Pakistan Journal of Statistics and Operation Research <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 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 variety of disciplines. Because of increasing submission rate, editoral board of PJSOR decided to publish it on quarterly basis from 2012. Brief chronicles is overseen by an Editorial Board comprised of academicians and scholars. We welcome you to submit your research for possible publication in PJSOR through our online submission system. Publication in PJSOR is absolutely free of charge.<br><a href=";tip=sid&amp;clean=0"><strong>ISSN : 1816 2711</strong></a>&nbsp; &nbsp;<strong>|&nbsp; &nbsp;<a href=";tip=sid&amp;clean=0">E- ISSN : 2220 5810</a></strong></p> College of Statistical and Actuarial Sciences en-US Pakistan Journal of Statistics and Operation Research 1816-2711 <p><strong>Authors who publish with this journal agree to the following terms:</strong></p> <ul> <li>Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a <a href="" target="_new">Creative Commons Attribution License</a> that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.&nbsp;</li> <li>Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.</li> <li>Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See <a href="" target="_new">The Effect of Open Access</a>).</li> </ul> <p>&nbsp;</p> Performance of the Hybrid Approach based on Rough Set Theory <p>One of the essential problems in data mining is the removal of negligible variables from the data set. This paper proposes a hybrid approach that uses rough set theory based algorithms to reduct the attribute selected from the data set and utilize reducts to raise the classification success of three learning methods; multinomial logistic regression, support vector machines and random forest using 5-fold cross validation. The performance of the hybrid approach is measured by related statistics. The results show that the hybrid approach is effective as its improved accuracy by 6-12% for the three learning methods.</p> Betul Kan Kilinc Yonca YAZIRLI Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-05-31 2020-05-31 217 224 10.18187/pjsor.v16i2.3069 The Weighted Power Lindley Distribution with Applications on the Life Time Data <p>In this paper, we have proposed a new version of power lindley distribution known as weighted power lindley distribution. The different structural properties of the newly model have been studied. The maximum likelihood estimators of the parameters and the Fishers information matrix have been discussed. It also provides more flexibility to analyze complex real data sets. &nbsp;An application of the model to a real data set is analyzed using the new distribution, which shows that the weighted power Lindley distribution can be used quite effectively in analyzing real lifetime data.</p> Aafaq A. Rather Gamze Özel Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-05-31 2020-05-31 225 237 10.18187/pjsor.v16i2.2931 On Bayesian estimation of step stress accelerated life testing for exponentiated Lomax distribution based on censored samples <p>In reliability analysis and life-testing experiments, the researcher is often interested in the effects of changing stress factors such as “temperature”, “voltage” and “load” on the lifetimes of the units. Step-stress (SS) test, which is a special class from the well-known accelerated life-tests, allows the experimenter to increase the stress levels at some constant times to obtain information on the unknown parameters of the life models more speedily than under usual operating conditions. In this paper, a simple SS model from the exponentiated Lomax (ExpLx) distribution when there is time limitation on the duration of the experiment is considered. Bayesian estimates of the parameters assuming a cumulative exposure model with lifetimes being ExpLx distribution are resultant using Markov chain Monte Carlo (M.C.M.C) procedures. Also, the credible intervals and predicted values of the scale parameter, reliability and hazard are derived. Finally, the numerical study and real data are presented to illustrate the proposed study</p> Refah Mohamed Alotaibi Hoda Ragab Rezk Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-05-31 2020-05-31 239 248 10.18187/pjsor.v16i2.2705 The four-parameter Fréchet distribution: Properties and applications <p>In this article, we propose a new four-parameter Fréchet distribution called the odd Lomax Fréchet distribution. The new model can be expressed as a linear mixture of Fréchet densities. We provide some of its mathematical properties. The estimation of the model parameters is performed by the maximum likelihood method. We illustrate the good performance of the maximum likelihood estimates via a detailed numerical simulation study. The importance and usefulness of the proposed distribution for modeling data are illustrated using two real data applications.</p> Mohamed Hamed Fahad Aldossary Ahmed Z. Afify Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-05-31 2020-05-31 249 264 10.18187/pjsor.v16i2.3097 Associated Factors of Cardiovascular Diseases in Pakistan: Assessment of Path Analyses Using Warp Partial Least Squares Estimation <p>Demographic and socio-economic (SE) factors are associated with modifiable, clinical factors and cardiovascular disease (CVDs). However, the inclusion of mediators in these relationships creates complex pathways which extend the roles of factors within the model. The traditional hierarchal logistic regression (HLR) is unable to estimate the transmittal effects of factors through different layers of factors of CVDs. The study aims to simultaneously estimate and validate the probable linear and non-linear relationships among factors of CVDs considering potential mediators. Four hundred sixty participants (312 males and 148 females) were selected through systematic sampling in this sex-matched case control (1:1 ratio) study conducted in the largest Cardiac Center of Pakistan. The information on demographic, SE, modifiable and clinical factors