https://pjsor.com/pjsor/issue/feedPakistan Journal of Statistics and Operation Research2024-03-09T15:26:33+05:00Editor PJSOReditor@pjsor.comOpen Journal Systems<p>Pakistan Journal of Statistics and Operation Research started in 2005 with the aim to promote and share scientific developments in the subject of statistics and its allied fields. Initially, PJSOR was a bi-annually double-blinded peer-reviewed publication containing articles about Statistics, Data Analysis, Teaching Methods, Operational Research, Actuarial Statistics, and application of statistical methods in a variety of disciplines. Because of the increasing submission rate, the editorial board of PJSOR decided to publish it on a quarterly basis from 2012. Brief chronicles are overseen by an <a title="PJSOR Editorial Board" href="https://pjsor.com/pjsor/board">Editorial Board</a> comprised of academicians and scholars. We welcome you to <a title="Submissions" href="http://pjsor.com/index.php/pjsor/about/submissions">submit</a> your research for possible publication in PJSOR through our online submission system. <strong>Publishing in PJSOR is absolutely free of charge (No Article Processing Charges)</strong>.<br><a href="https://portal.issn.org/resource/ISSN/2220-5810"><strong>ISSN : 1816 2711</strong></a> <strong>| <a href="https://portal.issn.org/resource/ISSN/2220-5810">E- ISSN : 2220 5810</a></strong></p>https://pjsor.com/pjsor/article/view/4044A Multiplicative Bias Correction Technique for Estimating Quantile Function with an Application2024-03-08T15:16:59+05:00NICHOLAS MAKUMInicholas.makumi@jkuat.ac.keRomanus Odhiambo Otienorodhiambo@must.ac.keGeorge Otieno Orwagorwa@buc.ac.keAlexis Habinezaalexhabk87@gmail.com<p>Smooth non-parametric quantile function estimators on basis of symmetric kernels exhibit boundary bias due to spill-over near the edges. An improved non-parametric estimator of a quantile function under simple random sampling without replacement is proposed, based on a multiplicative bias corrected distribution function. There is no spill-over around the edges with our new quantile estimator. The proposed quantile estimator's asymptotic properties are investigated. The suggested method is compared to existing estimators using real data set findings, demonstrating the improved performance.</p>2024-03-07T01:32:31+05:00Copyright (c) 2024 Pakistan Journal of Statistics and Operation Researchhttps://pjsor.com/pjsor/article/view/4216Censored and Uncensored Nikulin-Rao-Robson Distributional Validation: Characterizations, Classical and Bayesian estimation with Censored and Uncensored Applications2024-03-07T13:58:52+05:00Wahid A. M. Shehatawahid75maher@yahoo.comHafida Goualhafida.goual@univ-annaba.dzTalhi Hamidatalhihamida@yahoo.frAiachi Hibaaiachihiba@yahoo.comG.G. Hamedanigholamhoss.hamedani@marquette.eduAbdullah H. Al-Nefaieaalnefaie@kfu.edu.saMohamed Ibrahimmiahmed@kfu.edu.saNadeem Shafique Buttnshafique@kau.edu.saRania M. A. Osman12422022570882@pg.cu.edu.egHaitham M. Yousofhaitham.yousof@fcom.bu.edu.eg<p>In our paper, we introduce a novel extension of the Lomax distribution, aiming to enhance its applicability in various contexts. We emphasize a pragmatic approach in deriving mathematical properties of the new distribution, prioritizing its practical implications. Three distinct methods for characterizing the distribution are thoroughly discussed to provide a comprehensive understanding. The parameters of this newly proposed distribution are estimated through a diverse set of classical methodologies as well as Bayes’ method. Additionally, we develop the censored case maximum likelihood method to address scenarios where data may be incomplete. We meticulously compare the efficacy of likelihood estimation and Bayesian estimation using Pitman’s proximity criterion, thereby offering insights into their relative performance. For Bayesian estimation, we employ three distinct loss functions: the generalized quadratic, the Linex, and the entropy functions, each offering unique perspectives on the estimation process. Through extensive simulation experiments, we meticulously