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 class="show">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 class="show">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 class="show">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> Optimum Method for Determining Weibull Distribution Parameters Used in Wind Energy Estimation <p>One of the well-known methods for the determination of wind energy potential is the two-parameter Weibull distribution. It is clear that the success of the Weibull distribution for wind energy applications depends on the estimation of the parameters which can be determined by using various numerical methods. In the present study, Monte Carlo simulation method is performed by using six parameters estimation method that is used in the estimation of Weibull distribution parameters such as Maximum Likelihood Estimation (MLE), Least Squares Method (LSM), Method of Moments (MOM), Method of Logarithmic Moments (MLM), Percentile Method (PM), and L-Moment Method (LM), and is compared to Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). In this study, the wind energy potential of the Meşelik region in Eskişehir was modeled with two-parameter Weibull distribution. The average wind speed (m/s) data, which are gathered in 10-minute intervals from the measuring device installed 10 meters about the ground in Meşelik Campus of Eskişehir Osmangazi University, is used. As a result of the simulation study, it has been determined that MLE is the best parameter estimation method for two-parameter Weibull distribution in large sample sizes, and LM has the closest performance to MLE. The wind speed (m/h) data of the region has been successfully modeled with two-parameter Weibull distribution and the highest average wind power density has been obtained in July as 49.38295 (W/m<sup>2</sup>) while the lowest average wind power density has been obtained in October as 19.30044 (W/m<sup>2</sup>).</p> Ulku Erisoglu Nil Aras Hasan Donat Yildizay Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-12-02 2020-12-02 635 648 10.18187/pjsor.v16i4.3456 Statistical Inference for Inverted Kumaraswamy Distribution Based on Dual Generalized Order Statistics <p>In this paper, the shape parameters, reliability and hazard rate functions of the inverted Kumaraswamy distribution are estimated using maximum likelihood and Bayesian methods based on dual generalized order statistics. The Bayes estimators are derived under the squared error loss function as a symmetric loss function and the linear-exponential loss function as an asymmetric loss function based on dual generalized order statistics. Confidence and credible intervals for the parameters, reliability and hazard rate functions are obtained. All results are specialized to lower record values, also a numerical study is presented to illustrate the theoretical procedures.</p> Abeer Abd-Alla EL-Helbawy Gannat Ramadan AL-Dayian Asmaa Mohamed Abd AL-Fattah Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-12-02 2020-12-02 649 660 10.18187/pjsor.v16i4.2774 A New Probability Distribution Family Arising from Truncated Power Lomax Distribution with Application to Weibull Model <p>The truncated distributions have been widely studied, mainly in life-testing and reliability analysis.&nbsp; In this paper, we introduce a new right truncated generator related to power Lomax distribution, referred to right truncated power Lomax--G family. The proposed family is a generalization of recently [0, 1] truncated Lomax-G family. Statistical properties like; moments, moment generating function, probability weighted moments, quantile function, mean deviation, order statistics and Rényi entropy are derived. Five new sub-models from the truncated family are presented. Maximum likelihood estimation is investigated and simulation issues are discussed for truncated power Lomax Weibull model as particular case from the family. The flexibility of the truncated power Lomax Weibull is assessed by applying it to a real data set. The application indicates that the truncated power Lomax Weibull distribution model can give better fits than other well-known lifetime distributions.