Pub Date : 2020-09-01DOI: 10.2991/jsta.d.200827.002
S. Abbas, Fakhar Mustafa, Syed Ali Taqi, S. Cakmakyapan, G. Ozel
{"title":"A Note on Topp-Leone Odd Log-Logistic Inverse Exponential Distribution","authors":"S. Abbas, Fakhar Mustafa, Syed Ali Taqi, S. Cakmakyapan, G. Ozel","doi":"10.2991/jsta.d.200827.002","DOIUrl":"https://doi.org/10.2991/jsta.d.200827.002","url":null,"abstract":"","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"31 1","pages":"397-407"},"PeriodicalIF":1.0,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84730500","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 : 2020-09-01DOI: 10.2991/jsta.d.200826.001
S. Bagui, Jia Liu, S. Zhang
This article aims to make use of moment-generating functions (mgfs) to derive the density of mixture distributions from hierarchical models. When the mgf of a mixture distribution doesn’t exist, one can extend the approach to characteristic functions to derive the mixture density. This article uses a result given by E.R. Villa, L.A. Escobar, Am. Stat. 60 (2006), 75–80. The present work complements E.R. Villa, L.A. Escobar, Am. Stat. 60 (2006), 75–80 article with many new examples.
{"title":"Deriving Mixture Distributions Through Moment-Generating Functions","authors":"S. Bagui, Jia Liu, S. Zhang","doi":"10.2991/jsta.d.200826.001","DOIUrl":"https://doi.org/10.2991/jsta.d.200826.001","url":null,"abstract":"This article aims to make use of moment-generating functions (mgfs) to derive the density of mixture distributions from hierarchical models. When the mgf of a mixture distribution doesn’t exist, one can extend the approach to characteristic functions to derive the mixture density. This article uses a result given by E.R. Villa, L.A. Escobar, Am. Stat. 60 (2006), 75–80. The present work complements E.R. Villa, L.A. Escobar, Am. Stat. 60 (2006), 75–80 article with many new examples.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"25 1","pages":"383-390"},"PeriodicalIF":1.0,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77677485","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 : 2020-07-01DOI: 10.2991/jsta.d.200514.001
M. Arshad, Muhammad Iqbal, M. Ahmad
In this study, we have focused to propose a flexible model that demonstrates increasing, decreasing and upside-down bathtub-shaped density and failure rate functions. The proposed model refers to as the exponentiated power function (EPF) distribution. Some mathematical and reliability measures are developed and derived. We develop explicit expressions for the moments, quan- tile function and order statistics. Some shapes of the density and the reliability functions are sketched out and discussed. We suggest the method to estimate the unknown parameters of EPF by the maximum likelihood estimation. Two suitable lifetime datasets from engineering sector are used to explore the dominance of the EPF distribution.
{"title":"Exponentiated Power Function Distribution: Properties and Applications","authors":"M. Arshad, Muhammad Iqbal, M. Ahmad","doi":"10.2991/jsta.d.200514.001","DOIUrl":"https://doi.org/10.2991/jsta.d.200514.001","url":null,"abstract":"In this study, we have focused to propose a flexible model that demonstrates increasing, decreasing and upside-down bathtub-shaped density and failure rate functions. The proposed model refers to as the exponentiated power function (EPF) distribution. Some mathematical and reliability measures are developed and derived. We develop explicit expressions for the moments, quan- tile function and order statistics. Some shapes of the density and the reliability functions are sketched out and discussed. We suggest the method to estimate the unknown parameters of EPF by the maximum likelihood estimation. Two suitable lifetime datasets from engineering sector are used to explore the dominance of the EPF distribution.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"19 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72917041","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 : 2020-07-01DOI: 10.2991/jsta.d.200423.001
R. Ahmed, Farrukh Shehzad, Muhammad Jamil, H. M. K. Rasheed
Circular regular graph designs play an important role in the design of experiments where most of the balanced incomplete block designs require a large number of blocks. In this article, circular regular graph designs are constructed in blocks of size four through cyclic shifts. Without studying the complete design, some standard properties of the designs can be observed only through the sets of shifts. Therefore, method of cyclic shifts has an edge over existing methods.
