Pub Date : 2024-03-07DOI: 10.18187/pjsor.v20i1.4225
Samia Teghri, H. Goual, Hamami Loubna, Nadeem Shafique Butt, Abdelrahman M. Khedr, H. Yousof, M. Ibrahim, Moustafa Salem
Classical survival models assume homogeneity among the population of individuals who are susceptible to the event of interest. However, in many practical circumstances, there is a certain amount of unobserved heterogeneity that can be caused by a variety of sources, such as environmental or genetic factors. If the heterogeneity is ignored, many issues could arise, including an overestimation of the hazard rate and inaccurate estimates of the regression coefficients. Frailty models are usually used to model the heterogeneity among individuals. In this paper, we propose a novel univariate frailty model. The frailty variable is assumed to follow the Two Parameter Lindley distribution. The maximum likelihood method is used to estimate the model parameters. The baseline hazard functions are assumed to follow Weibull, Exponential, Gompertz, and Pareto distributions, and a simulation study is performed under this assumption. We examine the characteristics of the distribution and assess its performance compared to other distributions that are frequently applied in frailty modeling by using both Nikulin-Rao-Robson and Bagdonavicius-Nikulin goodness-of-fit tests to determine the adequacy of the model. We analyze a fresh medical dataset collected from an emergency hospital in Algeria to evaluate the effectiveness and applicability of the proposed model.
{"title":"A New Two-Parameters Lindley-Frailty Model: Censored and Uncensored Schemes under Different Baseline Models: Applications, Assessments, Censored and Uncensored Validation Testing","authors":"Samia Teghri, H. Goual, Hamami Loubna, Nadeem Shafique Butt, Abdelrahman M. Khedr, H. Yousof, M. Ibrahim, Moustafa Salem","doi":"10.18187/pjsor.v20i1.4225","DOIUrl":"https://doi.org/10.18187/pjsor.v20i1.4225","url":null,"abstract":"Classical survival models assume homogeneity among the population of individuals who are susceptible to the event of interest. However, in many practical circumstances, there is a certain amount of unobserved heterogeneity that can be caused by a variety of sources, such as environmental or genetic factors. If the heterogeneity is ignored, many issues could arise, including an overestimation of the hazard rate and inaccurate estimates of the regression coefficients. Frailty models are usually used to model the heterogeneity among individuals. In this paper, we propose a novel univariate frailty model. The frailty variable is assumed to follow the Two Parameter Lindley distribution. The maximum likelihood method is used to estimate the model parameters. The baseline hazard functions are assumed to follow Weibull, Exponential, Gompertz, and Pareto distributions, and a simulation study is performed under this assumption. We examine the characteristics of the distribution and assess its performance compared to other distributions that are frequently applied in frailty modeling by using both Nikulin-Rao-Robson and Bagdonavicius-Nikulin goodness-of-fit tests to determine the adequacy of the model. We analyze a fresh medical dataset collected from an emergency hospital in Algeria to evaluate the effectiveness and applicability of the proposed model. ","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140260050","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 : 2024-03-07DOI: 10.18187/pjsor.v20i1.3614
Mustapha Muhammad, Isyaku Muhammad, Mouna Bouchane, Muhammad Aslam, Sani Musa, Sadiya Ali Rano
This article introduces a new three-parameter lifetime model with an increasing and bathtub failure rate functions as an extension of the Mustapha type II distribution (MuII). The model can be very useful in statistical studies, reliability, computer sciences and engineering. Various mathematical and statistical properties of the distribution are discussed, such as moments, mean deviations, Bonferroni and Lorenz curves, entropy, order statistic, and extreme value distributions. Moreover, we consider the bivariate extension of the new model. Statistical inferences by the maximum likelihood method are discussed and assess by simulation studies. Applications of the proposed model to two right-skewed data are presented for illustration. The new model provides a better fit than some other existing distribution as measured by some model selection criteria and goodness of fits statistics.