</p> Amal Hassan Mohamed Sabry Ahmed Elsehetry Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-12-02 2020-12-02 661 674 10.18187/pjsor.v16i4.3442 The Three-parameters Marshall-Olkin Generalized Weibull Model with Properties and Different Applications to Real Data Sets <p>A new three-parameter life parametric model called the Marshall-Olkin generalized Weibull is defined and studied. Relevant properties are mathematically derived and analyzed. The new density exhibits various important symmetric and asymmetric shapes with different useful kurtosis. The new failure rate can be “constant”, “upside down-constant (reversed <strong>U</strong>-HRF-constant)”, “increasing then constant”, “monotonically increasing”, “J-HRF” and “monotonically decreasing”. The method of maximum likelihood is employed to estimate the unknown parameters. A graphical simulation is performed to assess the performance of the maximum likelihood estimation. We checked and proved empirically the importance, applicability and flexibility of the new Weibull model in modeling various symmetric and asymmetric types of data. The new distribution has a high ability to model different symmetric and asymmetric types of data.</p> Mohamed G. Khalil Wagdy M. Kamel Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-12-02 2020-12-02 675 688 10.18187/pjsor.v16i4.2339 ln-Type Variance Estimators in Simple Random Sampling <p>Until now, various types of estimators have been used for estimating the population variance in simple random sampling studies, including ratio, product, regression and exponential-type estimators. In this article, we propose a family of -type estimators for the first time in the simple random sampling and show that they are more efficient than the other types of estimators under certain conditions obtained theoretically. Numerical illustrations and a simulation study support our findings in theory. In addition, it has been shown how to determine the optimal points in order to reach the minimum MSE values with the properties of the <em>ln</em>-type estimators in the different data sets.</p> Hatice Oncel Cekim Cem Kadilar Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-12-02 2020-12-02 689 696 10.18187/pjsor.v16i4.3072 A Generalization of Lomax Distribution with Properties, Copula and Real Data Applications <p>A new generalization of Lomax distribution is derived and studied. Some of its useful properties are derived. A simple clayton copula is used to generate many bivariate and multivariate type models. We performed graphical simulations to assess the finite sample behavior of the estimations. The new model is employed in modelling three real data sets.</p> Hanaa Elgohari Haitham Yousof Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-12-02 2020-12-02 697 711 10.18187/pjsor.v16i4.3260 Testing the Semi Markov Model Using Monte Carlo Simulation Method for Predicting the Network Traffic <p>Semi-Markov processes can be considered as a generalization of both Markov and renewal processes. One of the principal characteristics of these processes is that in opposition to Markov models, they represent systems whose evolution is dependent not only on their last visited state but on the elapsed time since this state. Semi-Markov processes are replacing the exponential distribution of time intervals with an optional distribution. In this paper, we give a statistical approach to test the semi-Markov hypothesis. Moreover, we describe a Monte Carlo algorithm able to simulate the trajectories of the semi-Markov chain. This simulation method is used to test the semi-Markov model by comparing and analyzing the results with empirical data. We introduce the database of Network traffic which is employed for applying the Monte Carlo algorithm. The statistical characteristics of real and synthetic data from the models are compared. The comparison between the semi-Markov and the Markov models is done by computing the Autocorrelation functions and the probability density functions of the Network traffic real and simulated data as well. All the comparisons admit that the Markovian hypothesis is rejected in favor of the more general semi Markov one. Finally, the interval transition probabilities which show the future predictions of the Network traffic are given.</p> Shirin Kordnoori Hamidreza Mostafaei Shaghayegh Kordnoori Mohammadmohsen Ostadrahimi Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-12-02 2020-12-02 713 720 10.18187/pjsor.v16i4.3394 On Modified Burr XII-Inverse Weibull Distribution: Development, Properties, Characterizations and Applications <p>A flexible lifetime distribution with increasing, decreasing, inverted bathtub and modified bathtub hazard rate called Modified Burr XII-Inverse Weibull (MBXII-IW) is introduced and studied. The density function of MBXII-IW is exponential, left-skewed, right-skewed and symmetrical shaped.&nbsp; Descriptive measures on the basis of quantiles, moments, order statistics and reliability measures are theoretically established. The MBXII-IW distribution is characterized via different techniques. Parameters of MBXII-IW distribution are estimated using maximum likelihood method. The simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of MBXII-IW distribution is demonstrated by its application to real data sets: serum-reversal times and quarterly earnings.