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>Conditional Inference for the Weibull Extension Model Based on the Generalized Order Statistics
http://pjsor.com/index.php/pjsor/article/view/1893
<strong><strong></strong></strong><p>In recent years, a new class of models has been proposed to exhibit the bathtub-shaped failure rate functions. The Weibull extension model is one of these models, which is asymptotically related to the ordinary Weibull model and is capable of modeling the bathtub-shaped and increasing failure rate lifetime data. This paper presents the conditional inference for constructing the confidence intervals for the Weibull extension parameters based on the generalized order statistics. For measuring the performances of this approach comparing to the Asymptotic maximum likelihood estimates, Simulation studies have been carried out, that indicated the conditional intervals possess a good statistical properties and they can perform quite well even when the sample size is extremly small. An illustrative examples based on real data are given to illustrate the confidence intervals developed in this paper.<strong></strong></p><strong></strong>M. MaswadahA. A. EL-Faheem2018-06-012018-06-0114219921410.18187/pjsor.v14i2.1893A Two-Parameter Ratio-Product-Ratio Type Exponential Estimator for Finite Population Mean in Sample Surveys
http://pjsor.com/index.php/pjsor/article/view/1905
<p>This paper suggests a two-parameter ratio-product-ratio type exponential estimator for a finite population mean in simple random sampling without replacement (SRSWOR) following the methodology in the studies of Singh and Espejo (2003) and Chami et al (2012). The bias and mean squared error of the suggested estimator are obtained to the first degree of approximation. The conditions are obtained in which suggested estimator is more efficient than the sample mean, classical ratio and product estimators, ratio-type and product type exponential estimators. An empirical study is given in support of the present study.</p>Housila P SinghAnita Yadav2018-06-012018-06-0114221523210.18187/pjsor.v14i2.1905Inference on Constant-Stress Accelerated Life Testing Based on Geometric Process for Extension of the Exponential Distribution under Type-II Progressive Censoring
http://pjsor.com/index.php/pjsor/article/view/1493
<p>In this paper, the geometric process is introduced as a constant-stress accelerated model to analyze a series of life data that obtained from several increasing stress levels. The geometric process (GP) model is assumed when the lifetime of test units follows an extension of the exponential distribution. Based on progressive censoring, the maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of the model parameters are obtained. Moreover, a real dataset is analyzed to illustrate the proposed procedures. In addition, the approximate, bootstrap and credible confidence intervals (CIs) of the estimators are constructed. Finally, simulation studies are carried out to investigate the precision of the MLEs and BEs for the parameters involved.</p>Abd El-Raheem MohamedS. E. Abu-YoussefNahed S. A. AliA. M. Abd El-Raheem2018-06-012018-06-0114223325110.18187/pjsor.v14i2.1493A Unified Approach for Generalizing Some Families of Probability Distributions, with Applications to Reliability Theory
http://pjsor.com/index.php/pjsor/article/view/2219
In this paper, we propose a new method for generating families of continuous distributions based on the star-shaped property which grantees the existences of some well know properties for the generated classes and distributions for any non-negative random variables. We refer to the new class as the composed family or shortly ( ) family. We study some mathematical properties of the new family. Some special families and sub-models of it from the family are discussed. To examine the performance of our new family and the generated models in fitting several data we use two real sets of data; censored and uncensored then comparing the fitting of a new produced model called composed- Lomax Weibull with some well-known models, which provides the best fit to all of the data. A simulation has been performed to assess the behavior of the maximum likelihood estimates of the parameters under the finite samples.Ahmed A. FattahA-Hadi N. Ahmed2018-06-012018-06-0114225327310.18187/pjsor.v14i2.2219Circular Functional Relationship Model with Wrapped Cauchy Errors
http://pjsor.com/index.php/pjsor/article/view/1858
