Pakistan Journal of Statistics and Operation Research
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Pakistan Journal of Statistics and Operation Researchen-US<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="http://creativecommons.org/licenses/by/3.0/" 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.</li></ul><div> </div><ul><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></ul><div> </div><ul><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="http://opcit.eprints.org/oacitation-biblio.html" target="_new">The Effect of Open Access</a>).</li></ul><p><span><br /></span></p>editor@pjsor.com (Dr. Shahid Kamal)annum@pjsor.com (Support Team)Thu, 30 Nov 2017 20:24:43 +0000OJS 2.4.5.0http://blogs.law.harvard.edu/tech/rss60Sensitivity to Prior Specification in Bayesian Identification of Autoregressive Time Series Models
http://www.pjsor.com/index.php/pjsor/article/view/1498
In this paper we use the Kullback-Leibler divergence to measure the distance between the posteriors of the autoregressive (AR) model order, aiming to evaluate mathematically the sensitivity of the model identification to different types of priors of the model parameters. In particular, we consider three priors for the AR model coefficients, namely Jeffreys', g, and natural conjugate priors, and three priors for the model order including uniform, arithmetic, and geometric priors. Using a large number of Monte Carlo simulations with various values of the model coefficients, model order, and sample size, we evaluate the impact of the posteriors distance in the accuracy of the model identification. Simulation study results show that the posterior of the model order is sensitive to prior distributions, and the highest accuracy of the model identification is obtained from the posterior resulting from the g-prior. Same results are obtained from the application to real-world time series datasets.Ayman Aminhttp://www.pjsor.com/index.php/pjsor/article/view/1498Fri, 01 Dec 2017 00:00:00 +0000Variable Control Charts - Linear Failure Rate Distribution
http://www.pjsor.com/index.php/pjsor/article/view/1512
The well known Linear Failure Rate Distribution (LFRD) is considered. A process variate following LFRD is thought of in order to develop control charts for subgroup mean and subgroup range. In view of the limitations on LFRD the theoretical control limits are obtained through some approximations and the resulting control chart limits are worked out. Comparisons with the control limits of similar variable control charts is also presented.Metlapalli Chaitanya Priya, Rani R L Kantamhttp://www.pjsor.com/index.php/pjsor/article/view/1512Fri, 01 Dec 2017 00:00:00 +0000Characterizations of Kumaraswamy-Laplace, McDonald Inverse Weibull and New Generalized Exponential Distributions
http://www.pjsor.com/index.php/pjsor/article/view/1697
Nassar (2016) considers an interesting univariate continuous distribution called Kumaraswamy-Laplace which has different forms on two subintervals. He studies certain properties and applications of this distribution. Shahbaz et al. (2016) consider another interesting distribution called McDonald Inverse Weibull distribution. They present some basic properties of their distribution and study the estimations of the parameters as well as discussing its application via an illustrative example. What is lacking in both papers, in our opinion, is the characterizations of these two interesting distributions. the present work is intended to complete, in some way, the works of Nassar and Shahbaz et al. via establishing certain characterizations of these distributions in four directions. We also introduce several New generalized Exponential distributions and present their characterizations as well.Dr. G.G. Hamedanihttp://www.pjsor.com/index.php/pjsor/article/view/1697Fri, 01 Dec 2017 00:00:00 +0000Implementation of the - Constraint Method in Special Class of Multi-objective Fuzzy Bi-Level Nonlinear Problems
http://www.pjsor.com/index.php/pjsor/article/view/1698
Geometric programming problem is a powerful tool for solving some special type nonlinear programming problems. In the last few years we have seen a very rapid development on solving multiobjective geometric programming problem. A few mathematical programming methods namely fuzzy programming, goal programming and weighting methods have been applied in the recent past to find the compromise solution. In this paper, -constraint method has been applied in bi-level multiobjective geometric programming problem to find the Pareto optimal solution at each level. The equivalent mathematical programming problems are formulated to find their corresponding value of the objective function based on the duality theorem at eash level. Here, we have developed a new algorithm for fuzzy programming technique to solve bi-level multiobjective geometric programming problems to find an optimal compromise solution. Finally the solution procedure of the fuzzy technique is illustrated by a numerical exampleAzza Hassan Amerhttp://www.pjsor.com/index.php/pjsor/article/view/1698Fri, 01 Dec 2017 00:00:00 +0000On Using The Median Ranked Set Sampling for Developing Reliability Test Plans Under Generalized Exponential Distribution
http://www.pjsor.com/index.php/pjsor/article/view/1721
