusion and exclusion at any particular cycle depends on the player’s history as observed through the number of times he has been included or excluded previously. The focus of this paper is to study this pattern for cricketers who have represented their respective countries in One Day Internationals (ODIs). As observed in the study, there is a distinct difference in the inclusion and exclusion patterns of bowlers and batsmen, and hence the two groups have been studied separately. Respective survival functions over the cycles of inclusion and exclusion have been constructed for both groups. These reveal several interesting features regarding the chances of an ODI cricketer being retained or dropped from the team.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2020-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43290099","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 : 2020-01-01DOI: 10.6092/ISSN.1973-2201/9765
A. Abubakari, C. C. Kandza-Tadi, R. R. Dimmua
The Lomax distribution has a wide range of applications. Due to this, it has had many extensions to render it more flexible and useful to model real world data. In this study, a new family of distributions called the extended odd Lomax family of distributions is introduced by adding two extra shape parameters and one scale parameter. We derived several statistical properties of the new family of distributions. The parameters of the family of distributions are estimated by the use of maximum likelihood method and the consistency of the estimators investigated via Monte Carlo simulations. The usefulness and flexibility of the new family of distributions are illustrated by the use of two real datasets. The results show that the distributions adequately describe the datasets.
{"title":"Extended Odd Lomax Family of Distributions: Properties and Applications","authors":"A. Abubakari, C. C. Kandza-Tadi, R. R. Dimmua","doi":"10.6092/ISSN.1973-2201/9765","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/9765","url":null,"abstract":"The Lomax distribution has a wide range of applications. Due to this, it has had many extensions to render it more flexible and useful to model real world data. In this study, a new family of distributions called the extended odd Lomax family of distributions is introduced by adding two extra shape parameters and one scale parameter. We derived several statistical properties of the new family of distributions. The parameters of the family of distributions are estimated by the use of maximum likelihood method and the consistency of the estimators investigated via Monte Carlo simulations. The usefulness and flexibility of the new family of distributions are illustrated by the use of two real datasets. The results show that the distributions adequately describe the datasets.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71256463","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 : 2020-01-01DOI: 10.6092/ISSN.1973-2201/9887
A. S. Krishnan, S. Sunoj, P. Sankaran
Extropy is a recent addition to the family of information measures as a complementary dual of Shannon entropy, to measure the uncertainty contained in a probability distribution of a random variable. A probability distribution can be specified either in terms of the distribution function or by the quantile function. In many applied works, there do not have any tractable distribution function but the quantile function exists, where a study on the quantile-based extropy are of importance. The present paper thus focuses on deriving some properties of extropy and its related measures using quantile function. Some ordering relations of quantile-based residual extropy are presented. We also introduce the quantile-based extropy of order statistics and cumulative extropy and studied its properties. Some applications of empirical estimation of quantile-based extropy using simulation and real data analysis are investigated.
{"title":"Some Reliability Properties of Extropy and its Related Measures Using Quantile Function","authors":"A. S. Krishnan, S. Sunoj, P. Sankaran","doi":"10.6092/ISSN.1973-2201/9887","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/9887","url":null,"abstract":"Extropy is a recent addition to the family of information measures as a complementary dual of Shannon entropy, to measure the uncertainty contained in a probability distribution of a random variable. A probability distribution can be specified either in terms of the distribution function or by the quantile function. In many applied works, there do not have any tractable distribution function but the quantile function exists, where a study on the quantile-based extropy are of importance. The present paper thus focuses on deriving some properties of extropy and its related measures using quantile function. Some ordering relations of quantile-based residual extropy are presented. We also introduce the quantile-based extropy of order statistics and cumulative extropy and studied its properties. Some applications of empirical estimation of quantile-based extropy using simulation and real data analysis are investigated.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71256690","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 : 2019-11-06DOI: 10.6092/ISSN.1973-2201/9331
A. S. Nik, A. Asgharzadeh, S. Nadarajah
Bourguignon et al. (2016) introduced a new Pareto-type distribution to model income and reliability data. The aim of this paper is to estimate the parameters of this distribution from both frequentist and Bayesian view points. The maximum likelihood estimates, method of moment estimates, percentile estimates, least square and weighted least square estimates and maximum product of spacing estimates are considered as frequentist estimates. We have also considered the Bayes estimates of the unknown parameters and the associated credible intervals. The Bayes estimates are computed using an importance sampling method. To evaluate the performance of the different estimates, a Monte Carlo simulation study is carried out. Some real life data sets have been analyzed for illustrative purposes.
