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On The New Modified Burr XII Distribution: Development, Properties, Characterizations and Applications 新型改性Burr XII分布的发展、性质、表征及应用
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2023-06-02 DOI: 10.18187/pjsor.v19i2.3350
F. Bhatti, G. Hamedani, M. C. Korkmaz, H. Yousof, M. Ahmad
{"title":"On The New Modified Burr XII Distribution: Development, Properties, Characterizations and Applications","authors":"F. Bhatti, G. Hamedani, M. C. Korkmaz, H. Yousof, M. Ahmad","doi":"10.18187/pjsor.v19i2.3350","DOIUrl":"https://doi.org/10.18187/pjsor.v19i2.3350","url":null,"abstract":"A new distribution with flexible hazard rate function is introduced which is called new modified Burr XII (NMBXII) distribution. The proposed distribution is derived from the T-X family technique and compounding the generalized Nadarajah–Haghighi (GNH) and gamma distributions. We highlighted the shapes of NMBXII density and failure rate functions. The density function of NMBXII model can take shapes such as J, reverse J, positively skewed and symmetrical.  The proposed model can produce almost all types of failure rates such as increasing, decreasing, increasing-decreasing, decreasing-increasing, bimodal, inverted bathtub and modified bathtub. To show the importance of the proposed distribution, we established various mathematical properties such as quantiles, moments, incomplete moments, inequality measures, residual life functions and reliability measures theoretically.  We have characterized the NMBXII distribution via two techniques. We addressed the maximum likelihood estimation technique for model parameters. The precision of the MLEs is estimated via a simulation study. We have considered three real data sets for applications to demonstrate the potentiality and utility of the NMBXII model. Then, we have established empirically that the proposed model is suitable for tax revenue, time periods between successive earthquakes and flood discharges applications. Finally, various model selection criteria, the goodness of fit statistics and graphical tools were used to examine the adequacy of the NMBXII distribution. ","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41665753","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}
引用次数: 3
Remarks on the Paper ”On the product and Quotient of Pareto and Rayleigh Random Variables” 关于“Pareto和Rayleigh随机变量的乘积和商”一文的注记
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2023-06-02 DOI: 10.18187/pjsor.v19i2.4311
G. Hamedani
{"title":"Remarks on the Paper ”On the product and Quotient of Pareto and Rayleigh Random Variables”","authors":"G. Hamedani","doi":"10.18187/pjsor.v19i2.4311","DOIUrl":"https://doi.org/10.18187/pjsor.v19i2.4311","url":null,"abstract":"Obeid and Kadry (2019) tried to study the product and quotient of the independent Pareto and Rayleigh random variables. The distributions they obtained are incorrect and in fact there is no closed form distributions as discussed here. We will mention the errors made and try to establish the correct versions of the probability density functions of these distributions for the truncated Pareto and Rayleigh random variables.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46579520","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}
引用次数: 0
A New Inverse Kumaraswamy Family of Distributions: Properties and Application 一个新的逆Kumaraswamy分布族：性质与应用
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2023-06-02 DOI: 10.18187/pjsor.v19i2.4295
A. M. Daghistani, Bander Al-Zahrani, M. Shahbaz
{"title":"A New Inverse Kumaraswamy Family of Distributions: Properties and Application","authors":"A. M. Daghistani, Bander Al-Zahrani, M. Shahbaz","doi":"10.18187/pjsor.v19i2.4295","DOIUrl":"https://doi.org/10.18187/pjsor.v19i2.4295","url":null,"abstract":"The Kumaraswamy distribution is an important probability distribution used to model several hydrological problems as well as various natural phenomena whose process values are bounded on both sides. In this paper, we introduce a new family of inverse Kumaraswamy distribution and then explore its statistical properties. Conventional maximum likelihood estimators are considered for the parameters of this distribution and estimation based on dual generalized order statistics is outlined. A particular sub-model of this family; namely, the inverse Kumaraswamy- Weibull distribution is considered and some of its statistical properties are obtained. Estimation efficiency is numerically evaluated via a simulation study and two real-data applications of the proposed distribution are provided as well.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43618084","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}
引用次数: 0
Bayesian Estimation in Rayleigh Distribution under a Distance Type Loss Function 距离型损失函数下瑞利分布的贝叶斯估计
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2023-06-02 DOI: 10.18187/pjsor.v19i2.4130
B. Seal, P. Banerjee, Shreya Bhunia, S. Ghosh