evaluate the performance of all estimation methods under various conditions, providing valuable insights into their practical utility. Furthermore, we conduct a comparative analysis between the Bayesian technique and the censored maximum likelihood method using the BB algorithm, facilitating a nuanced understanding of their respective strengths and weaknesses. In addition to estimation methodologies, we delve into the construction of the Nikulin-Rao-Robson statistic for the new model under both uncensored and censored cases. Detailed simulation studies and the presentation of two real-world applications elucidate the practical significance of our proposed statistics in diverse scenarios. Overall, our paper not only introduces a novel extension of the Lomax distribution but also provides a comprehensive exploration of various estimation techniques and statistical measures, underpinning its practical relevance across different domains.</p>2024-03-07T01:36:03+05:00Copyright (c) 2024 Pakistan Journal of Statistics and Operation Researchhttps://pjsor.com/pjsor/article/view/4296Statistical Inference on Process Capability Index Cpyk for Inverse Rayleigh Distribution under Progressive Censoring2024-03-09T15:26:33+05:00Kadir Karakayakkarakaya@selcuk.edu.trİsmail Kınacıikinaci@selcuk.edu.trYunus Akdoğanyakdogan@selcuk.edu.trBuğra Saraçoğlubugrasarac@selcuk.edu.trCoşkun Kuşcoskun@selcuk.edu.tr<p>In quality engineering, process capability indexes are used to determine the capability of a process. The well-known of the process capability indexes are Cp, Cpk, Cpm, and Cpmk. These indexes assume the normality of the product lifetime. \citet{maiti2010generalizing} suggested a Cpyk as a generalized process capability index without distributional assumption. In this paper, the maximum likelihood and Bayesian inference on the Cpyk are studied under progressive censoring when the underlying distribution is inverse Rayleigh distribution. Furthermore, Bayesian credible and highest posterior density intervals are discussed with the MCMC procedure. Several types of bootsrap confidence intervals are also considered. A Monte Carlo simulation is conducted in terms of the coverage probabilities and mean lengths of the proposed intervals. An illustrative example is presented to close the paper.</p> <p> </p>2024-03-07T01:37:45+05:00Copyright (c) 2024 Pakistan Journal of Statistics and Operation Researchhttps://pjsor.com/pjsor/article/view/3614A new bathtub and increasing failure rate model: An extension of the Mustapha type II distribution2024-03-09T15:26:22+05:00Mustapha Muhammadmmuhammad.mth@buk.edu.ngIsyaku Muhammadisyakuedu@yahoo.comMouna Bouchanemouna.bouchane@gmail.comMuhammad AslamAkhan_201185@yahoo.comSani Musamusasani1010@gmail.comSadiya Ali Ranosadiyarano@yahoo.com<p>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.</p>2024-03-07T01:43:38+05:00Copyright (c) 2024 Pakistan Journal of Statistics and Operation Researchhttps://pjsor.com/pjsor/article/view/4307A generating family of unit-Garima distribution: Properties, likelihood inference, and application2024-03-09T15:26:13+05:00Sirinapa Ayuyuensirinapaa@rmutt.ac.thWinai Bodhisuwanfsciwnb@ku.ac.th<p>This article proposes the unit Garima (UGa) distribution for analysing proportion data. Some statistical properties of the UGa distribution are investigated, including survival and hazard functions, order statistics, quantile function, and stress-strength reliability measure. Next, a new family of continuous distributions, called the unit Garima-generated (UGa-G) family of distributions, is studied. The UGa-G family of distributions has the feature to use the UGa distribution as the main generator and the concept of the T-X family of distributions. Some UGa-G family sub-models are provided, such as the UGa-Beta, UGa-Weibull, and UGa-normal distributions. The maximum likelihood method is used to estimate the model parameters for the statistical aspect. A Monte Carlo simulation for the percentile bootstrap confidence intervals for each parameter of the proposed distributions is provided. Applications to eight practical data sets are given to demonstrate the usefulness of the proposed distributions.