</p> Fiaz Ahmad Bhatti G. G. Hamedani Haitham M. Yousof Azeem Ali Munir Ahmad Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-12-02 2020-12-02 721 735 10.18187/pjsor.v16i4.2622 Economic and Economic-Statistical Design of Multivariate Bayesian Control Chart with Variable Sampling Intervals <p>Due to the proper performance of Bayesian control chart in detecting process shifts, it recently has become the subject of interest. It has been proved that on Bayesian and traditional control charts, the economic and statistical performances of the variable sampling interval (VSI) scheme are superior to those of the fixed ratio sampling (FRS) strategy in detecting small to moderate shifts. This paper studies the VSI multivariate Bayesian control chart based on economic and economic-statistical designs. Since finding the distribution of Bayesian statistic is t complicated, we apply Monte Carlo method and we employ artificial bee colony (ABC) algorithm to obtain the optimal design parameters (sample size, sampling intervals, warning limit and control limit). In the end, this case study is compared with VSI Hotelling’s T2 control chart and it is shown that this approach is more desirable statistically and economically.</p> Masoud Tavakoli Reza Pourtaheri Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-12-02 2020-12-02 737 750 10.18187/pjsor.v16i4.3417 A Multi-Attribute Assisted Performance Deduction and Related Value in Triple Helix Innovation Networks <p>Typically, Triple Helix relations, between, Higher Education Institutions, Governments and Industry(s) are inferred from patents and research output. Systemic determination of the relationship is because of observations over a period. It is, however, possible to analyze this relation from a system present from the word-go. This then allows for the interaction to be analyzed on the basis of performance and logically gains for participation by all the agents. Several models have been proposed to deduce the Triple Helix Relation and these hold. This paper has however introduced a new dimension to the analysis, by viewing participation from an investor point of view with decision making being of a complex and deductive nature based on the performance of higher education systems or institutions. The TOPSIS supported performance deductions helps synthesis decision solutions that facilitates value determination of performance and its resultant impact on investment gains. Possible future implications for this, are also provided</p> Honxing Yao Henry Asante Antwi Evans Takyi Ankomah-Asare Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-12-02 2020-12-02 751 760 10.18187/pjsor.v16i4.2814 Incorporation of Preferences into Supply Chains DEA Efficiency: A Geometric Attribution Approach <p>Among many applications, several studies using Data Envelopment Analysis (DEA) have examined and studied the efficiency of supply chains. However, the majority of existing approaches dealing with this research area have ignored the important factor of decision makers’ preferences. The main objective of this article is to provide consistent DEA models that allow for efficiency analysis in order to determine the optimal allocation of resources according to these preferences. We propose three cases that are inspired from the geometric decomposition of preference attributions: (1) horizontal attribution, which is when decision makers treat each supply chain as a single non-detachable entity; (2) vertical attribution, which is when decision makers consider supply chains detachable and (3) combined attribution, which is when decision makers concurrently assign weights to the supply chain and to its members. Based on this suggested decomposition, new DEA models are developed, and an illustrative example is applied. The obtained results are relevant and show that DEA is capable of easily incorporating the preferences of decision-makers without resorting to weight restrictions on inputs or outputs.</p> Walid Abdelfattah Mohammed Sadok Cherif Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-12-02 2020-12-02 761 774 10.18187/pjsor.v16i4.2578 The Odd Log-Logistic Poisson Inverse Rayleigh Distribution: Statistical Properties and Applications <p>In this work, a new extension of the Inverse Rayleigh model is proposed and studied. We derive some of its fundamental properties. We assess the performance of the maximum likelihood estimators via a simulation study. The importance of the new model is shown via two applications to real data sets. The new model is better fit than other important competitive models based on two real data sets.