本文介绍了一种新的三参数寿命模型，该模型具有递增和浴缸失效率函数，是对穆斯塔法 II 型分布（MuII）的扩展。该模型在统计研究、可靠性、计算机科学和工程学方面非常有用。我们讨论了该分布的各种数学和统计特性，如矩、平均偏差、Bonferroni 和 Lorenz 曲线、熵、阶次统计量和极值分布。此外，我们还考虑了新模型的二元扩展。讨论了最大似然法的统计推断，并通过模拟研究进行了评估。为了说明问题，我们将所提出的模型应用于两个右偏数据。通过一些模型选择标准和拟合优度统计来衡量，新模型比其他现有分布提供了更好的拟合。
{"title":"A new bathtub and increasing failure rate model: An extension of the Mustapha type II distribution","authors":"Mustapha Muhammad, Isyaku Muhammad, Mouna Bouchane, Muhammad Aslam, Sani Musa, Sadiya Ali Rano","doi":"10.18187/pjsor.v20i1.3614","DOIUrl":"https://doi.org/10.18187/pjsor.v20i1.3614","url":null,"abstract":"This article introduces a new three-parameter lifetime model with an increasing and bathtub failure rate functions as an extension of the Mustapha type II distribution (MuII). The model can be very useful in statistical studies, reliability, computer sciences and engineering. Various mathematical and statistical properties of the distribution are discussed, such as moments, mean deviations, Bonferroni and Lorenz curves, entropy, order statistic, and extreme value distributions. Moreover, we consider the bivariate extension of the new model. Statistical inferences by the maximum likelihood method are discussed and assess by simulation studies. Applications of the proposed model to two right-skewed data are presented for illustration. The new model provides a better fit than some other existing distribution as measured by some model selection criteria and goodness of fits statistics.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140260076","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 : 2024-03-07DOI: 10.18187/pjsor.v20i1.4197
Muhammad Akram Ramadhan Ibrahim, N. Jaini, K.M.N. Ku Khalif
The paper aims to suggest the ranking of an optimal solution when there exists more than one Nash equilibrium in the game theory solution concept. Many studies tend to merge the game theory with the multi criteria decision-making (MCDM) method to cater the real-situation problems. In the paper, a novel hybrid non-cooperative static game in game theory is combines with the trade-off ranking (TOR) method in MCDM. The proposed hybrid method is used to rank multiple Nash equilibria concerning some criteria. The methodology for both static game and TOR method are explained in the paper. The game theory model used is a two-player non-constant-sum static game. The proposed methodology is tested using international cooperation in Iran. The result suggests the ranking of the combined strategies using the proposed method.
本文旨在提出博弈论求解概念中存在不止一个纳什均衡时的最优解排序。许多研究倾向于将博弈论与多准则决策（MCDM）方法相结合，以解决现实问题。本文将博弈论中的一种新型混合非合作静态博弈与 MCDM 中的权衡排序（TOR）方法相结合。所提出的混合方法用于对多个纳什均衡方案进行排序。文中解释了静态博弈和 TOR 方法的方法论。使用的博弈论模型是双人非恒和静态博弈。提出的方法利用伊朗的国际合作进行了测试。结果表明，使用建议的方法可以对组合策略进行排序。
{"title":"Nash equilibrium selection using a hybrid two-player static game with trade-off ranking method","authors":"Muhammad Akram Ramadhan Ibrahim, N. Jaini, K.M.N. Ku Khalif","doi":"10.18187/pjsor.v20i1.4197","DOIUrl":"https://doi.org/10.18187/pjsor.v20i1.4197","url":null,"abstract":"The paper aims to suggest the ranking of an optimal solution when there exists more than one Nash equilibrium in the game theory solution concept. Many studies tend to merge the game theory with the multi criteria decision-making (MCDM) method to cater the real-situation problems. In the paper, a novel hybrid non-cooperative static game in game theory is combines with the trade-off ranking (TOR) method in MCDM. The proposed hybrid method is used to rank multiple Nash equilibria concerning some criteria. The methodology for both static game and TOR method are explained in the paper. The game theory model used is a two-player non-constant-sum static game. The proposed methodology is tested using international cooperation in Iran. The result suggests the ranking of the combined strategies using the proposed method.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140397233","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 : 2023-12-06DOI: 10.18187/pjsor.v19i4.4423
D. J. Moloy, M. A. Ali, F. Alam
Researchers from various fields of science encounter phenomena of interest, and they seek to model the occurrences scientifically. An important approach of performing modeling is to use probability distributions. Probability distributions are probabilistic models that have many applications in different research areas, including, but not limited to, environmental and financial studies. In this paper, we study a quartic transmuted Weibull distribution from a general quartic transmutation family of distributions as a generalization and an alternative to the well-known Weibull distribution. We also investigate the practical application of this generalization by modeling climate-related data sets and check the goodness-of-fit of the proposed model. The statistical properties of the proposed model, which includes non-central moments, generating functions, survival function, and hazard function, are derived. Different estimation methods to