Pakistan Journal of Statistics and Operation Research
http://pjsor.com/index.php/pjsor
Pakistan Journal of Statistics and Operation ResearchCollege of Statistical and Actuarial Sciencesen-USPakistan Journal of Statistics and Operation Research1816-2711<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="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>Bayesian Inference for Double Seasonal Moving Average Models: A Gibbs Sampling Approach
http://pjsor.com/index.php/pjsor/article/view/1647
In this paper we use the Gibbs sampling algorithm to develop a Bayesian inference for multiplicative double seasonal moving average (DSMA) models. Assuming the model errors are normally distributed and using natural conjugate priors, we show that the conditional posterior distribution of the model parameters and variance are multivariate normal and inverse gamma respectively, and then we apply the Gibbs sampling to approximate empirically the marginal posterior distributions. The proposed Bayesian methodology is illustrated using simulation study.Ayman Amin2017-08-312017-08-3113348349910.18187/pjsor.v13i3.1647Bayesian Analysis of the Mixture of Frechet Distribution under Different Loss Functions
http://pjsor.com/index.php/pjsor/article/view/1703
This paper has to do with 3-component mixture of the Frechet dis- tributions when the shape parameter is known under Bayesian view point. The type-I right censored sampling scheme is considered due to its extensive use in reliability theory and survival analysis. Taking dif- ferent non-informative and informative priors, Bayes estimates of the parameter of the mixture model along with their posterior risks are derived under squared error loss function, precautionary loss function and DeGroot loss function. In case, no or little prior information is available, elicitation of hyper parameters is given. In order to study numerically, the execution of the Bayes estimators under different loss functions, their statistical properties have been simulated for different sample sizes and test termination times. A real life data example is also given to illustrate the study.Tabasam SultanaMuhammad AslamJavid Shabbir2017-09-012017-09-0113350152810.18187/pjsor.v13i3.1703The Extended Fréchet Distribution: Properties and Applications
http://pjsor.com/index.php/pjsor/article/view/2058
<p>In this paper, we study a new model called the Burr X exponentiated Frechet Distribution. The new model exhibits unimodal, unimodal then buthtab and buthtab hazard rates. Various properties of the new model are explored including moments, generating function, probability weighted moments, Stress-strength model and order statisics. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimates are discussed. We compare the flexibility of the proposed model with other extensions of the Frechet distribution by means of two real data sets.</p>Mohamed ZayedNadeem Shahfique Butt2017-09-012017-09-0113352954310.18187/pjsor.v13i3.2058Exponentiated Lomax Geometric Distribution: Properties and Applications
http://pjsor.com/index.php/pjsor/article/view/1437
<p>In this paper, a new four-parameter lifetime distribution, called the exponentiated Lomax geometric (<em>ELG</em>) is introduced. The new lifetime distribution contains the Lomax geometric and exponentiated Pareto geometric as new sub-models. Explicit algebraic formulas of probability density function, survival and hazard functions are derived. Various structural properties of the new model are derived including; quantile function, Re'nyi entropy, moments, probability weighted moments, order statistic, Lorenz and Bonferroni curves. The estimation of the model parameters is performed by maximum likelihood method and inference for a large sample is discussed. The flexibility and potentiality of the new model in comparison with some other distributions are shown via an application to a real data set. We hope that the new model will be an adequate model for applications in various studies.</p>Amal Soliman HassanMarwa Abdallah Abdelghafar2017-09-012017-09-0113354556610.18187/pjsor.v13i3.1437Obtaining Strata Boundaries under Proportional Allocation with Varying Cost of Every Unit
http://pjsor.com/index.php/pjsor/article/view/1719
<p>One of the main reasons for stratifying the population is to produce a gain in precision of the estimates, in the sample surveys. For achieving this, one of the problem is determination of optimum strata boundaries. The strata boundaries should be obtained in such a way, so that it can reasonably expect to reduce the cost of the survey as much as possible without sacrificing the accuracy or alternatively, reducing the margin of error to the greatest possible extent for the same expected cost. In this paper, we have discussed the way of obtaining optimum strata boundaries when the cost of every unit varies in the whole strata. The problem is formulated as non-linear programming problem which is solved by using Bellman’s principle of optimality. For numerical illustration an example is presented for uniformly distributed study variable.</p>Faizan DanishS.E.H. RizviM. Iqbal JeelaniJavaid Ahmad Reashi2017-09-012017-09-0113356757410.18187/pjsor.v13i3.1719Inference for exponentiated general class of distributions based on record values
http://pjsor.com/index.php/pjsor/article/view/2069
<p>The main objective of this paper is to suggest and study a new exponentiated general class (EGC) of distributions. Maximum likelihood, Bayesian and empirical Bayesian estimators of the parameter of the EGC of distributions based on lower record values are obtained. Furthermore, Bayesian prediction of future records is considered. Based on lower record values, the exponentiated Weibull distribution, its special cases of distributions and exponentiated Gompertz distribution are applied to the EGC of distributions. </p>Samah N. SindiGannat R. Al-DayianSaman Hanif Shahbaz2017-09-012017-09-0113357558710.18187/pjsor.v13i3.2069Design of Attribute Control Chart Based on Regression Estimator
http://pjsor.com/index.php/pjsor/article/view/1418