</p>2024-03-07T01:53:27+05:00Copyright (c) 2024 Pakistan Journal of Statistics and Operation Researchhttps://pjsor.com/pjsor/article/view/4448A New Cubic Transmuted Inverse Weibull Distribution: Theory and Applications2024-03-08T15:26:11+05:00Md. Tusharuzzaman Tushartusherkgc@gmail.comSaman Hanif Shahbazshmohamad2@kau.edu.saMd. Mahabubur Rahmanmmriu.stat@gmail.comMuhammad Qaiser Shahbazmkmohamad@kau.edu.sa<p>This paper introduces a new cubic transmutation of the inverse Weibull distribution, known as a cubic transmuted inverse Weibull distribution. The model is thought to be useful for the analysis of complex life data, modeling failure times, accessing product reliability, and many other fields like economics, hydrology, biology, and engineering. Some statistical features of the proposed distribution are explored. These include moments, generating functions, quantile functions, reliability functions, and hazard rate functions. The distribution of order statistics for the proposed cubic transmuted inverse Weibull distribution is also studied. The maximum likelihood estimation approach is used to estimate the model parameters. The effectiveness of the estimation is investigated through extensive simulation study. The suitability of the proposed distribution has been studied by using five real-life datasets. It is found that the proposed distribution is the most suitable fit for the used data sets.</p>2024-03-07T01:55:27+05:00Copyright (c) 2024 Pakistan Journal of Statistics and Operation Researchhttps://pjsor.com/pjsor/article/view/4197Nash equilibrium selection using a hybrid two-player static game with trade-off ranking method2024-03-08T15:26:00+05:00Muhammad Akram Ramadhan Ibrahimakramahsumino@gmail.comNor Izzati Jainiati@ump.edu.myKU MUHAMMAD NAIM KU KHALIFkunaim@ump.edu.my<p>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.</p>2024-03-07T01:56:40+05:00Copyright (c) 2024 Pakistan Journal of Statistics and Operation Researchhttps://pjsor.com/pjsor/article/view/4225A New Two-Parameters Lindley-Frailty Model: Censored and Uncensored Schemes under Different Baseline Models: Applications, Assessments, Censored and Uncensored Validation Testing2024-03-07T15:25:26+05:00Samia Teghrisamia.teghri@univ-annaba.orgHafida Goualhafida.goual@univ-annaba.dzHamami Loubnaloubna.hamami@univ-annaba.orgNadeem Shafique Buttnshafique@kau.edu.saAbdelrahman M. Khedrabdelrahman.khedr@fcom.bu.edu.egHaitham M. Yousofhaitham.yousof@fcom.bu.edu.egMohamed Ibrahimmiahmed@kfu.edu.saMoustafa Salemmoustafasalemstat@com.dmu.edu.eg<p>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. </p>2024-03-07T02:00:45+05:00Copyright (c) 2024 Pakistan Journal of Statistics and Operation Researchhttps://pjsor.com/pjsor/article/view/4410Process Capability Analysis for Simple Linear Profiles in Multistage Processes2024-03-07T15:25:17+05:00Saeed Adibfaradibfar.saeed@gmail.comRassoul Noorossanarnoorossana@uco.edu<p>When a process is statistically under control, one may be interested in assessing the process performance based on the specification limits provided by the customer. This evaluation is referred to as process capability analysis. Manufacturing operations are often involved with multistage processes, in which the output of a stage is the input of its subsequent stage. This property is known as the cascade property. Existing methods in capability analysis studies are not applicable when a process or product is represented by profiles. This study presents a method to conduct process capability analysis in a multistage process when quality of a product or process is characterized by a simple linear profile. The performance of the proposed method for a two-stage process is evaluated by numerical simulation using an example from the literature. The results indicate that the proposed method eliminates the effect of the cascade property for different shift sizes and autocorrelations.</p>2024-03-07T02:02:38+05:00Copyright (c) 2024 Pakistan Journal of Statistics and Operation Research