estimate the parameters of the proposed quartic transmuted distribution: the maximum likelihood estimation method, the maximum product of spacings method, two least-squares-based methods, and three goodness-of-fit-based estimation methods. Numerical illustration and an extensive comparative Monte Carlo simulation study are conducted to investigate the performance of the estimators of the considered inferential methods. Regarding estimation methods, simulation outcomes indicated that the maximum likelihood estimation (MLE), Anderson-Darling estimation (ADE) and right Anderson-Darling (RADE) methods in general outperformed the other considered methods in terms of estimation efficiency for large sample size, while all considered estimation methods performed almost same in terms of goodness-of-fit regardless the values of shape and transmuted parameters. Two real-life data sets are used to demonstrate the suggested estimation methods, the applicability and flexibility of the proposed distribution compared to Weibull, transmuted Weibull, and cubic transmuted Weibull distributions. Weighted least squares estimation (WLSE) and least squares estimation (LSE) methods provided best model fitting estimates of the proposed distribution for Wheaton River and rainfall data respectively. The proposed quartic transmuted Weibull distribution provide significantly improved fit for the two datasets as compared with other distributions.
{"title":"Modeling Climate data using the Quartic Transmuted Weibull Distribution and Different Estimation Methods","authors":"D. J. Moloy, M. A. Ali, F. Alam","doi":"10.18187/pjsor.v19i4.4423","DOIUrl":"https://doi.org/10.18187/pjsor.v19i4.4423","url":null,"abstract":"Researchers from various fields of science encounter phenomena of interest, and they seek to model the occurrences scientifically. An important approach of performing modeling is to use probability distributions. Probability distributions are probabilistic models that have many applications in different research areas, including, but not limited to, environmental and financial studies. In this paper, we study a quartic transmuted Weibull distribution from a general quartic transmutation family of distributions as a generalization and an alternative to the well-known Weibull distribution. We also investigate the practical application of this generalization by modeling climate-related data sets and check the goodness-of-fit of the proposed model. The statistical properties of the proposed model, which includes non-central moments, generating functions, survival function, and hazard function, are derived. Different estimation methods to estimate the parameters of the proposed quartic transmuted distribution: the maximum likelihood estimation method, the maximum product of spacings method, two least-squares-based methods, and three goodness-of-fit-based estimation methods. Numerical illustration and an extensive comparative Monte Carlo simulation study are conducted to investigate the performance of the estimators of the considered inferential methods. Regarding estimation methods, simulation outcomes indicated that the maximum likelihood estimation (MLE), Anderson-Darling estimation (ADE) and right Anderson-Darling (RADE) methods in general outperformed the other considered methods in terms of estimation efficiency for large sample size, while all considered estimation methods performed almost same in terms of goodness-of-fit regardless the values of shape and transmuted parameters. Two real-life data sets are used to demonstrate the suggested estimation methods, the applicability and flexibility of the proposed distribution compared to Weibull, transmuted Weibull, and cubic transmuted Weibull distributions. Weighted least squares estimation (WLSE) and least squares estimation (LSE) methods provided best model fitting estimates of the proposed distribution for Wheaton River and rainfall data respectively. The proposed quartic transmuted Weibull distribution provide significantly improved fit for the two datasets as compared with other distributions.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138596255","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 : 2023-12-06DOI: 10.18187/pjsor.v19i4.4435
A. Hanandeh, Amer Al-omari
In this article, we address the problem of estimating the parameters of Farlie-Gumbel-Morgenstern bivariate Weibull distribution using ranked set sample (RSS) design. The suggested estimators of the FGMBW distribution parameters are compared with their counterparts based on simple random sampling (SRS) via Monte Carlo simulations studies. An example of a real data set consists of times (in days) to the first and second recurrence of infection for 30 kidney patients is considered for illustration. It turns out that the RSS estimators results in an improvement in efficiency as compared to the simple random sampling estimators based on the same number of measured units for all cases considered in this study.