In this article a new single sampling plan based on ranked data scheme is proposed. Two main requirements are considered for the new plan: the lifetime of the test units is assumed to follow the generalized exponential distribution; and the data are selected by using the median ranked set sampling scheme from a large lot. The distribution function characterization under the median ranked set sampling scheme is derived assuming that the set size is known; the minimum number of set cycle and consequently the minimum sample size necessary to ensure the specified average life are obtained and the operating characteristic values of the ranked sampling plans as well as the producer’s risk are presented. An illustrative examples based on the results obtained are given.Amjad D. Al-Nasser, Fatima S. Gogahhttp://www.pjsor.com/index.php/pjsor/article/view/1721Fri, 01 Dec 2017 00:00:00 +0000Manipulation-based ranked set sampling scheme
http://www.pjsor.com/index.php/pjsor/article/view/1539
Cost-effective and efficient sampling methods are of main concern in many social, biological and environmental studies. In this article, an efficient sampling scheme, named manipulation-based ranked set sampling (MBRSS) scheme is introduced with its properties for estimating population mean and median. The MBRSS is a mixture of simple random sampling (SRS), ranked set sampling (RSS) and median ranked set sampling (MRSS) schemes and is applicable in the situation when ordinary RSS cannot be conducted. It is shown that the proposed scheme provides unbiased mean estimator provided underlying distribution is symmetric. For asymmetric distributions, a weighted mean is proposed, where optimal weights are computed using Shannon's entropy. Monte Carlo simulation is used to ascertain effectiveness of the proposed mean and median estimators in the presence of outliers. We also compared the efficiency of MBRSS and truncation-based ranked set sampling (TBRSS) scheme with respect to SRS under the situation of perfect and imperfect ranking i.e error in rankings with respect to variable of interest. It is observed, on the basis of theoretical and numerical studies that MBRSS is more efficient than SRS. Further, a real data set is used to illustrate the proposed MBRSS scheme.Azhar Mehmood Abbasi, Muhammad Yousaf Shahdhttp://www.pjsor.com/index.php/pjsor/article/view/1539Fri, 01 Dec 2017 00:00:00 +0000Exact Distribution of Random Weighted Convolution of Some Beta Distributions Through an Integral Transform
http://www.pjsor.com/index.php/pjsor/article/view/1868
We give the exact distribution of the average of n independent beta random variables weighted by the selected cuts of (0; 1) by the order statistics of a random sample of size n−1 from the uniform distribution U(0; 1), for each n. A new integral transformation that is similar to generalized Stieltjes transform is given with various properties. Integral representation of the Gauss-hypergeometric function in some parts is employed to achieve the exact distribution. Also the result of Soltani and Roozegar [On distribution of randomly ordered uniform incremental weighted averages: Divided dierence approach. Statist Probab Lett. 2012;82(5):1012{1020] with the new transform is achieved. Finally, several new examples of this family of distributions are investigated.Rasool Roozegar, Abouzar Bazyarihttp://www.pjsor.com/index.php/pjsor/article/view/1868Wed, 01 Nov 2017 00:00:00 +0000An Extended Burr XII Distribution: Properties, Inference and Applications
http://www.pjsor.com/index.php/pjsor/article/view/1965
<p>We propose and study a new continuous model named the Marshall-Olkin exponentiated Burr XII (MOEBXII) distribution. It contains several special cases, namely the Marshall-Olkin exponentiated log-logistic, Marshall-Olkin exponentiated Lomax, Marshall-Olkin Burr XII, Marshall-Olkin log-logistic, Marshall-Olkin Lomax distributions, among others, and most importantly includes all four of the most common types of hazard function: monotonically increasing or decreasing, bathtub and arc-shaped hazard functions. Some of its structural properties are obtained such as the ordinary and incomplete moments, quantile and generating functions, order statistics and probability weighted moments. The maximum likelihood and least square methods are used to estimate the model parameters. A simulation study is performed to evaluate the precision of the estimates from both methods. The usefulness of the new model is illustrated by means of two real data sets.</p>Gauss Cordeiro, Mohamed Mead, Ahmed Z. Afify, Adriano Suzuki, Amarat Abd El-Gaiedhttp://www.pjsor.com/index.php/pjsor/article/view/1965Fri, 01 Dec 2017 00:00:00 +0000An Optimum Multivariate-Multiobjective Stratified Sampling Design: Fuzzy Programming Approach
http://www.pjsor.com/index.php/pjsor/article/view/1834
In stratified sampling design when the cost of measuring the units is not significant in each stratum, the estimation of population mean or total constructed from a selected sample according to Neyman allocation is advisable. In general the practical use of Neyman allocation suffers from a number of limitations, when there is no information about strata standard deviations except about the equality of standard deviations between some of the strata, then the precision of the estimate may be increased by pooling the strata with equal standard deviations as a single stratum and the problem of allocation is resolved by using Neyman and proportional allocations simultaneously. In this paper the case of multiple pooling of the standard deviations of the estimates in a multivariate stratified sampling for more than three strata. The problem is formulated as a Multiobjective Nonlinear Programming Problem and its solution procedure is suggested by using Fuzzy Programming approach.Rahul Varshney, Srikant Gupta, Irfan Alihttp://www.pjsor.com/index.php/pjsor/article/view/1834Fri, 01 Dec 2017 00:00:00 +0000Simultaneous Estimation of Mean of Sensitive Variable and Sensitivity level by using Generalized Optional Scrambling