</p> Ibrahim Elbatal Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-12-02 2020-12-02 775 787 10.18187/pjsor.v16i4.2930 An Extension of Log-Logistic Distribution for Analyzing Survival Data In this paper, a new generalization of Log Logistic Distribution using Alpha Power Transformation is proposed. The new distribution is named Alpha Power Log-Logistic Distribution. A comprehensive account of some of its statistical properties are derived. The maximum likelihood estimation procedure is used to estimate the parameters. The importance and utility of the proposed model are proved empirically using two real life data sets. Aliya Syed Malik S.P. Ahmad Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-12-02 2020-12-02 789 801 10.18187/pjsor.v16i4.2961 A New Method to Solve Interval Transportation Problems <p>transportation problem (ITP) in which the cost-coefficients of the objective function, source and destination parameters are all in the form of interval. In this paper, the single objective interval transportation problem is transformed into an equivalent crisp bi-objective transportation problem where the left-limit and width of the interval are to be minimized. The solution to this bi-objective model is then obtained with the help of fuzzy programming technique. The proposed solution procedure has been demonstrated with the help of a numerical example. A comparative study has also been made between the proposed solution method and the method proposed by Das et al.(1999) .</p> Abdul Quddoos Ummey Habiba Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-12-02 2020-12-02 802 811 10.18187/pjsor.v16i4.3269 Chen Pareto Distribution:Properties and Application <p>In this work, a new distribution called the Chen Pareto distribution was derived using the Chen-G family of distributions. The mixture representation of the distribution was obtained. Furthermore, some statistical properties such as moments, moment generating functions, order statistics properties of the distribution were explored. The parameter estimation for the distribution was done using the maximum likelihood estimation method and the performance of estimators was assessed by conducting an extensive simulation study. The distribution was applied to a real dataset in which it performs best when compared to some related distributions</p> Phillip Awodutire Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-12-02 2020-12-02 812 826 10.18187/pjsor.v16i4.3418 The normal-tangent-G class of probabilistic distributions: properties and real data modellin <p>This paper introduces a novel class of probability distributions called normal-tangent-G, whose submodels are parsi- monious and bring no additional parameters besides the baseline’s. We demonstrate that these submodels are iden- tifiable as long as the baseline is. We present some properties of the class, including the series representation of its probability density function (pdf) and two special cases. Monte Carlo simulations are carried out to study the behav- ior of the maximum likelihood estimates (MLEs) of the parameters for a particular submodel. We also perform an application of it to a real dataset to exemplify the modelling benefits of the class.</p> Fábio Silveira Frank Gomes-Silva Cícero Brito Moacyr Cunha-Filho Jader Jale Felipe Gusmão Sílvio Xavier-Júnior Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-12-02 2020-12-02 827 838 10.18187/pjsor.v16i4.3443 A linear programming-based approach to estimate discrete probability functions with given quantiles <p>The aim of this paper is to estimate probability distribution functions with maximum entropy and known quantiles‎. ‎The paper formulates the problem as a nonlinear optimization problem‎, ‎and converts it into a system of nonlinear equations by Lagrange multipliers method‎. ‎Finally‎, ‎an efficient method is proposed to obtain a solution of the nonlinear system‎. ‎The method needs to solve a linear programming problem in each iteration‎. ‎Since linear programming problems can be solved in a reasonable time‎, ‎our proposed method is faster than generic methods of solving nonlinear programming problems‎. ‎Several computational experiment are provided to demonstrate the performance and validation of our proposed method‎.</p> Zohre Nikooravesh Javad Tayyebi Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-12-02 2020-12-02 839 849 10.18187/pjsor.v16i4.2978 Characterizations of the New Poisson-Weighted Exponential and the Exponentiated Weibull-Geometric Discrete Distributions <p>Certain characterizations of the new Poisson-weighted exponentiated and the exponentiated Weibull-geometric discrete distributions introduced by Altun(2019) and by Famoye(2019), respectively, are presented here with the intention of completing, in some way, their works.</p> G.G. Hamedani Copyright (c) 2020 Pakistan Journal of Statistics and Operation Research 2020-12-02 2020-12-02 851 854 10.18187/pjsor.v16i4.3465