Pub Date : 2021-01-01DOI: 10.2991/JSTA.D.210105.001
Mohammed Amine Meraou, M. Z. Raqab
In this paper, we propose a new class of distributions by compounding Lindley distributed random variates with the number of variates being zero-truncated Poisson distribution. This model is called a compound zero-truncated Poisson–Lindley distribution with two parameters. Different statistical properties of the proposed model are discussed. We describe different methods of estimation for the unknown parameters involved in the model. These methods include maximum likelihood, least squares, weighted least squares, Cramer–vonMises, maximum product of spacings, Anderson–Darling and right-tail Anderson–Darling methods. Numerical simulation experiments are conducted to assess the performance of the so obtained estimators developed from these methods. Finally, the potentiality of the model is studied using one real data set representing the monthly highest snowfall during February 2018, for a subset of stations in the Global Historical Climatological Network of USA.
{"title":"Statistical Properties and Different Estimation Procedures of Poisson–Lindley Distribution","authors":"Mohammed Amine Meraou, M. Z. Raqab","doi":"10.2991/JSTA.D.210105.001","DOIUrl":"https://doi.org/10.2991/JSTA.D.210105.001","url":null,"abstract":"In this paper, we propose a new class of distributions by compounding Lindley distributed random variates with the number of variates being zero-truncated Poisson distribution. This model is called a compound zero-truncated Poisson–Lindley distribution with two parameters. Different statistical properties of the proposed model are discussed. We describe different methods of estimation for the unknown parameters involved in the model. These methods include maximum likelihood, least squares, weighted least squares, Cramer–vonMises, maximum product of spacings, Anderson–Darling and right-tail Anderson–Darling methods. Numerical simulation experiments are conducted to assess the performance of the so obtained estimators developed from these methods. Finally, the potentiality of the model is studied using one real data set representing the monthly highest snowfall during February 2018, for a subset of stations in the Global Historical Climatological Network of USA.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"63 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76511554","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 : 2021-01-01DOI: 10.2991/JSTA.D.210115.001
Caner Tanış, Buğra Saraçoğlu, Coşkun Kuş, A. Pekgor, K. Karakaya
This paper introduces a new lifetime distribution bymixing the first two lower record values and various distributional properties are examined. Statistical inference on distribution parameters are discussedwith five estimators. AMonte Carlo simulation study is carried out to evaluate the risk behavior of these estimators for different sample of sizes. The distribution modeling analysis is provided based on real data to demonstrate the fitting ability of the proposed model. In addition, a lifetime regression model is described by re-parameterization on the log lifetimes. The superiority of proposed regression model is revealed in well-known models.
{"title":"Transmuted Lower Record Type Fréchet Distribution with Lifetime Regression Analysis Based on Type I-Censored Data","authors":"Caner Tanış, Buğra Saraçoğlu, Coşkun Kuş, A. Pekgor, K. Karakaya","doi":"10.2991/JSTA.D.210115.001","DOIUrl":"https://doi.org/10.2991/JSTA.D.210115.001","url":null,"abstract":"This paper introduces a new lifetime distribution bymixing the first two lower record values and various distributional properties are examined. Statistical inference on distribution parameters are discussedwith five estimators. AMonte Carlo simulation study is carried out to evaluate the risk behavior of these estimators for different sample of sizes. The distribution modeling analysis is provided based on real data to demonstrate the fitting ability of the proposed model. In addition, a lifetime regression model is described by re-parameterization on the log lifetimes. The superiority of proposed regression model is revealed in well-known models.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"87 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79739058","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 : 2021-01-01DOI: 10.2991/JSTA.D.210111.002
M. Khalaj, F. Khalaj
This study considers a new aspect of the belief function theory to define a belief set, which is characterized by truth, uncertainty and falsity belief degrees as a 3D vector representation. Then, based on the implication of a belief set, one of the similarity measures (i.e., Cosine, Jaccard and Dice) between two belief sets is defined. Furthermore, the weighted similarity measure of these different species between each alternative and ideal alternative is presented in order to rank alternatives and determine the best one. Finally, a comparison between similarity measures and an application of a new method based on similarity measures between two belief sets in the decision-making process is calculated to show the capability and validity of the proposed method.
{"title":"Similarity Measure Based on the Belief Function Theory: Application in a Decision-Making Process","authors":"M. Khalaj, F. Khalaj","doi":"10.2991/JSTA.D.210111.002","DOIUrl":"https://doi.org/10.2991/JSTA.D.210111.002","url":null,"abstract":"This study considers a new aspect of the belief function theory to define a belief set, which is characterized by truth, uncertainty and falsity belief degrees as a 3D vector representation. Then, based on the implication of a belief set, one of the similarity measures (i.e., Cosine, Jaccard and Dice) between two belief sets is defined. Furthermore, the weighted similarity measure of these different species between each alternative and ideal alternative is presented in order to rank alternatives and determine the best one. Finally, a comparison between similarity measures and an application of a new method based on similarity measures between two belief sets in the decision-making process is calculated to show the capability and validity of the proposed method.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90433067","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 : 2021-01-01DOI: 10.2991/jsta.d.201228.001
B. Mahanty, G. Mishra
In this paper, an unbiased estimator is constructed by using a linear combination of an estimator of study variable and mean per unit estimator of an auxiliary variable under simple random sampling without replacement scheme. The efficiency of the estimator under optimality compared with themean per unit estimator, an almost unbiased ratio estimator, an unbiased product estimator, and a regression estimator both theoretically and with the numerical illustration.