{"title":"Construction of Some Circular Regular Graph Designs in Blocks of Size Four Using Cyclic Shifts","authors":"R. Ahmed, Farrukh Shehzad, Muhammad Jamil, H. M. K. Rasheed","doi":"10.2991/jsta.d.200423.001","DOIUrl":"https://doi.org/10.2991/jsta.d.200423.001","url":null,"abstract":"Circular regular graph designs play an important role in the design of experiments where most of the balanced incomplete block designs require a large number of blocks. In this article, circular regular graph designs are constructed in blocks of size four through cyclic shifts. Without studying the complete design, some standard properties of the designs can be observed only through the sets of shifts. Therefore, method of cyclic shifts has an edge over existing methods.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"28 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84602029","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 : 2020-07-01DOI: 10.2991/jsta.d.200714.001
Anwar Hassan, Mehraj Ahmad
In this paper a generalized exponential distribution is considered for analyzing left-censored lifetime data as such mecha-nisms are applicable when the observations become available in an ordered manner with some cases where the origin and the event both occur prior to the start of follow-up. In the present study a test procedure is developed which will approxi-mate a prescribed operating characteristics curve. We also done testing of hypothesis and tried to find values of r and C subject to the operating characteristics curve be such that L . α 1 / = Pr ( accept α = α 1 when α 1 isthetruevalue ) = 1 − γ and L . α 2 / = Pr ( accept α = α 1 when α 2 isthetruevalue ) ≤ β . By simulation technique it has been shown that a suitable value of r is to be used for different values of γ and β . The by Atlantis B.V. This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
{"title":"Behavior of OC Curve of Generalized Exponentiated Data","authors":"Anwar Hassan, Mehraj Ahmad","doi":"10.2991/jsta.d.200714.001","DOIUrl":"https://doi.org/10.2991/jsta.d.200714.001","url":null,"abstract":"In this paper a generalized exponential distribution is considered for analyzing left-censored lifetime data as such mecha-nisms are applicable when the observations become available in an ordered manner with some cases where the origin and the event both occur prior to the start of follow-up. In the present study a test procedure is developed which will approxi-mate a prescribed operating characteristics curve. We also done testing of hypothesis and tried to find values of r and C subject to the operating characteristics curve be such that L . α 1 / = Pr ( accept α = α 1 when α 1 isthetruevalue ) = 1 − γ and L . α 2 / = Pr ( accept α = α 1 when α 2 isthetruevalue ) ≤ β . By simulation technique it has been shown that a suitable value of r is to be used for different values of γ and β . The by Atlantis B.V. This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"33 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90508778","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 : 2020-07-01DOI: 10.2991/jsta.d.200508.001
H. Rimsha, Dais George
This paper we introduced a new distribution namely the multivariate Esscher transformed Laplace distribution. Various properties of the distribution are studied and the applications are discussed. Further we develop an autoregressive process with multi-variateETLmarginalandstudyitsproperties.ALevyprocessbasedonthismultivariateinfinitelydivisibledistributionisknown as Laplace motion, and its marginal distributions are multivariate generalized Esscher transformed Laplace distribution.
{"title":"Multivariate Escher Transformed Laplace Distribution and Its Generalization","authors":"H. Rimsha, Dais George","doi":"10.2991/jsta.d.200508.001","DOIUrl":"https://doi.org/10.2991/jsta.d.200508.001","url":null,"abstract":"This paper we introduced a new distribution namely the multivariate Esscher transformed Laplace distribution. Various properties of the distribution are studied and the applications are discussed. Further we develop an autoregressive process with multi-variateETLmarginalandstudyitsproperties.ALevyprocessbasedonthismultivariateinfinitelydivisibledistributionisknown as Laplace motion, and its marginal distributions are multivariate generalized Esscher transformed Laplace distribution.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"74 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74645100","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 : 2020-06-01DOI: 10.2991/jsta.d.200512.002
F. Louzada, V. Cancho, P. Ferreira
In this paper we propose a new three-parameters lifetime distribution with increasing, decreasing and bathtub failure rate dependingonitsparameters.Theproperties oftheproposed distributionarediscussed,includingexplicitalgebraicformulaefor its reliability and failure rate functions, quantiles and moments. A simulation study is performed in order to verify the behavior of the maximum likelihood estimates. The methodology is illustrated on a real data set.
{"title":"The Exponentiated Poisson-Exponential Distribution: A Distribution with Increasing, Decreasing and Bathtub Failure Rate","authors":"F. Louzada, V. Cancho, P. Ferreira","doi":"10.2991/jsta.d.200512.002","DOIUrl":"https://doi.org/10.2991/jsta.d.200512.002","url":null,"abstract":"In this paper we propose a new three-parameters lifetime distribution with increasing, decreasing and bathtub failure rate dependingonitsparameters.Theproperties oftheproposed distributionarediscussed,includingexplicitalgebraicformulaefor its reliability and failure rate functions, quantiles and moments. A simulation study is performed in order to verify the behavior of the maximum likelihood estimates. The methodology is illustrated on a real data set.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"47 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76143872","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 : 2020-06-01DOI: 10.2991/jsta.d.200507.003
N. Uddin, M. Hasan
A new test statistic is proposed to test the equality of two normal means when the data is partially paired and partially unpaired. The test statistic is based on a linear combination of the differences of both paired and unpaired sample means. Using t-distribution as the approximate null distribution, the proposed method is evaluated against some other standard methods known in the literature. For samples from normal and logistic distributions with equal variances, the proposed method appears to perform better than other methods with respect to power while keeping the type I error rates very competitive.