{"title":"Bayesian Estimation in Rayleigh Distribution under a Distance Type Loss Function","authors":"B. Seal, P. Banerjee, Shreya Bhunia, S. Ghosh","doi":"10.18187/pjsor.v19i2.4130","DOIUrl":"https://doi.org/10.18187/pjsor.v19i2.4130","url":null,"abstract":"Estimation of unknown parameters using different loss functions encompasses a major area in the decision theory. Specifically, distance loss functions are preferable as it measures the discrepancies between two probability density functions from the same family indexed by different parameters. In this article, Hellinger distance loss function is considered for scale parameter λ of two-parameter Rayleigh distribution. After simplifications, form of loss is obtained and that is meaningful if parameter is not large and Bayes estimate of λ is calculated under that loss function. So, the Bayes estimate may be termed as ‘Pseudo Bayes estimate’ with respect to the actual Hellinger distance loss function as it is obtained using approximations to actual loss. To compare the performance of the estimator under these loss functions, we also consider weighted squared error loss function (WSELF) which is usually used for the estimation of the scale parameter. An extensive simulation   is carried out to study the behaviour of the Bayes estimators under the three different loss functions, i.e. simplified, actual and WSE loss functions. From the numericalresults it is found that the estimators perform well under the Hellinger distance loss function in comparison with the traditionally used WSELF. Also, we demonstrate the methodology by analyzing two real-life datasets.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46830071","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}
引用次数: 0
GOLD DISTRIBUTION Another Look on the Generalization of Lindely Distribution GOLD分布——对Lindely分布推广的再认识
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2023-06-02 DOI: 10.18187/pjsor.v19i2.3255
Mohammad Al-Talib, Amjad D. Al-Nasser, E. Ciavolino
{"title":"GOLD DISTRIBUTION Another Look on the Generalization of Lindely Distribution","authors":"Mohammad Al-Talib, Amjad D. Al-Nasser, E. Ciavolino","doi":"10.18187/pjsor.v19i2.3255","DOIUrl":"https://doi.org/10.18187/pjsor.v19i2.3255","url":null,"abstract":"In this paper, a new generalization of one parameter Lindely distribution is proposed. The new distribution is a mixture distribution of Gamma distributions with fixed scale parameter and variable shape parameter. The distribution is called 'GOLD Distribution' as it is a generalization for several distributions such as exponential, Lindely, Sujatha, Amarendra, Devya and Shambhu distributions. The probability density and cumulative density functions are derived. Also, the statistical properties of the GOLD distribution are discussed. Parameter estimation using the maximum likelihood and the method of moments are given. Moreover, an illustration of the usefulness of the GOLD distribution in survival data analysis is discussed based on a real lifetime data.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49478045","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}
引用次数: 1
The Ordinal Regression to Analyze Radical Intention of Muslim Indonesian Students through Personality Type and Tolerance Approach 从人格类型和容忍度分析印尼穆斯林学生激进倾向的有序回归
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2023-06-02 DOI: 10.18187/pjsor.v19i2.3932
A. Meiza
{"title":"The Ordinal Regression to Analyze Radical Intention of Muslim Indonesian Students through Personality Type and Tolerance Approach","authors":"A. Meiza","doi":"10.18187/pjsor.v19i2.3932","DOIUrl":"https://doi.org/10.18187/pjsor.v19i2.3932","url":null,"abstract":"This paper presents a result of research about the student’s radical intention related to their tolerance and personality type. This research was a collaboration between Statistics, Psychology, and Politics. The main research variable that is radical intention has a psychological construct that is theoretically built with a social approach and political point of view. As a big country, Indonesia has various pluralism i.e ethnic and religion, so that it requires a high tolerance attitude to live in a harmony. Students as the next generation and important elements in society are expected to avoid intolerance. The research subjects were 175 students from an Islamic university in Indonesia. The data were analyzed with Ordinal Regression which intention of radicalism (ordinal) as the dependent variable, personality type (nominal), and tolerance attitude level (ordinal) as independent variables. The majority of these students have good moral values so they can tolerate the difference. From the regression analysis, the type personality and tolerance attitude have a significant effect on radicalism intention.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42189248","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}
引用次数: 0
A Generalization of Burr Type XII Distribution with Properties, Copula and Modeling Symmetric and Skewed Real Data Sets Burr型XII分布的性质、Copula及对称和斜交实数据集建模的推广
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2023-03-06 DOI: 10.18187/pjsor.v19i1.3377
Mohamed G. Khalil, Emadeldin I. A. Ali
{"title":"A Generalization of Burr Type XII Distribution with Properties, Copula and Modeling Symmetric and Skewed Real Data Sets","authors":"Mohamed G. Khalil, Emadeldin I. A. Ali","doi":"10.18187/pjsor.v19i1.3377","DOIUrl":"https://doi.org/10.18187/pjsor.v19i1.3377","url":null,"abstract":"A new generalization of Burr type XII model is introduced and studied. The genesis of the new model is based on the family of Cordeiro et al. (2016). The new model generalizes at least eight important sub-models. The new density can be unimodal, symmetric and left skewed. Some useful properties related to the new model are derived. The Clayton Copula-based construction is used to generate many bivariate and multivariate type distributions. Graphically, we performed the simulation experiments to assess of the finite sample behavior of the estimations.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41681384","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}