{"title":"Estimation based on Ranked Set Sampling for Farlie--Gumbel--Morgenstern Bivariate Weibull Distribution Parameters with an application to medical data","authors":"A. Hanandeh, Amer Al-omari","doi":"10.18187/pjsor.v19i4.4435","DOIUrl":"https://doi.org/10.18187/pjsor.v19i4.4435","url":null,"abstract":"In this article, we address the problem of estimating the parameters of Farlie-Gumbel-Morgenstern bivariate Weibull distribution using ranked set sample (RSS) design. The suggested estimators of the FGMBW distribution parameters are compared with their counterparts based on simple random sampling (SRS) via Monte Carlo simulations studies. An example of a real data set consists of times (in days) to the first and second recurrence of infection for 30 kidney patients is considered for illustration. It turns out that the RSS estimators results in an improvement in efficiency as compared to the simple random sampling estimators based on the same number of measured units for all cases considered in this study.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138594730","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 : 2023-12-06DOI: 10.18187/pjsor.v19i4.4211
Elif Yıldırım
The logistic regression is generally preferred when there is no big difference in the occurrence frequencies of two possible results for the considered event. However, for the events occurring rarely such as wars, economic crisis and natural disasters, namely having relatively small occurrence frequency when compared to the general events, the logistic regression gives biased parameter estimations. Therefore, the logistic regression underestimates the occurrence probability of the rare events. In this study, black hole algorithm is proposed and used to obtain unbiased estimation parameters for rare events, instead of using the classical logistic regression approach. In order to estimate the logistic regression parameter for the cases dichotomous event groups are rare, we propose a black hole algorithm (BHA) approach. For the samples with different rareness degrees, we obtain the parameter values and their bias and root mean square errors for BHA and logistic regression, and then compare them. Moreover, we also investigate the classification performance of two methods on a real life data. As a result, we obtained that BHA gives less biased estimates in simulation and real-life data compared to logistic regression.
{"title":"Black hole algorithm as a heuristic approach for rare event classification problem","authors":"Elif Yıldırım","doi":"10.18187/pjsor.v19i4.4211","DOIUrl":"https://doi.org/10.18187/pjsor.v19i4.4211","url":null,"abstract":"The logistic regression is generally preferred when there is no big difference in the occurrence frequencies of two possible results for the considered event. However, for the events occurring rarely such as wars, economic crisis and natural disasters, namely having relatively small occurrence frequency when compared to the general events, the logistic regression gives biased parameter estimations. Therefore, the logistic regression underestimates the occurrence probability of the rare events. In this study, black hole algorithm is proposed and used to obtain unbiased estimation parameters for rare events, instead of using the classical logistic regression approach. In order to estimate the logistic regression parameter for the cases dichotomous event groups are rare, we propose a black hole algorithm (BHA) approach. For the samples with different rareness degrees, we obtain the parameter values and their bias and root mean square errors for BHA and logistic regression, and then compare them. Moreover, we also investigate the classification performance of two methods on a real life data. As a result, we obtained that BHA gives less biased estimates in simulation and real-life data compared to logistic regression.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138597527","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 : 2023-12-06DOI: 10.18187/pjsor.v19i4.4146
Reny Rian Marliana, Maya Suhayati, Sri Bekti Handayani Ningsih
In this academic work a comparison between a Bayesian-Structural Equation Modelling (B-SEM) and a Partial Least Squares-Structural Equation Modelling (PLS-SEM) on a relationship amongst self-directed learning readiness (SDLR), E-learning readiness, and learning motivation of undergraduate students throughout the outbreak of Covid-19 is studied. The B-SEM is built using prior distribution i.e., inverse-Gamma, inverse-Wishart, and normal distribution on specific parameters of the model with 19000 iterations on Markov Chain Monte Carlo (MCMC) algorithm. Whereas the PLS-SEM is established using Ordinary Least Squares (OLS) method, PLS algorithm with 300 iterations, and 5000 subsamples on bootstrapping. The objective of this study is to get the most compatible model which represent the relationship between three latent variables in this study. Schwarz’s Bayesian Information Criteria (BIC) is used on model selection between these two models. Data were obtained from 214 undergraduate students with three majors of study at the Faculty of Information Technology, Sebelas April university in Indonesia. Both models produce the same output which depict that self-directed learning readiness significantly affects the learning motivation of the students, while there is not a significant effect of e-learning readiness on learning motivation. With the lower BIC value, which is a negative value, PLS-SEM is more fitted for portray the influence of self-directed learning readiness, and e-learning readiness to learning motivation of students than B-SEM model.
