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> en-US <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> (Editor PJSOR) (Support Team) Thu, 03 Jun 2021 18:20:41 +0500 OJS 60 Improved Estimators using Exponential Function for the Population Mean in Simple and Stratified Random Samplings <p class="Abstract">In this article, we investigated estimators with the exponential function for the estimation of the population mean in the simple and stratified random samplings. Family of estimators based on the exponential function is proposed for both sampling methods. The proposed estimators are compared with estimators in literature. Moreover, we provide an application on different data sets to demonstrate the efficiency of the proposed estimators. As a result, the proposed estimators are more efficient than other estimators in literature under the obtained conditions in theory.</p> CEREN UNAL, CEM KADILAR Copyright (c) 2021 Pakistan Journal of Statistics and Operation Research Thu, 03 Jun 2021 15:36:42 +0500 Weighted Power Lomax Distribution and its Length Biased Version: Properties and Estimation Based on Censored Samples <p>In this paper, a weighted version of the power Lomax distribution referred to the weighted power Lomax distribution, is introduced. The new distribution comprises the length biased and the area biased of the power Lomax distribution as new models as well as containing an existing model as the length biased Lomax distribution as special model. Essential distributional properties of the weighted power Lomax distribution are studied. Maximum likelihood and maximum product spacing methods are proposed for estimating the population parameters in cases of complete and Type-II censored samples. Asymptotic confidence intervals of the model parameters are obtained. A sample generation algorithm along with a Monte Carlo simulation study is provided to demonstrate the pattern of the estimates for different sample sizes. Finally, a real-life data set is analyzed as an illustration and its length biased distribution is compared with some other lifetime distributions.</p> Amal Soliman Hassan , Ehab M. Almetwally , Mundher Abdullah Khaleel, Heba Fathy Nagy Copyright (c) 2021 Pakistan Journal of Statistics and Operation Research Thu, 03 Jun 2021 15:43:39 +0500 Group Acceptance Sampling Plan for Resubmitted Lots: Size Biased Lomax Distribution <p>This research reveals a group acceptance sampling plan (GASP) for lot resubmitting is designed for conditions wherein an item life is taken from the size biased Lomax distribution (SBLD). The plan parameters of the GASP are obtained by fulfilling the prefixed producer’s and consumer’s risks as per the test completion time and the number of testers. The projected plan needs a minimal sample size in comparison with the standard GASP. This proposed plan is justified with an example.</p> Srinivasa Rao Gadde, Naga Durgamamba A Copyright (c) 2021 Pakistan Journal of Statistics and Operation Research Thu, 03 Jun 2021 15:53:39 +0500 The Balakrishnan-Alpha-Beta-Skew-Normal Distribution: Properties and Applications <p>In this paper, a new form of alpha-beta-skew distribution is proposed under Balakrishnan (2002) mechanism and investigated some of its related distributions. The most important feature of this new distribution is that it is versatile enough to support both unimodal and bimodal as well as multimodal behaviors of the distribution. The moments, distributional properties and some extensions of the proposed distribution have also been studied.&nbsp; Finally, the suitability of the proposed distribution has been tested by conducting data fitting experiment and comparing the values of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) with the values of some other related distributions. Likelihood Ratio testis used for discriminating between normal and the proposed distributions.</p> Sricharan Shah, Partha Jyoti Hazarika, Subrata Chakraborty, M. Masoom Ali Copyright (c) 2021 Pakistan Journal of Statistics and Operation Research Thu, 03 Jun 2021 15:57:35 +0500 A New One-term Approximation to the Standard Normal Distribution <p>This paper deals with a new, simple one-term approximation to the cumulative distribution function (c.d.f) of the standard normal distribution which does not have closed form representation. The accuracy of the proposed approximation measured using maximum absolute error (M.S.E) and the same criteria is used to compare this approximation with the existing one-term approximation approaches available in the literature. Our approximation has a maximum absolute error of about 0.0016 and this accuracy is sufficient for most practical applications.