of CVDs was recorded. Warp partial least squares (PLS) based on warp 3 algorithm was used to estimate the simultaneous linear and non-linear path coefficients of the proposed model of study. The study found that demographic and SE factors played a significant role in shaping the modifiable factors which further transmit their impact to CVDs. However, this transmitted impact of modifiable factors on CVDs was mediated through metabolic syndrome abnormalities (MSA) except self-reported subjective stress (SSS). Sleep satisfaction and negative dietary habits were the mediators between the relationship of SSS and MSA. Physical activity is the strongest factor associated with CVDs status. The proposed path analyses, verifying the mediation role of MSA in the pathways of relationships which would help in identifying the risky group of population and guide in formulating the health promotion policies for the reduction of CVDs burden. Further, Warp 3 algorithm is the better option to estimate complex models containing linear and non-linear relationship in the same model.</p> Mirza Rizwan Sajid Noryanti Muhammad Roslinazairimah Zakaria Ahmad Shahbaz Ahmad Nauman Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-05-31 2020-05-31 265 277 10.18187/pjsor.v16i2.3075 A General Base of Power Transformation to Improve the Boundary Effect in Kernel Density without Shoulder Condition <p>In this paper, a general base of power transformation under the kernel method is suggested and applied in the line transect sampling to estimate abundance. The suggested estimator performs well at the boundary compared to the classical kernel estimator without using the shoulder condition assumption. The transformed estimator show smaller value of mean squared error and absolute bias from the efficiency results obtained using simulation.</p> Baker Ishaq Albadareen Noriszura Ismail Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-05-31 2020-05-31 279 285 10.18187/pjsor.v16i2.3164 Sustainable Survival Pyramid Model to Balance Four Factors of Cost, Quality, Risk and Time Limitation in Project Management under Uncertainty <p class="icsmbodytext">The final agreement on the timing of project completion is one of the obvious problems between project managers and their clients. There have been numerous reports of customers requesting shorter completion times than previously announced. This request will definitely affect the three project factors of overall cost, final quality of the project, and risk of implementation. This paper proposes a multipurpose cumulative complex linear programming to minimize "project overhead," "increase projects total risk" and "increase overall project quality" due to “time constraints." In other words, the proposed study is fully implemented among the four goals mentioned to shorten the project duration. Computational experiments have also been used to evaluate the performance of the proposed model. The main objective of this paper is to optimize the integration of the four factors of the survival pyramid (time, cost, quality, and risk) in industrial projects simultaneously under uncertainty. An innovative solution based on the multi-objective genetic algorithm (NSGA-II) is presented. This model is then used to solve a problem in another study and its results, strengths, and weaknesses compared to the previous model are evaluated. The results show the performance of the proposed model in all four factors is better than the previous models.</p> Mehdi Safaei Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-05-31 2020-05-31 287 294 10.18187/pjsor.v16i2.3203 Joint Modeling of a Longitudinal Measurement and Parametric Survival Data with Application to Primary Biliary Cirrhosis Study <p>Although longitudinal and survival data are collected in the same study, they are usually analyzed separately. Measurement errors and missing data problems arise because of separate analysis of these two data. Therefore, joint model should be used instead of separate analysis. The standard joint model frequently used in the literature is obtained by combining the linear mixed effect model of longitudinal data and Cox regression model with survival data. Nevertheless, to use the Cox regression model for survival data, the assumption of proportional hazards must be provided. Parametric survival sub-models should be used instead of the Cox regression model for the survival sub-model of the JM where the assumption is not provided. In this article, parametric joint modeling of longitudinal data and survival data that do not provide the assumption of proportional hazards are investigated. For the survival data, the model with Exponential, Weibull, Log-normal, Log-logistic, and Gamma accelerated failure time models and the linear mixed effect model are combined with random effects and the models were applied in primary biliary cirrhosis data set obtained from Mayo Clinic. After determining the best parametric joint model according to Akaike and Bayesian information criterions, the best available model was compared with standard joint model and of separate analysis of survival data and longitudinal data. As a results, in the studies where longitudinal and survival data are obtained together, it is seen that the parametric joint model gives more better results than the standard joint model when the proportional hazard assumption is not provided.</p> Elif Dil Duru Karasoy Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-05-31 2020-05-31 295 304 10.18187/pjsor.v16i2.3131 Some New Goodness-of-fit Tests for Rayleigh Distribution <p>In this paper, we introduce some new goodness-of-fit tests for the Rayleigh distribution based on Jeffreys, Lin-Wong and Renyi divergence measures. Then, the new proposed tests are compared with other tests in the literature. We compare the power of considered tests for some alternative distributions whose powers are calculated by Monte Carlo simulation. Finally, we conclude that entropy-based tests have a good performance in terms of power and among them Jeffreys test is the best one.