{"title":"An Unbiased Estimator of Finite Population Mean Using Auxiliary Information","authors":"B. Mahanty, G. Mishra","doi":"10.2991/jsta.d.201228.001","DOIUrl":"https://doi.org/10.2991/jsta.d.201228.001","url":null,"abstract":"In this paper, an unbiased estimator is constructed by using a linear combination of an estimator of study variable and mean per unit estimator of an auxiliary variable under simple random sampling without replacement scheme. The efficiency of the estimator under optimality compared with themean per unit estimator, an almost unbiased ratio estimator, an unbiased product estimator, and a regression estimator both theoretically and with the numerical illustration.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"6 2 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88036505","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 : 2020-12-01DOI: 10.2991/jsta.d.201211.001
Parya Parviz, H. Panahi
{"title":"Classical and Bayesian Inference for the Burr Type XII Distribution Under Generalized Progressive Type I Hybrid Censored Sample","authors":"Parya Parviz, H. Panahi","doi":"10.2991/jsta.d.201211.001","DOIUrl":"https://doi.org/10.2991/jsta.d.201211.001","url":null,"abstract":"","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"29 1","pages":"547-557"},"PeriodicalIF":1.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84405363","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 : 2020-12-01DOI: 10.2991/jsta.d.201202.001
S. A. Wani, Anwar Hassan, S. Shafi, S. Shafi
{"title":"Pranav Quasi Gamma Distribution: Properties and Applications","authors":"S. A. Wani, Anwar Hassan, S. Shafi, S. Shafi","doi":"10.2991/jsta.d.201202.001","DOIUrl":"https://doi.org/10.2991/jsta.d.201202.001","url":null,"abstract":"","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"24 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77985749","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 : 2020-12-01DOI: 10.2991/jsta.d.201208.001
P. Jamshidi, M. Maleki, Z. Khodadadi
{"title":"Modified Maximum Likelihood Estimations of the Epsilon-Skew-Normal Family","authors":"P. Jamshidi, M. Maleki, Z. Khodadadi","doi":"10.2991/jsta.d.201208.001","DOIUrl":"https://doi.org/10.2991/jsta.d.201208.001","url":null,"abstract":"","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"188 1","pages":"481-486"},"PeriodicalIF":1.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74434899","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 : 2020-12-01DOI: 10.2991/jsta.d.201116.001
Mohammad Kazemi, A. Jafari, S. Tahmasebi
This paper introduces a new four-parameter extension of the generalized Gompertz distributions. This distribution involves somewell-knowndistributions such as extension of generalized exponential, generalized exponential, and generalizedGompertz distributions. In addition, it can have a decreasing, increasing, upside-down bathtub, and bathtub-shaped hazard rate function depending on its parameters. Some mathematical properties of this new distribution, such as moments, quantiles, hazard rate function, and reversible hazard rate function are obtained. In addition, the density function and the moments of the ordered statistics of this new distribution is provided. The parameters of model are estimated using the maximum likelihood method. Also, a real data set was used to illustrate the validity of the proposed distribution.
{"title":"A Modification of the Gompertz Distribution Based on the Class of Extended-Weibull Distributions","authors":"Mohammad Kazemi, A. Jafari, S. Tahmasebi","doi":"10.2991/jsta.d.201116.001","DOIUrl":"https://doi.org/10.2991/jsta.d.201116.001","url":null,"abstract":"This paper introduces a new four-parameter extension of the generalized Gompertz distributions. This distribution involves somewell-knowndistributions such as extension of generalized exponential, generalized exponential, and generalizedGompertz distributions. In addition, it can have a decreasing, increasing, upside-down bathtub, and bathtub-shaped hazard rate function depending on its parameters. Some mathematical properties of this new distribution, such as moments, quantiles, hazard rate function, and reversible hazard rate function are obtained. In addition, the density function and the moments of the ordered statistics of this new distribution is provided. The parameters of model are estimated using the maximum likelihood method. Also, a real data set was used to illustrate the validity of the proposed distribution.","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81794110","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 : 2020-10-01DOI: 10.2991/jsta.d.201016.001
Langat Reuben Cheruiyot
{"title":"Local Linear Regression Estimator on the Boundary Correction in Nonparametric Regression Estimation","authors":"Langat Reuben Cheruiyot","doi":"10.2991/jsta.d.201016.001","DOIUrl":"https://doi.org/10.2991/jsta.d.201016.001","url":null,"abstract":"","PeriodicalId":45080,"journal":{"name":"Journal of Statistical Theory and Applications","volume":"12 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73948093","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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