<p>This paper extends the simple linear regression model with wrapped Cauchy error to the functional case when both variables are subjected to wrapped Cauchy errors. Assuming the ratio between the two error variances is known and the slope parameter equals one the maximum likelihood estimates are obtained. The closed-form expression for the maximum likelihood estimators are not available and the estimates are obtained iteratively by choosing a suitable initial values. The quality of estimates and the accuracy of the model are illustrated via simulations and the results revealed an acceptable performance of the estimators where they are unbiased, consistent and robust. The sampling variances of the model parameters are obtained via bootstrapping methods and consequently the confidence intervals were constructed. The proposed model is illustrated with an application on the analysis of wind directions data at two cities in the Gaza strip, Palestine.</p>Ali Hassan AbuzaidWalaa Abu El-labanAbdul Ghapor Hussin2018-06-012018-06-0114227528710.18187/pjsor.v14i2.1858Comparison of Significant Approaches of Penalized Spline Regression (P-splines)
http://pjsor.com/index.php/pjsor/article/view/1948
<p>Over the last two decades P-Splines have become a popular modeling tool in a wide class of statistical contexts. Fundamentally, semiparametric regression methods combine the leads of parametric and nonparametric approaches to regression analysis, while in precise, penalized spline regression uses the knowledge of nonparametric spline smoothing as a generalization of smoothing splines that let more suppleness in a choice of model with respect to the basis functions and the penalty. The present article compares two significant approaches of penalized spline regression models named as p-splines based on different basis functions with numerous knot selections and various types of penalties. These model fits have been applied on Wood Strength data to compare by calculating nonlinear least square method; also approaches are compared on several aspects: numerical immovability, quality of fit, derivative estimation and smoothing. This comparison will help us to fit best suitable model for conforming best suitable conditions and scenarios.</p>Saira SharifShahid Kamal2018-06-012018-06-0114228930310.18187/pjsor.v14i2.1948The Odd Exponentiated Half-Logistic Burr XII Distribution
http://pjsor.com/index.php/pjsor/article/view/2285
<p>A new lifetime model called the odd exponentiated half-logistic Burr XII is defined and studied. Its density function<br />can be expressed as a linear mixture of Burr XII densities. The proposed model is capable of modeling various <br />shapes of hazard rate including decreasing, increasing, decreasing-increasing-constant, reversed J-shape, J-shape, <br />unimodal or bathtub shapes. Various of its structural properties are investigated. The maximum likelihood method is <br />adopted to estimate the model parameters. The flexibility of the new model is proved empirically using two real data <br />sets. It can serve as an alternative model to other lifetime distributions in the existing literature for modeling positive <br />real data in many areas</p>Maha AldahlanAhmed Z. Afify2018-06-012018-06-0114230531710.18187/pjsor.v14i2.2285Extended Half-Logistic Distribution with Theory and Lifetime Data Application
http://pjsor.com/index.php/pjsor/article/view/2396
<p>In this paper, we introduce a new three-parameter lifetime model called the extended half-logistic (EHL) distribution. We derive various of its structural properties including moments, quantile and generating functions, mixture representation for probability density function, and reliability curves. The maximum likelihood, ordinary and weighted least square methods are used to estimate the model parameters. Simulation results to assess the performance of the estimation methods are discussed. We conclude that the maximum likelihood is the most suitable method to estimate model parameters for the small sample size. While the weighted least square method is the best for the large sample size. Finally, we prove empirically the importance and flexibility of the new model in modeling a real lifetime dataset.</p>Emrah AltunMuhammad Nauman KhanMorad AlizadehGamze OzelNadeem Shafique Butt2018-06-012018-06-0114231933110.18187/pjsor.v14i2.2396New distributions in designing of double acceptance sampling plan with application
http://pjsor.com/index.php/pjsor/article/view/2060