引用次数: 1
The Marshall-Olkin Pranav distribution: Theory and applications Marshall-Olkin-Pranav分布：理论与应用
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2023-03-06 DOI: 10.18187/pjsor.v19i1.4058
Rehab Alsultan
{"title":"The Marshall-Olkin Pranav distribution: Theory and applications","authors":"Rehab Alsultan","doi":"10.18187/pjsor.v19i1.4058","DOIUrl":"https://doi.org/10.18187/pjsor.v19i1.4058","url":null,"abstract":"\u0000 \u0000 \u0000 \u0000The current paper presented new two-parameter life processes distribution, the Marshall-Olkin Pranav (MOEP) distribution. This study combines the Marshall-Olkin method with the Pranav distribution to produce a more accessible and flexible model used to perform data survival techniques. Some of its critical statistical features are presented in this study. For instance, we mentioned its survival , hazard, reversed hazard, and cumulative hazard rate function. Then we discussed its Moment generating functions, The characteristic function, Incomplete moments, R`enyi and Entropies, and stochastic orderings. The research utilized maximization of chance in estimating parameters. These tests are done through simulations to achieve the desired results. After its attainment, real-life data was used to test the new model, which possesses the best goodness of fit. \u0000 \u0000 \u0000 \u0000","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45787260","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}
引用次数: 0
Comparison of Infinite Capacity FM/FEk/1 Queuing Performance Using Fuzzy Queuing Model and Intuitionistic Fuzzy Queuing Model with Erlang Service Rates 基于模糊排队模型和基于Erlang服务率的直觉模糊排队模型的无限容量FM/FEk/1排队性能比较
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2023-03-06 DOI: 10.18187/pjsor.v19i1.4055
A. S, M. Shanmugasundari
{"title":"Comparison of Infinite Capacity FM/FEk/1 Queuing Performance Using Fuzzy Queuing Model and Intuitionistic Fuzzy Queuing Model with Erlang Service Rates","authors":"A. S, M. Shanmugasundari","doi":"10.18187/pjsor.v19i1.4055","DOIUrl":"https://doi.org/10.18187/pjsor.v19i1.4055","url":null,"abstract":"In this work, we suggest an analytic technique with triangular fuzzy and triangular intuitionistic fuzzy numbers to compute the membership functions of considerable state-executing proportion in Erlang service models. The inter-entry rate, which is Poisson, and the admin (service) rate, which is Erlang, are both fuzzy-natured in this case, with FEk designating the Erlang probabilistic deviation with k exponentially phase. The numeric antecedents are shown to validate the model's plausibility, FM/FEk/1. A contextual inquiry is also carried out, comparing individual fuzzy figures. Intuitionistic fuzzy queueing models that are comprehensible are more categorical than fuzzy queueing models. Expanding the fuzzy queuing model to an intuitionistic fuzzy environment can boost the implementation of the queuing model. The purpose of this study is to assess the performance of a single server Erlang queuing model with infinite capacity using fuzzy queuing theory and intuitionistic fuzzy queuing theory. The fuzzy queuing theory model's performance evaluations are reported as a range of outcomes, but the intuitionistic fuzzy queuing theory model provides a myriad of values. In this context, the arrival and the service rate are both triangular and intuitionistic triangular fuzzy numbers. An assessment is made to find evaluation criteria using a design protocol in which fuzzy values are kept as they are and not made into crisp values, and two statistical problems are solved to understand the existence of the method.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47643007","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}
引用次数: 0
Kumaraswamy Esscher Transformed Laplace Distribution: Properties, Application and Extensions Kumaraswamy Esscher变换拉普拉斯分布：性质、应用和扩展
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2023-03-06 DOI: 10.18187/pjsor.v19i1.3818
Dais George, Rimsha H.
{"title":"Kumaraswamy Esscher Transformed Laplace Distribution: Properties, Application and Extensions","authors":"Dais George, Rimsha H.","doi":"10.18187/pjsor.v19i1.3818","DOIUrl":"https://doi.org/10.18187/pjsor.v19i1.3818","url":null,"abstract":"In this article, we introduce a new generalized family of Esscher transformed Laplace distribution, namely the Kumaraswamy Esscher transformed Laplace distribution. We study the various properties of the distribution including the survival function, hazard rate function, cumulative hazard rate function and reverse hazard rate function. The parameters of the distribution are estimated using the maximum likelihood method of estimation. A real application of this distribution on breaking stress of carbon fibres is also considered. Further, we introduce and study the exponentiated and transmuted exponentiated Kumaraswamy Esscher transformed Laplace distributions.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44976549","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}
引用次数: 0
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