</p> Ahmad Hanandeh, Omar Eidous Copyright (c) 2021 Pakistan Journal of Statistics and Operation Research Thu, 03 Jun 2021 16:07:34 +0500 Generalized Lindley Family with application on Wind Speed Data <p>In this study we introduce a new extended class of continuous distributions named generalized Lindley family of distributions. Some properties of the new generator, including ordinary moments, quantile, generating and entropy functions, which hold for any baseline model, are presented. The method of maximum likelihood is used for estimating the model parameters. The flexibility of the new family of distributions is shown via an application on the wind speed data set. The results shows that the proposed family is better than well-known distributions including log-logistic, Burr, Dagum, Frechet, Pearson, Dagum, Lindley, Weibull and exponential distributions.</p> Selen Cakmakyapan, Gamze Ozel Copyright (c) 2021 Pakistan Journal of Statistics and Operation Research Thu, 03 Jun 2021 16:12:16 +0500 A new parametric lifetime model with modified chi-square type test for right censored validation, characterizations and different estimation methods <p>A new three-parameter extension of the generalized Nadarajah-Haghighi model is introduced and studied. Some of its statistical properties are derived. Characterization results are presented. The failure rate can be "increasing", "decreasing", "bathtub", "upside-down", "upside-down-constant", "increasing-constant" or "constant". Different non-Bayesian estimation methods under uncensored scheme are considered. Numerical simulations are performed for comparing the estimation methods using different sample sizes. The censored Barzilai-Borwein algorithm is employed via a simulation study. Using the approach of the Bagdonavicius-Nikulin chi-square goodness-of-fit test for validation under the right censored data, we propose a modified chi-square goodness-of-fit test for the new model. Based on the maximum likelihood estimators on initial data, the modified Bagdonavicius-Nikulin chi-square goodness-of-fit test recovers the loss in information. The modified Bagdonavicius-Nikulin test for validation under the right censored data is applied to four real and right censored data sets. The new model is compared with many other competitive models by means of a real data set.</p> Haitham Yousof, Khaoula Aidi, G.G. Hamedani, Mohamed Ibrahim Copyright (c) 2021 Pakistan Journal of Statistics and Operation Research Thu, 03 Jun 2021 16:18:21 +0500 A Full-Newton Step Interior Point Method for Fractional Programming Problem Involving Second Order Cone Constraint <p>Some efficient interior-point methods (IPMs) are based on using a self-concordant barrier&nbsp;function related to the feasibility set of the underlying problem.<br>Here, we use IPMs for solving fractional programming problems involving second order cone constraints. We propose a logarithmic barrier function to show the self concordant property and present an algorithm to compute $\varepsilon-$solution of a fractional programming problem. Finally, we provide a numerical example to illustrate the approach.</p> Mansour Saraj, Ali Sadeghi, Nezam Mahdavi Amiri Copyright (c) 2021 Pakistan Journal of Statistics and Operation Research Thu, 03 Jun 2021 16:25:41 +0500 Testing the proportionality assumption for specified covariate in the cox model <p>In this paper, I propose a test for proportional hazards assumption for specified covariates. The test<br>is based on a general alternative in sense that hazards rates under different values of covariates the<br>rate is not only constant as in the Cox model, but it may cross, go away, and may be monotonic<br>with time. The limit distribution of the test statistic is derived. Finite samples properties of the<br>test power are analyzed by simulation. Application of the proposed test on Real data examples are<br>considered.</p> HAFDI Mohamed Ali Copyright (c) 2021 Pakistan Journal of Statistics and Operation Research Thu, 03 Jun 2021 16:32:23 +0500 The Transmuted Inverted Nadarajah-Haghighi Distribution With an Application to Lifetime Data <p>In this paper, we propose a new lifetime distribution. We discuss several mathematical properties of the new distribu- tion. Certain characterizations of the new distribution are provided. We study the maximum likelihood estimation and asymptotic interval estimation of the unknown parameters. A simulation study, as well as an application of the new distribution to failure data, are also presented. We end the paper with a number of remarks.