This paper presents a statistical analysis control chart for nonconforming units in quality control. In many situations the Shewhart control charts for nonconforming units may not be suitable or cannot be used, as for many processes, the assumptions of binomial distribution may deviate or may provide inadequate model. In this Study we propose a new control chart based on regression estimator of proportion based on single auxiliary variable, namely the Pr chart and compared its performance with P and Q chart with probability to signal as a performance measure. It has been observed that the proposed chart is superior to the P and Q chart. This study will help quality practitioners to choose an efficient alternative to the classical P and Q charts for monitoring nonconforming units in industrial process.Nadia MushtaqDr. Muhammad AslamJaffer Hussaian2017-09-012017-09-0113358960110.18187/pjsor.v13i3.1418The Exponential Pareto Power Series Distribution: Theory and Applications
http://pjsor.com/index.php/pjsor/article/view/2072
<p>A new lifetime class of distributions is introduced by compounding the exponential Pareto and power series distributions. The compounding procedure follows the same set-up carried out by Adamidis and Loukas (1998). We obtain several properties of the new class including ordinary and conditional, mean deviations, Bonferroni and Lorenz curves, residual and reversed residual lifes and order statistics. The maximum likelihood estimation procedure is carried out to estimate the model parameters. We present three special models of the proposed class.</p>I. ElbatalMohamed ZayedMahdi RasekhiNadeem Shafique Butt2017-09-012017-09-0113360361510.18187/pjsor.v13i3.2072A New Five-Parameter Fréchet Model for Extreme Values
http://pjsor.com/index.php/pjsor/article/view/1727
A new five parameter Fréchet model for Extreme Values was proposed and studied. Various mathematical properties including moments, quantiles, and moment generating function were derived. Incomplete moments and probability weighted moments were also obtained. The maximum likelihood method was used to estimate the model parameters. The flexibility of the derived model was accessed using two real data set applications.Muhammad Ahsan ul HaqHaitham M. YousofSharqa Hashmi2017-09-012017-09-0113361763210.18187/pjsor.v13i3.1727Stress Affection of Two Scale Truncated Generalized Logistic Parameters with Progressive Censoring
http://pjsor.com/index.php/pjsor/article/view/1427
<p>This paper deals with non-Bayesian estimation problem of constant-stress Accelerated Life Tests (ALTs) when the lifetime of the items follow truncated Generalized Logistic Distribution (GLD). Some considerations on inference based on the use of asymptotically normality of the ML estimators are presented considering the stress effects on the two scale parameters of the truncated GLD with a k-level constant-stress ALT under progressive type-I censored grouped data. The EM algorithm method is used to obtain the estimators of the unknown parameters. In addition, estimator of the two scale parameters, reliability function under usual conditions and Fisher information matrix of the estimators are given. Finally, we present a Simulation Study to illustrate the proposed procedure.</p>Salma Omar BleedAbdallah Mohamed Abdelfattah2017-09-012017-09-0113363364610.18187/pjsor.v13i3.1427An exponential and log ratio estimator of population mean using auxiliary information in double sampling
http://pjsor.com/index.php/pjsor/article/view/2059
<p>In this study an improved version of ratio type exponential estimator is been proposed for estimating average of study variable when the population parameter(s) information of second auxiliary variable is available. The proposed estimator compared with usual unbiased estimator and conventional ratio estimators numerically and hypothetically. The mean square error is also obtained and checked the efficiency of the proposed estimator with usual ratio, Singh and Vishwakarma (2007), Singh et al. (2008), Noor-ul-Amin and Hanif (2012), Yadav et al. (2013) and Sanaullah et al. (2015) estimators.</p>Yasir HassanMuhammad IsmailAamir Sanaullah2017-09-012017-09-0113364765610.18187/pjsor.v13i3.2059A Short note on the Paper (New Characterizations of the Pareto Distribution
http://pjsor.com/index.php/pjsor/article/view/1879
Nofal and El Gebaly (2017), presented certain characterizations of the Pareto distribution based on the conditional expectations of power of the order statistics. In this short note we show that the same results can easily be obtained in terms of the power of the random variable.Dr. G.G. HamedaniM. Rasekhi2017-09-012017-09-0113365766010.18187/pjsor.v13i3.1879Generalized P-phased Regression Estimators with Single and Two Auxiliary Variables
http://pjsor.com/index.php/pjsor/article/view/1573
<p>Multiphase sampling has been the concept not being utilized is estimation of ratio and regression estimator widely. In the recent study we have proposed new dimension of sampling survey of estimations by proposing two generalized p-phase regression estimators with single and two auxiliary variables for estimating population mean. The proposed estimators are the generalized p-phase cases of Hanif et al (2015) and Hanif (2007) respectively. Both the estimators from which we took motivation are now special cases of our proposed estimators. We have derived unbiasedness, expression of Mean Square Errors along with family of estimators based upon p-phased generalization. We have derived expression of MSE in such a way that these expression can be used to obtained results for every phase we desire. By conducting empirical study on proposed estimators we have shown many situation in which MSE can be reduced by increasing number of phases. Hence, our study will open new horizon in the field of multiphase sampling where a lot of challenges are waiting to be resolved by proposing new estimators for phases above 2<sup>nd</sup> phase.</p>Farhan HameedHina Khan2017-09-012017-09-0113366168510.18187/pjsor.v13i3.1573The Extended Burr XII Distribution with Variable Shapes for the Hazard Rate
http://pjsor.com/index.php/pjsor/article/view/2083
<p>We define and study a new continuous distribution called the exponentiated Weibull Burr XII. Its density function can be expressed as a linear mixture of Burr XII. Its hazard rate is very flexibile in accomodating various shapes including constant, decreasing, increasing, J-shape, unimodal or bathtub shapes. Various of its structural properties are investigated including explicit expressions for the ordinary and incomplete moments, generating function, mean residual life, mean inactivity time and order statistics. We adopted the maximum likelihood method for estimating the model parameters. The flexibility of the new family is illustrated by means of a real data application.</p>T. H. M. AbouelmagdM. S. HamedAhmed Z. Afify2017-09-012017-09-0113368769810.18187/pjsor.v13i3.2083