Pakistan Journal of Statistics and Operation Research 2023-12-07T01:50:17+05:00 Editor PJSOR Open 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="">Editorial Board</a> comprised of academicians and scholars. We welcome you to <a title="Submissions" href="">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=""><strong>ISSN : 1816 2711</strong></a>&nbsp; &nbsp;<strong>|&nbsp; &nbsp;<a href="">E- ISSN : 2220 5810</a></strong></p> The Marshall–Olkin Pareto Type-I Distribution: Properties, Inference under Complete and Censored Samples with Application to Breast Cancer Data 2023-12-06T19:41:01+05:00 Maha A. Aldahlan Abdelhamid M. Rabie Mostafa Abdelhamid Abdul Hadi N. Ahmed Ahmed Z. Afify <p>In this paper, we introduce the Marshall–Olkin Pareto type-I (MOPTI) distribution. Structural properties of the MOPTI distribution including the quantile function, mean residual life, and a new theorem for strength-stress measure are introduced. Five methods of estimation for the MOPTI parameters based on complete samples are presented. Furthermore, we explore the estimation of the MOPTI parameters under type-I and type-II censoring. Two Monte Carlo simulation studies are conducted to evaluate the performance of the estimation methods under complete and censored samples. A real-life data set is used to validate the proposed methods.</p> 2023-12-05T11:43:00+05:00 Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research Black hole algorithm as a heuristic approach for rare event classification problem 2023-12-06T19:40:34+05:00 Elif Yıldırım <p>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.</p> 2023-12-06T00:34:19+05:00 Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research Schwarz’s Bayesian Information Criteria: A Model Selection Between Bayesian-SEM and Partial Least Squares-SEM 2023-12-06T19:40:25+05:00 Reny Rian Marliana Maya Suhayati Sri Bekti Handayani Ningsih <p>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.</p> 2023-12-06T00:40:16+05:00 Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research Modeling Climate data using the Quartic Transmuted Weibull Distribution and Different Estimation Methods 2023-12-06T19:40:17+05:00 Deluar Jahan Moloy M. A. Ali Farouq Mohammad A. Alam <p>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.</p> 2023-12-06T00:45:03+05:00 Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research Estimation based on Ranked Set Sampling for Farlie--Gumbel--Morgenstern Bivariate Weibull Distribution Parameters with an application to medical data 2023-12-06T19:40:08+05:00 Ahmad Hanandeh Amer Al-omari <p>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.</p> 2023-12-06T01:57:37+05:00 Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research A Novel Accelerated Failure Time Model: Characterizations, Validation Testing, Different Estimation Methods and Applications in Engineering and Medicine 2023-12-06T19:39:59+05:00 Haitham M. Yousof Hafida Goual Meribout Kaouter Khaoula G.G. Hamedani Abdullah H. Al-Aefaie Mohamed Ibrahim Nadeem Shafique Butt Moustafa Salem <p>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.</p> 2023-12-06T02:07:17+05:00 Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research Modeling Real-life Data Sets with a Novel G Family of Continuous Probability Distributions: Statistical Properties, and Copulas 2023-12-06T19:40:52+05:00 Murtadha Mansour Abdullah Afif Masmoudi <p>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.</p> 2023-12-06T00:00:00+05:00 Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research Multimodal Alpha Skew Normal Distribution: A New Distribution to Model Skewed Multimodal Observations 2023-12-07T01:50:17+05:00 Partha Jyoti Hazarika Sricharan Shah Subrata Chakraborty Morad Alizadeh G.G. Hamedani <p>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.</p> 2023-12-06T02:15:11+05:00 Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research Estimation of the Parameters of the Modified Weibull Distribution with Bathtub-shaped Failure Rate Function 2023-12-06T19:40:43+05:00 Adam Abdelrahman Hussein Adam Hakan SavaÅŸ Sazak <p>In this study, we propose two estimators called the 3-step MML and the combined estimators of the parameters of the modified Weibull distribution which is used in reliability models with bathtub-shaped failure rate function. The simulations show the superiority of both estimators over the graphical estimators. Particularly, the combined estimators are the better of the two. Two real-life data applications also show the superiority of the proposed estimators compared to the graphical estimators.</p> 2023-12-06T00:00:00+05:00 Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research