<p>In this paper, acceptance sampling plans as, double for the lifetime tests is truncated at pre-fixed time to determine on acceptance or rejection of the submitted lots are provided. The probability distributions of the lifetime of the product are determined based on three distributions: generalized inverse Weibull, skew-generalized inverse Weibull and compound inverse Rayleigh. The median lifetime of the test unit as the quality parameter is considered. The minimum sample sizes to assure that the actual median life is more than the specified life, OC values according to different quality levels and the minimum ratios of the actual median life to the specified life at the determined level of producer's risk for acceptance sampling plans are obtained. Numerical cases are introduced to illustrate the applications of acceptance sampling plans. </p>Mervat MahdyBasma Ahmed2018-06-012018-06-0114233334610.18187/pjsor.v13i3.2060The Kumaraswamy Weibull Geometric Distribution with Applications
http://pjsor.com/index.php/pjsor/article/view/1551
In this work, we study the kumaraswamy weibull geometric ($Kw-WG$) distribution which includes as special cases, several models such as the kumaraswamy weibull distribution, kumaraswamy exponential distribution, weibull geometric distribution, exponential geometric distribution, to name a few. This distribution was monotone and non-monotone hazard rate functions, which are useful in lifetime data analysis and reliability. We derive some basic properties of the $Kw-WG$ distribution including noncentral $r$th-moments, skewness, kurtosis, generating functions, mean deviations, mean residual life, entropy, order statistics and certain characterizations of our distribution. The method of maximum likelihood is used for estimating the model parameters and a simulation study to investigate the behavior of this estimation is presented. Finally, an application of the new distribution and its comparison with recent flexible generalization of weibull distribution is illustrated via two real data sets.Mahdi RasekhiMorad AlizadehG.G. Hamedani2018-06-012018-06-0114234736610.18187/pjsor.v14i2.1551New Shewhart and EWMA Type Control Charts using Exponential Type Estimator with Two Auxiliary Variables under Two Phase Sampling
http://pjsor.com/index.php/pjsor/article/view/1262
<p>In this paper, two new control charts have been proposed, one is shewhart-type and other one is EWMA-type control chart. The proposed control charts are based on the exponential type estimator for mean proposed by Noor-ul-Amin and Hanif (2012). We name them as DS-Shewhart control chart and DS-EWMA control chart. The results shows that the DS-Shewhart control chart shows more efficient results to traditional/simple Shewhart and EWMA control charts whereas, the DS-EWMA control chart shows more efficient results to traditional Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) control charts because they uses the information from two phase sampling with two auxiliary variables. The proposed control charts can be used for efficient monitoring of the production process in manufacturing industries. The control limits of the proposed chart are based on estimator, its mean square errors and bias. A simulated example has been used to compare the proposed and traditional/simple EWMA and CUSUM control charts performance based on the average run length-out of control (ARL<sub>1</sub>). It is observed that the proposed chart performs better than existing EWMA and CUSUM control charts. At the end of the paper a real life implementation of the proposed control charts is also provided.</p>Syed Muhammad Muslim RazaMuhammad Moeen Butt2018-06-012018-06-0114236738610.18187/pjsor.v14i2.1262Static Mean-Variance portfolio optimization under general sources of uncertainty
http://pjsor.com/index.php/pjsor/article/view/1963
<p>The only source of uncertainty in the standard Markowitz’s static Mean-Variance portfolio selection model is the future price of assets. This paper studies the static Mean-Variance portfolio selection model under general sources of uncertainty which generalizes the Markowitz’s model. It is shown that how the generalized problem can be reformulated as a quadratic program. Sufficient conditions are provided under which the standard and the generalized models produce the same set of optimal portfolios. Some sources of uncertainty and relevant examples are investigated. An illustrative example is provided to demonstrate the model.</p>Reza KeykhaeiBardia Panahbehagh2018-06-012018-06-0114238740210.18187/pjsor.v14i2.1963A New Five - Parameter Lifetime Model: Theory and Applications
http://pjsor.com/index.php/pjsor/article/view/1851