{"title":"Comparing Two Means Using Partially Paired and Unpaired Data","authors":"N. Uddin, M. Hasan","doi":"10.2991/jsta.d.200507.003","DOIUrl":"https://doi.org/10.2991/jsta.d.200507.003","url":null,"abstract":"A new test statistic is proposed to test the equality of two normal means when the data is partially paired and partially unpaired. The test statistic is based on a linear combination of the differences of both paired and unpaired sample means. Using t-distribution as the approximate null distribution, the proposed method is evaluated against some other standard methods known in the literature. For samples from normal and logistic distributions with equal variances, the proposed method appears to perform better than other methods with respect to power while keeping the type I error rates very competitive.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"8 1","pages":"238-247"},"PeriodicalIF":1.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84736408","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 : 2020-06-01DOI: 10.2991/jsta.d.200422.001
Vida Shantia, S. K. Ghoreishi
The available heteroscedastic hierarchical models perform well for a wide range of real-world data, but for the data sets which exhibit heteroscedasticity mainly due to the lack of constant means rather than unequal variances, the existing models tend to overestimate the variance of the second level model which in turn will cause substantial bias in the parameter estimates. Therefore, in this study, we develop heteroscedastic hierarchical models, called double-heteroscedastic hierarchical models, that take into account the heterogeneity in the means for the second level of the models, in addition to considering the heterogeneity of variance for the first level of the models. In these models, we assume that the vector of means in the second level is sparse. We derive Stein’s unbiased risk estimators (SURE) for the parameters in the model based on data decomposition and study their risk properties both in theory and in numerical experiments under the squared loss. The comparison between our SURE estimator and the classical estimators such as empirical Bayes maximum likelihood estimator (EBMLE) and empirical Bayes moment estimator (EBMOM) is illustrated through a simulation study. Finally, we apply our model to a Baseball data set.
{"title":"Empirical Estimation for Sparse Double-Heteroscedastic Hierarchical Normal Models","authors":"Vida Shantia, S. K. Ghoreishi","doi":"10.2991/jsta.d.200422.001","DOIUrl":"https://doi.org/10.2991/jsta.d.200422.001","url":null,"abstract":"The available heteroscedastic hierarchical models perform well for a wide range of real-world data, but for the data sets which exhibit heteroscedasticity mainly due to the lack of constant means rather than unequal variances, the existing models tend to overestimate the variance of the second level model which in turn will cause substantial bias in the parameter estimates. Therefore, in this study, we develop heteroscedastic hierarchical models, called double-heteroscedastic hierarchical models, that take into account the heterogeneity in the means for the second level of the models, in addition to considering the heterogeneity of variance for the first level of the models. In these models, we assume that the vector of means in the second level is sparse. We derive Stein’s unbiased risk estimators (SURE) for the parameters in the model based on data decomposition and study their risk properties both in theory and in numerical experiments under the squared loss. The comparison between our SURE estimator and the classical estimators such as empirical Bayes maximum likelihood estimator (EBMLE) and empirical Bayes moment estimator (EBMOM) is illustrated through a simulation study. Finally, we apply our model to a Baseball data set.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"31 1","pages":"148-161"},"PeriodicalIF":1.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89770474","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 : 2020-06-01DOI: 10.2991/jsta.d.200512.001
K. Krishnamoorthy, T. Nguyen, Yongli Sang
The problems of comparing several exponential distributions based on type II censored samples are considered. Likelihood ratio tests (LRTs) for comparing several location parameters, comparing several scale parameters and for homogeneity of distributions are derived. The LRTs for all three problems are exact as their null distributions do not depend on any unknown parameters. Algorithms are provided to estimate the exact p-values or the percentiles of null distributions. Approximations to the null distributions that are accurate even for small sample sizes are provided. For testing the equality of scale parameters, the proposed LRT is compared with the tests based on union-intersection method and an iterative procedure. Comparison studies indicate that the LRT is more powerful than the existing ones for most parameter values. The methods are illustrated using an example involving elapsed times from randomization to diagnosis of a serious infection of chronic granulomatous disease that were collected from three different hospitals.
{"title":"Tests for Comparing Several Two-Parameter Exponential Distributions Based on Uncensored/Censored Samples","authors":"K. Krishnamoorthy, T. Nguyen, Yongli Sang","doi":"10.2991/jsta.d.200512.001","DOIUrl":"https://doi.org/10.2991/jsta.d.200512.001","url":null,"abstract":"The problems of comparing several exponential distributions based on type II censored samples are considered. Likelihood ratio tests (LRTs) for comparing several location parameters, comparing several scale parameters and for homogeneity of distributions are derived. The LRTs for all three problems are exact as their null distributions do not depend on any unknown parameters. Algorithms are provided to estimate the exact p-values or the percentiles of null distributions. Approximations to the null distributions that are accurate even for small sample sizes are provided. For testing the equality of scale parameters, the proposed LRT is compared with the tests based on union-intersection method and an iterative procedure. Comparison studies indicate that the LRT is more powerful than the existing ones for most parameter values. The methods are illustrated using an example involving elapsed times from randomization to diagnosis of a serious infection of chronic granulomatous disease that were collected from three different hospitals.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"2 1","pages":"248-260"},"PeriodicalIF":1.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78860129","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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