{"title":"Comparisons of Methods of Estimation for a New Pareto-type Distribution","authors":"A. S. Nik, A. Asgharzadeh, S. Nadarajah","doi":"10.6092/ISSN.1973-2201/9331","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/9331","url":null,"abstract":"Bourguignon et al. (2016) introduced a new Pareto-type distribution to model income and reliability data. The aim of this paper is to estimate the parameters of this distribution from both frequentist and Bayesian view points. The maximum likelihood estimates, method of moment estimates, percentile estimates, least square and weighted least square estimates and maximum product of spacing estimates are considered as frequentist estimates. We have also considered the Bayes estimates of the unknown parameters and the associated credible intervals. The Bayes estimates are computed using an importance sampling method. To evaluate the performance of the different estimates, a Monte Carlo simulation study is carried out. Some real life data sets have been analyzed for illustrative purposes.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2019-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47291555","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 : 2019-11-06DOI: 10.6092/ISSN.1973-2201/8782
A. Yadav
In this article, we proposed and studied the inverted exponentiated gamma distribution (IEGD). IEGD is obtained by considering the inverse transformation of exponentiated gamma variate. This distribution has been motivated by the extensive use of the exponentiated gamma model in many applied areas and also due to the fact that this new generalization provides more flexibility to analyze real data with upside down bathtub (UBT) hazard rate. The shape of the distribution has been traced mathematically and found that the proposed model is compatible with UBT hazard rate models. The tail area property is also presented based on the idea of Marshall and Olkin (2007) and it is concluded that the new model belongs to the family of heavy-tailed distributions. Some other characteristics such as reliability, hazard, the quantile function, skewness and kurtosis, stochastic ordering, stress-strength reliability and order statistics have been explicitly derived. The classical and Bayesian estimation procedures have been discussed to estimate the unknown parameter of IEGD. The performances of classical and Bayes estimators are studied in terms of average mean square error (MSE) by conducting Monte Carlo simulations. Finally, a real data set with UBT type hazard rate is analyzed for the illustrative purpose of the study.
{"title":"The Inverted Exponentiated Gamma Distribution: A Heavy-Tailed Model with Upside Down Bathtub Shaped Hazard Rate","authors":"A. Yadav","doi":"10.6092/ISSN.1973-2201/8782","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/8782","url":null,"abstract":"In this article, we proposed and studied the inverted exponentiated gamma distribution (IEGD). IEGD is obtained by considering the inverse transformation of exponentiated gamma variate. This distribution has been motivated by the extensive use of the exponentiated gamma model in many applied areas and also due to the fact that this new generalization provides more flexibility to analyze real data with upside down bathtub (UBT) hazard rate. The shape of the distribution has been traced mathematically and found that the proposed model is compatible with UBT hazard rate models. The tail area property is also presented based on the idea of Marshall and Olkin (2007) and it is concluded that the new model belongs to the family of heavy-tailed distributions. Some other characteristics such as reliability, hazard, the quantile function, skewness and kurtosis, stochastic ordering, stress-strength reliability and order statistics have been explicitly derived. The classical and Bayesian estimation procedures have been discussed to estimate the unknown parameter of IEGD. The performances of classical and Bayes estimators are studied in terms of average mean square error (MSE) by conducting Monte Carlo simulations. Finally, a real data set with UBT type hazard rate is analyzed for the illustrative purpose of the study.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2019-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47564797","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 : 2019-11-06DOI: 10.6092/ISSN.1973-2201/8462
Jayakumar Kuttan Pillai, Girish Babu Moolath
A new generalization of the Frechet distribution is introduced and studied. Its structural properties including the quantile function, random number generation, moments, moment generating function and order statistics are investigated. The unknown parameters of the model are estimated using maximum likelihood estimation method and a simulation study is carried out to check the performance of the method. The new model is applied to a real data set to prove empirically its flexibility.