</p> <p>&nbsp;</p> Seyed Mahdi Amir Jahanshahi Arezo Habibi Rad Vahid Fakoor Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-05-31 2020-05-31 305 315 10.18187/pjsor.v16i2.3087 Two-Echelon Supply Chain Model with Demand Dependent On Price, Promotional Effort and Service Level in Crisp and Fuzzy Environments <p>This article explores a supply chain model consisting of a single manufacturer and two competing retailers. The manufacturer, as a Stackelberg leader specifies a wholesale price and bears servicing costs of the products. Then, both the retailers advertise the products and sell them to the customers. So, the demand of the products is influenced by selling price, service level and also promotional effort. On the basis of this gaming structure, two mathematical models have been formed - crisp model, where each member of the chain exactly knows all the cost parameters and fuzzy model where those cost parameters are considered as fuzzy numbers. Optimal strategies for the manufacturer and the retailers are determined and some numerical examples have been given. Finally, how perturbations of parameters affect the profits of the chain members have been determined.</p> Sahidul Islam Sayan Chandra Deb Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-06-03 2020-06-03 317 329 10.18187/pjsor.v16i2.3091 The Marshall-Olkin Extended Power Lomax Distribution with Applications <p>In this article, we dened a new four-parameter model called Marshall-Olkin extended power Lomax distribution and studied its properties. Limiting distributions of sample maxima and sample minima are derived. The reliability of a system when both stress and strength follows the new distribution is discussed and associated characteristics are computed for simulated data. Finally, utilizing maximum likelihood estimation, the goodness of the distribution is tested for real data.</p> JIJU GILLARIOSE Lishamol Tomy Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-06-03 2020-06-03 331 341 10.18187/pjsor.v16i2.2805 The Poisson Topp Leone Generator of Distributions for Lifetime Data: Theory, Characterizations and Applications <p><span style="background-color: #ffffff;">We study a new family of distributions defined by the minimum of the Poisson random number of independent identically distributed random variables having a Topp Leone-G distribution (see Rezaei et al., (2016)). Some mathematical<br>properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics, reliability and entropies are derived. Maximum likelihood estimation of the model parameters is investigated. Some special models of the new<br>family are discussed. An application is carried out on&nbsp; real data set applications sets to show the potentiality of the proposed family.</span></p> Faton Merovci Haitham Yousof G. G Hamedani Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-06-03 2020-06-03 343 355 10.18187/pjsor.v16i2.3230 Bayesian Estimation and Prediction Based on Progressively First Failure Censored Scheme from a Mixture of Weibull and Lomax Distributions <p>This paper develops Bayesian estimation and prediction, for a mixture of Weibull and Lomax distributions, in the context of the new life test plan called progressive first failure censored samples. Maximum likelihood &nbsp;estimation and Bayes estimation, under informative and non-informative priors, are obtained using Markov Chain Monte Carlo methods, based on the symmetric square error Loss function and the asymmetric linear exponential (LINEX) and general entropy loss functions. The maximum likelihood estimates and the different Bayes estimates are compared via a Monte Carlo simulation study. Finally, Bayesian prediction intervals for future observations are obtained using a numerical example</p> Mohamed M. Mahmoud Manal Mohamed Nassar Marwa Ahmed Aefa Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-06-03 2020-06-03 357 372 10.18187/pjsor.v16i2.2442 A Generalization of Reciprocal Exponential Model: Clayton Copula, Statistical Properties and Modeling Skewed and Symmetric Real Data Sets <p>We introduce a new extension of the reciprocal Exponential distribution for modeling the extreme values. We used the Morgenstern family and the clayton copula for deriving many bivariate and multivariate extensions of the new model. Some of its properties are derived. We assessed the performance of the maximum likelihood estimators (MLEs) via a graphical simulation study. The assessment was based on the sample size. The new reciprocal model is employed for modeling the skewed and the symmetric real data sets. The new reciprocal model is better than some other important competitive models in statistical modeling.</p> M. M. Mansour Nadeem Shafique Butt Haitham Yousof S. I. Ansari Mohamed Ibrahim Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-06-03 2020-06-03 373 386 10.18187/pjsor.v16i2.3298 Permutation Tests for Two-sample Location Problem Under Extreme Ranked Set Sampling <p>In this paper, permutation test of comparing two-independent samples is investigated in the context of extreme ranked set sampling (ERSS). Three test statistics are proposed. The statistical power of these new test statistics are evaluated numerically. The results are compared with the statistical power of the classical independent two-sample $t$-test, Mann-Whitney $U$ test, and the usual two-sample permutation test under simple random sampling (SRS). In addition, the method of computing a confidence interval for the two-sample permutation problem under ERSS is explained. The performance of this method is compared with the intervals obtained by SRS and Mann-Whitney procedures in terms of empirical coverage probability and expected length. The comparison shows that the proposed statistics outperform their counterparts. Finally, the application of the proposed statistics is illustrated using a real life example.</p> Monjed H. Samuh Ridwan A. Sanusi Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-06-03 2020-06-03 387 408 10.18187/pjsor.v16i2.2746