在本学术工作中，比较了贝叶斯结构方程模型(B-SEM)和偏最小二乘结构方程模型(PLS-SEM)在2019冠状病毒病爆发期间本科生自主学习准备(SDLR)、电子学习准备和学习动机之间的关系。B-SEM使用先验分布，即反gamma、反wishart和正态分布对模型的特定参数进行构建，使用Markov Chain Monte Carlo (MCMC)算法进行19000次迭代。而PLS- sem则采用普通最小二乘(OLS)方法，PLS算法迭代300次，自举5000个子样本。本研究的目的是获得最相容的模型来代表本研究中三个潜在变量之间的关系。采用Schwarz的贝叶斯信息准则(BIC)对两种模型进行模型选择。数据来自印度尼西亚Sebelas April大学信息技术学院三个专业的214名本科生。两个模型的输出结果一致，即自主学习准备显著影响学生的学习动机，而网络学习准备对学习动机的影响不显著。与B-SEM模型相比，PLS-SEM模型的BIC值较低，为负值，更适合描述自主学习准备和网络学习准备对学生学习动机的影响。
{"title":"Schwarz’s Bayesian Information Criteria: A Model Selection Between Bayesian-SEM and Partial Least Squares-SEM","authors":"Reny Rian Marliana, Maya Suhayati, Sri Bekti Handayani Ningsih","doi":"10.18187/pjsor.v19i4.4146","DOIUrl":"https://doi.org/10.18187/pjsor.v19i4.4146","url":null,"abstract":"In this academic work a comparison between a Bayesian-Structural Equation Modelling (B-SEM) and a Partial Least Squares-Structural Equation Modelling (PLS-SEM) on a relationship amongst self-directed learning readiness (SDLR), E-learning readiness, and learning motivation of undergraduate students throughout the outbreak of Covid-19 is studied. The B-SEM is built using prior distribution i.e., inverse-Gamma, inverse-Wishart, and normal distribution on specific parameters of the model with 19000 iterations on Markov Chain Monte Carlo (MCMC) algorithm. Whereas the PLS-SEM is established using Ordinary Least Squares (OLS) method, PLS algorithm with 300 iterations, and 5000 subsamples on bootstrapping. The objective of this study is to get the most compatible model which represent the relationship between three latent variables in this study. Schwarz’s Bayesian Information Criteria (BIC) is used on model selection between these two models. Data were obtained from 214 undergraduate students with three majors of study at the Faculty of Information Technology, Sebelas April university in Indonesia. Both models produce the same output which depict that self-directed learning readiness significantly affects the learning motivation of the students, while there is not a significant effect of e-learning readiness on learning motivation. With the lower BIC value, which is a negative value, PLS-SEM is more fitted for portray the influence of self-directed learning readiness, and e-learning readiness to learning motivation of students than B-SEM model.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138594664","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 : 2023-12-06DOI: 10.18187/pjsor.v19i4.3554
H. Yousof, H. Goual, Meribout Kaouter Khaoula, G. Hamedani, Abdullah H. Al-Aefaie, M. Ibrahim, Nadeem Shafique Butt, Moustafa Salem
In this paper, we present a new exponential accelerated failure time model. Some of its properties and characterization results are derived. Different estimation methods are considered for assessing the finite sample behaviour of the estimators. Simulation studies for comparing the estimation methods are performed. Finally, we present a novel modified chi-square test for the novel exponential accelerated failure time model in both complete and right censored data cases. The validity of the new model is checked by using the theoretical global of the Nikulin-Rao-Robson. The maximum likelihood method is considered for this purpose. Two simulation studies are performed to assess the exponential accelerated failure time model and the efficiency of the Nikulin-Rao-Robson test statistic, respectively. Three real data sets are considered for illustrating the efficiency of the test statistic in validation.