http://www.pjsor.com/index.php/pjsor/article/view/1966
<p>Randomized response technique introduces anonymity into subjects' responses hence encouraging more honest responses. In quantitative randomized response model, additive and multiplicative models have been developed to reduce bias. However, additive and multiplicative models may not be sufficient to reduce this bias so the generalized optional scrambling randomized response model proposed is able to reduce these problems. We also improved mean estimation utilizing information from a non-sensitive auxiliary variable by way of ratio and regression estimators in the proposed model. </p>Muhammad Noor-ul-Amin, Nadia Mushtaq, Muhammad Hanifhttp://www.pjsor.com/index.php/pjsor/article/view/1966Fri, 01 Dec 2017 00:00:00 +0000Concomitants of Generalized Order Statistics for a Bivariate Weibull Distribution
http://www.pjsor.com/index.php/pjsor/article/view/2139
<p>In this paper we have studied the distribution of <em>r</em>–th concomitant and joint distribution of <em>r</em>–th and <em>s</em>–th concomitant of generalized order statistics for a bivariate Weibull distribution. We have derived the expression for single and product moments. Numerical study has also been conducted to see the behavior of mean of concomitants for selected values of the parameters.</p>Saman Hanif Shahbaz, Muhammad Qaiser Shahbazhttp://www.pjsor.com/index.php/pjsor/article/view/2139Fri, 01 Dec 2017 00:00:00 +0000Bayesian modeling to paired comparison data via the Pareto distribution
http://www.pjsor.com/index.php/pjsor/article/view/1924
<p>A probabilistic approach to build models for paired comparison experiments based on the comparison of two Pareto variables is considered. Analysis of the proposed model is carried out in classical as well as Bayesian frameworks. Informative and uninformative priors are employed to accommodate the prior information. Simulation study is conducted to assess the suitablily and performance of the model under theoretical conditions. Appropriateness of fit of the is also carried out. Entire inferential procedure is illustrated by comparing certain cricket teams using real dataset.</p>Nasir Abbas, Muhammad Aslam Aslamhttp://www.pjsor.com/index.php/pjsor/article/view/1924Wed, 01 Nov 2017 00:00:00 +0000Some Extended Classes of Distributions: Characterizations and Properties
http://www.pjsor.com/index.php/pjsor/article/view/2147
<p>Based on a simple relationship between two truncated moments and certain functions of the th order statistic, we characterize some extended classes of distributions recently proposed in the statistical literature, videlicet Beta-G, Gamma-G, Kumaraswamy-G and McDonald-G. Several properties of these extended classes and some special cases are discussed. We compare these classes in terms of goodness-of-fit criteria using some baseline distributions by means of two real data sets. </p>G G. Hamedani, G. M. Cordeiro, M. C. S. Lima, A.D. C. Nascimentohttp://www.pjsor.com/index.php/pjsor/article/view/2147Fri, 01 Dec 2017 00:00:00 +0000Comparison of Different Entropy Measures for Selected Models
http://www.pjsor.com/index.php/pjsor/article/view/1797
In this article, the differential entropy and -entropy for Nakagami-mu distribution is derived. In addition, the differential entropy and -entropy for some selected versions of these distributions are obtained. Further, numerical comparisons are assessed to indicate which selection distribution has advantages over the other selection in terms of relative loss in entropy.Mervat Mahdy, Dina Samirhttp://www.pjsor.com/index.php/pjsor/article/view/1797Wed, 01 Nov 2017 00:00:00 +0000Estimation of using Modifications of Ranked Set Sampling for Weibull Distribution
http://www.pjsor.com/index.php/pjsor/article/view/2056
<p>In statistical literature, estimation of R=P(X<Y) is a commonly-investigated problem, and consequently, there have been considerable number of studies dealing with its estimation of it under simple random sampling (SRS). However, in recent years, the ranked set sampling (RSS) method have been widely-used in the estimation of R. In this study, we consider the estimation of R when the distribution of the both stress and strength are Weibull under the modification of RSS, which are extreme ranked set sampling (ERSS), median ranked set sampling (MRSS) and percentile ranked set sampling (PRSS). We obtain the estimators of R using the maximum likelihood (ML) and the modified maximum likelihood (MML) methodologies under these modifications. Then the performances of proposed estimators are compared with the corresponding ML and MML estimators of R using SRS via a Monte-Carlo simulation study.</p>Fatma Gul Akgul, Birdal Senogluhttp://www.pjsor.com/index.php/pjsor/article/view/2056Fri, 01 Dec 2017 00:00:00 +0000