<p>In this paper we defined a new lifetime model called the the Exponentiated additive Weibull (EAW) distribution. The proposed distribution has a number of well-known lifetime distributions as special sub-models, such as the additive Weibull, exponentiated modified Weibull, exponentiated Weibull and generalized linear failure rate distributions among others. We obtain quantile, moments, moment generating functions, incomplete moment, residual life and reversed Failure Rate Functions, mean deviations, Bonferroni and Lorenz curves. The method of maximum likelihood is used for estimating the model parameters. Applications illustrate the potentiality of the proposed distribution.</p>A. AljouieeIbrahim ElbatalHazem Al-Mofleh2018-06-012018-06-0114240342010.18187/pjsor.v14i2.1851Regression Modeling of Competing Risks Survival Data in the Presence of Covariates Based on a Generalized Weibull Distribution: A Simulation Study
http://pjsor.com/index.php/pjsor/article/view/1929
<p>In survival analysis or medical studies each person can be exposed to more than one type of outcomes which occurrence of one of them prevents the other outcomes' occurrence; this situation is called the competing risks. Assessing the effect of covariates on the survival time (or failure time) is one of the purposes in competing risks analysis. In this paper, we study a competing risks model in the presence of covariates when the causes of failures follow generalized Weibull distributions. Covariates are entered to the model through the scale parameter of this distribution. Also in this study the competing risks are considered to be independent. Parameter estimation has been done by the maximum likelihood approach, in a real data set and a simulation study has shown the advantages of proposed model.</p>Soraya MoamerAhmad Reza BaghestaniMohamad Amin Pourhoseingholi2018-06-012018-06-0114242143310.18187/pjsor.v14i2.1929Assessment of a Dietary Consultation Model for Effective Diabetes Care in Saudi Population using Partial Least Squares Estimation
http://pjsor.com/index.php/pjsor/article/view/2249
<p>The relationship between dietary habits and diabetes has not been studied efficiently in Saudi Arabia and the available diabetes risk models does not focus much on diet, nor do they capture the overall dietary behaviors. The purpose of this research was to test empirically the hypothesised dietary consultation model that has been proposed for more effective diabetes care. This exploratory study was conducted on type 2 diabetic Saudi patients visiting the Primary Health Care Centres in Almajmaah city. The data comprising 350 patients were collected from 5<sup>th</sup> February – 24<sup>th</sup> April, 2017 through systematic sampling technique using direct investigation method. Data was collected through four questionnaires. Composite scores were extracted for all variables under study and analysed by Partial Least Squares-Structural Equation Modelling approach using SmartPLS 3.2.6 software. Evaluation of formative outer and inner model relationships validated the hypothesised dietary consultation model. Power of study, coefficient of determination, effect size, total effects, and model fit index further validated the findings. The validated dietary consultation model facilitates a new healthcare paradigm which can give a better understanding of diabetes management at stakeholder and individual level. Healthcare givers should pay special emphasis on diabetics’ diabetes mellitus knowledge, dietary knowledge, and dietary attitude, as these factors influence each other, dietary practices and HbA1c. Healthcare givers can use this model alone or by integrating it with available diabetes risk models to carry out the dietary assessment of type 2 diabetics.</p>Waqas SamiTahir AnsariNadeem Shafique ButtMohd Rashid Bin Ab Hamid2018-06-012018-06-0114243545010.18187/pjsor.v14i2.2249A General Transmuted Family of Distributions
http://pjsor.com/index.php/pjsor/article/view/2334
In this article we have proposed a general transmuted family of distributions with emphasis on the cubic transmuted family of distributions. This new class of distributions provide additional exibility in modeling the bi-modal data. The proposed cubic transmuted family of distributions has been linked with the T-X family of distributions proposed by Alzaatreh et al. (2013). Some members of the proposed family of distributions have been discussed. The cubic transmuted exponential distribution has been discussed in detail and various statistical properties of the distribution have been explored. The maximum likelihood estimation for parameters of cubic transmuted exponential distribution has also been discussed alongside Monte Carlo simulation study to assess the performance of the estimation procedure. Finally, the cubic transmuted exponential distribution has been tted to real datasets to investigate it's applicability.Md. Mahabubur RahmanBander Al-ZahraniMuhammad Qaiser Shahbaz2018-06-012018-06-0114245146910.18187/pjsor.v14i2.2334