{"title":"A Novel Accelerated Failure Time Model: Characterizations, Validation Testing, Different Estimation Methods and Applications in Engineering and Medicine","authors":"H. Yousof, H. Goual, Meribout Kaouter Khaoula, G. Hamedani, Abdullah H. Al-Aefaie, M. Ibrahim, Nadeem Shafique Butt, Moustafa Salem","doi":"10.18187/pjsor.v19i4.3554","DOIUrl":"https://doi.org/10.18187/pjsor.v19i4.3554","url":null,"abstract":"In this paper, we present a new exponential accelerated failure time model. Some of its properties and characterization results are derived. Different estimation methods are considered for assessing the finite sample behaviour of the estimators. Simulation studies for comparing the estimation methods are performed. Finally, we present a novel modified chi-square test for the novel exponential accelerated failure time model in both complete and right censored data cases. The validity of the new model is checked by using the theoretical global of the Nikulin-Rao-Robson. The maximum likelihood method is considered for this purpose. Two simulation studies are performed to assess the exponential accelerated failure time model and the efficiency of the Nikulin-Rao-Robson test statistic, respectively. Three real data sets are considered for illustrating the efficiency of the test statistic in validation.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138597598","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 : 2023-12-06DOI: 10.18187/pjsor.v19i4.2972
M. Abdullah, A. Masmoudi
This work presents a novel two-parameter G family of continuous probability distributions with compounded parameters. To determine and examine the pertinent mathematical properties, calculations are performed. In one of the special sections, the standard inverse-Rayleigh baseline model is mathematically and statistically emphasized. We generated a number of bivariate and multivariate distributions using the copula method. These new distributions will aid in the modelling of bivariate and multivariate data. The applicability and flexibility of the new compounded two-parameters-G family are demonstrated through three applications to real-life data sets. These examples demonstrate the applicability of the family.
{"title":"Modeling Real-life Data Sets with a Novel G Family of Continuous Probability Distributions: Statistical Properties, and Copulas","authors":"M. Abdullah, A. Masmoudi","doi":"10.18187/pjsor.v19i4.2972","DOIUrl":"https://doi.org/10.18187/pjsor.v19i4.2972","url":null,"abstract":"This work presents a novel two-parameter G family of continuous probability distributions with compounded parameters. To determine and examine the pertinent mathematical properties, calculations are performed. In one of the special sections, the standard inverse-Rayleigh baseline model is mathematically and statistically emphasized. We generated a number of bivariate and multivariate distributions using the copula method. These new distributions will aid in the modelling of bivariate and multivariate data. The applicability and flexibility of the new compounded two-parameters-G family are demonstrated through three applications to real-life data sets. These examples demonstrate the applicability of the family.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138594569","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 : 2023-12-06DOI: 10.18187/pjsor.v19i4.4232
P. Hazarika, Sricharan Shah, Subrata Chakraborty, M. Alizadeh, G. Hamedani
Multimodal alpha skew normal (MMASN) distribution is proposed for modelling skewed observations in the presence of multiple modality at arbitrary points. To this end the multimodal skew normal distribution of Chakraborty et al. (2015) is extended by integrating it with alpha skew normal distribution of Elal-Olivero (2010). Cumulative distribution function (cdf), moments, skewness and kurtosis of the proposed distribution are derived in compact form. The data modelling ability of the proposed distribution is checked by considering three multimodal data sets from literature in comparison to some nested and known distributions. Akaike Information Criterion (AIC) and the likelihood ratio (LR) test, both clearly favored proposed model over its nested models as expected.
提出了多模态α偏正态分布(MMASN)，用于在任意点存在多模态时对偏态观测值进行建模。为此，通过将Chakraborty等人(2015)的多模态偏态正态分布与Elal-Olivero(2010)的α偏态正态分布进行积分，扩展了Chakraborty等人(2015)的多模态偏态正态分布。以紧凑形式导出了该分布的累积分布函数(cdf)、矩、偏度和峰度。通过将文献中的三个多模态数据集与一些嵌套分布和已知分布进行比较，验证了所提出分布的数据建模能力。赤池信息准则(Akaike Information Criterion, AIC)和似然比(likelihood ratio, LR)检验结果与预期一致，都明显倾向于建议模型而非嵌套模型。
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