{"title":"A New Generalization of the Fréchet Distribution: Properties and Application","authors":"Jayakumar Kuttan Pillai, Girish Babu Moolath","doi":"10.6092/ISSN.1973-2201/8462","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/8462","url":null,"abstract":"A new generalization of the Frechet distribution is introduced and studied. Its structural properties including the quantile function, random number generation, moments, moment generating function and order statistics are investigated. The unknown parameters of the model are estimated using maximum likelihood estimation method and a simulation study is carried out to check the performance of the method. The new model is applied to a real data set to prove empirically its flexibility.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2019-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46285045","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 : 2019-11-06DOI: 10.6092/ISSN.1973-2201/7496
Bindu Krishnan, Dais George
The Weibull distribution is one of the widely known lifetime distribution that has been extensively used for modelling data in reliability and survival analysis. A generalization of both the Marshall-OlkinWeibull distribution and the Weibull truncated negative binomial distribution is introduced and studied in this article. Various distributional properties of the new distribution are derived. Estimation of model parameters using the method of maximum likelihood is discussed. Applications to a real data set is provided to show the flexibility and potentiality of the new distribution over other Weibull models. The first order autoregressive minification process with the new distribution as marginal is also developed. We hope that the new model will serve as a good alternative to other models available in the literature for modeling positive real data in several areas.
{"title":"The Marshall-Olkin Weibull Truncated Negative Binomial Distribution and its Applications","authors":"Bindu Krishnan, Dais George","doi":"10.6092/ISSN.1973-2201/7496","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/7496","url":null,"abstract":"The Weibull distribution is one of the widely known lifetime distribution that has been extensively used for modelling data in reliability and survival analysis. A generalization of both the Marshall-OlkinWeibull distribution and the Weibull truncated negative binomial distribution is introduced and studied in this article. Various distributional properties of the new distribution are derived. Estimation of model parameters using the method of maximum likelihood is discussed. Applications to a real data set is provided to show the flexibility and potentiality of the new distribution over other Weibull models. The first order autoregressive minification process with the new distribution as marginal is also developed. We hope that the new model will serve as a good alternative to other models available in the literature for modeling positive real data in several areas.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2019-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46365855","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 : 2019-11-06DOI: 10.6092/ISSN.1973-2201/8930
Cherif Ahmat Tidiane Aidara
In this paper, we present two new algorithms that use the shuffled Sobol sequence to generate the bootstrap resampling designs in multiple frame surveys. We investigate the performance of the proposed algorithms in a simulation study using a three-overlapping frame setup design. The samples were selected independently from the frames using a stratified simple random sampling design. The performance of the proposed methods is comparable with the already established ones such as the Lohr-Rao bootstrap methods for multiple frame surveys in terms of relative percentage bias, coefficient of variation, and empirical coverage probabilities of 95 percent confidence interval.
{"title":"Quasi Random Resampling Designs for Multiple Frame Surveys","authors":"Cherif Ahmat Tidiane Aidara","doi":"10.6092/ISSN.1973-2201/8930","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/8930","url":null,"abstract":"In this paper, we present two new algorithms that use the shuffled Sobol sequence to generate the bootstrap resampling designs in multiple frame surveys. We investigate the performance of the proposed algorithms in a simulation study using a three-overlapping frame setup design. The samples were selected independently from the frames using a stratified simple random sampling design. The performance of the proposed methods is comparable with the already established ones such as the Lohr-Rao bootstrap methods for multiple frame surveys in terms of relative percentage bias, coefficient of variation, and empirical coverage probabilities of 95 percent confidence interval.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2019-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49560598","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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