</p> Aliyeh Toumaj, S.M.T.K. MirMostafaee, G.G. Hamedani Copyright (c) 2021 Pakistan Journal of Statistics and Operation Research Thu, 03 Jun 2021 16:37:03 +0500 Classical and Bayesian inference approaches for the exponentiated discrete Weibull model with censored data and a cure fraction <p>In this paper, we introduce maximum likelihood and Bayesian parameter estimation for the exponentiated discrete Weibull (EDW) distribution in presence of randomly right censored data. We also consider the inclusion of a cure fraction in the model. The performance of the maximum likelihood estimation approach is assessed by conducting an extensive simulation study with different sample sizes and different values for the parameters of the EDW distribution. The usefuness of the proposed model is illustrated with two examples considering real data sets.</p> Jorge Alberto Achcar, Edson Zangiacomi Martinez, Bruno Caparroz Lopes de Freitas, Marcos Vinicius de Oliveira Peres Copyright (c) 2021 Pakistan Journal of Statistics and Operation Research Thu, 03 Jun 2021 16:41:08 +0500 A Novel Weighted Ensemble Method to Overcome the Impact of Under-fitting and Over-fitting on the Classification Accuracy of the Imbalanced Data Sets <p>In the data mining communal, imbalanced class dispersal data sets have established mounting consideration. The evolving field of data mining and information discovery seeks to establish precise and effective computational tools for the investigation of such data sets to excerpt innovative facts from statistics. Sampling methods re-balance the imbalanced data sets consequently improve the enactment of classifiers. For the classification of the imbalanced data sets, over-fitting and under-fitting are the two striking problems. In this study, a novel weighted ensemble method is anticipated to diminish the influence of over-fitting and under-fitting while classifying these kinds of data sets. Forty imbalanced data sets with varying imbalance ratios are engaged to conduct a comparative study. The enactment of the projected method is compared with four customary classifiers including decision tree(DT), k-nearest neighbor (KNN), support vector machines (SVM), and neural network (NN). This evaluation is completed with two over-sampling procedures, an adaptive synthetic sampling approach (ADASYN), and a synthetic minority over-sampling (SMOTE) technique. The projected scheme remained efficacious in diminishing the impact of over-fitting and under-fitting on the classification of these data sets.</p> Ghulam Fatima, Sana Saeed Copyright (c) 2021 Pakistan Journal of Statistics and Operation Research Thu, 03 Jun 2021 16:53:01 +0500 On Truncated Zeghdoudi Distribution : Posterior Analysis under Different Loss Functions for Type II Censored Data <p>We perform a Bayesian analysis of the upper trunacated Zeghdoudi distribution based on type II censored data. Using various loss functions including the generalised quadratic, entropy and Linex functions, we obtain Bayes estimators and the corresponding posterior risks. As tractable analytical forms of these estimators is out of reach, we propose the use of simulations based on Markov chain Monte-carlo methods to study their performance. Given nitial values of model parameters, we also obtain maximum likelihood estimators. Using Pitmanw closeness criterion and integrated mean square error we&nbsp; compare their performance with those of the Bayesian estimators. Finally, we illustrate our approach through an example using a set of real data.</p> Hamida Talhi, Hiba Aiachi Copyright (c) 2021 Pakistan Journal of Statistics and Operation Research Thu, 03 Jun 2021 16:58:47 +0500 Marshall-Olkin Lehmann Lomax Distribution: Theory, Statistical Properties, Copulas and Real Data Modeling <p>In this work, a new four-parameter lifetime probability distribution called the Marshall-Olkin Lehmann Lomax distribution is defined and studied. The density function of the new distribution "asymmetric right skewed" and "symmetric" and the corresponding hazard rate can be monotonically increasing, increasing-constant, constant, upside down and monotonically decreasing. The coefficient of skewness can be negative and positive. We derive some new bivariate versions via Farlie Gumbel Morgenstern family, modified Farlie Gumbel Morgenstern family, Clayton Copula and Renyi's entropy.The method of maximum likelihood is used to estimate the unknown parameters. Using "biases" and "mean squared errors", a simulation study is performed for assessing the finite behavior of the maximum likelihood estimators.</p> Mohamed Aboraya Copyright (c) 2021 Pakistan Journal of Statistics and Operation Research Thu, 03 Jun 2021 17:02:37 +0500