Pakistan Journal of Statistics and Operation Research
http://www.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>The Generalized Transmuted Poisson-G Family of Distributions: Theory, Characterizations and Applications
http://www.pjsor.com/index.php/pjsor/article/view/2527
<span class="fontstyle0">In this work, we introduce a new class of continuous distributions called the generalized poisson<br />family which extends the quadratic rank transmutation map. We provide some special models for the<br />new family. Some of its mathematical properties including Rényi and q-entropies, order statistics and<br />characterizations are derived. The estimations of the model parameters is performed by maximum<br />likelihood method. The Monte Carlo simulations is used for assessing the performance of the maximum<br />likelihood estimators. The ‡exibility of the proposed family is illustrated by means of two applications<br />to real data sets.</span>Haitham YousofAhmed Z AfifyMorad AlizadehG. G. HamedaniS. JahanshahiIndranil Ghosh2018-12-252018-12-2514475977910.18187/pjsor.v14i4.2527Estimation of Stress-Strength Reliability For Weibull Distribution Based on Type-II Right Censored Ranked Set Sampling Data
http://www.pjsor.com/index.php/pjsor/article/view/2239
<p>In this paper, we consider the estimation of stress-strength reliability under the type-II right censored data when the distributions of both the stress and the strength are Weibull. First, we discuss the estimation of based on simple random sampling (SRS). Then, we use the effective and the efficient alternative of SRS which is known to be the ranked set sampling (RSS) to estimate . In the estimation procedure of , we use two different approaches they are i) maximum likelihood (ML) which requires an iterative method and ii) modified maximum likelihood (MML) which has an explicit form. Monte-Carlo simulation study is performed to identify the efficient sampling method (i.e., SRS or RSS) and the efficient estimation method (i.e., ML or MML). Finally, strength and wind speed data sets are analyzed to illustrate the proposed methods in practice.</p>Fatma Gül AkgülBirdal Şenoğlu2018-12-252018-12-2514478180610.18187/pjsor.v14i4.2239New General Transmuted Family of Distributions with Applications
http://www.pjsor.com/index.php/pjsor/article/view/2655
<p>In this paper, we have introduced a new family of general transmuted distributions and have studied the cubic transmuted family of distributions in detail. This new class of distributions oers more distributional exibility when bi-modality appear in the data sets. Some special members of the proposed cubic transmuted family of distributions have been discussed. We have investigated, in detail, the proposed cubic transmuted family of distributions for parent exponential distribution. The statistical properties along with the reliability behavior for the cubic transmuted exponential distribution have been studied. We have obtained the expressions for single and joint order statistics when a sample is available from the cubic transmuted exponential distribution. Maximum likelihood estimation of parameters for cubic transmuted exponential distribution has also been discussed. We have also discussed the simulation and real data applications of the proposed distribution.</p>Md. Mahabubur RahmanBander Al-ZahraniMuhammad Qaiser Shahbaz2018-12-252018-12-2514480782910.18187/pjsor.v14i4.2655New Fuzzy Entropy Measure of Order α
http://www.pjsor.com/index.php/pjsor/article/view/2501
<p>In this article, a new fuzzy entropy measure of order α is proposed. The fuzzy entropy axiomatic requirements are discussed for the new measure, and an empirical comparison are made with several entropy measures including Shannon, Rényi and Kapur. It turns out, the proposed measure satisfies all axiomatic and outperform the other entropy measures in terms of the fuzziness degree. </p>Mohammad Al-TalibAmjad Al-Nasser2018-12-252018-12-2514483183810.18187/pjsor.v14i4.2501A note on Asymptotical Efficiency of the Goodness of Fit Tests Based on disjoint k-spacings Statistic
http://www.pjsor.com/index.php/pjsor/article/view/1951
<p><span style="font-size: medium;">In this paper Pitman's asymptotic efficiencies (AE) as well as Kallenberg's intermediate AE of the goodness-of-fit tests based on higher-order non-overlapping spacings is considered. We study log statistic as well as entropy type statistic based on k-spacings when k may tend to infinity as n approaches infinity. It certainly compliments the available results for fixed k and provides more general result. We show that both types of statistics based on higher ordered spacings have higher efficiencies in Pitman's sense compared to their counterparts based on simple spacings. It is also shown that the Kallenberg's intermediate AE of such test coincides with its Pitman's AE, the power of the tests are also discussed.</span></p>Muhammad Naeem2018-12-252018-12-2514483985110.18187/pjsor.v14i4.1951Bayesian and Maximum Likelihood Estimation for the Weibull Generalized Exponential Distribution Parameters Using Progressive Censoring Schemes
http://www.pjsor.com/index.php/pjsor/article/view/2600
<p class="SAP11-PaperTitle">In this paper we consider the estimation of the Weibull Generalized Exponential Distribution (WGED) Parameters with Progressive Censoring Schemes. In order to obtain the optimal censoring scheme for WGED, more than one method of estimation was used to reach a better scheme with the best method of estimation. The maximum likelihood method and the method of Bayesian estimation for (square error and Linex) loss function have been used. Monte carlo simulation is used for comparison between the two methods of estimation under censoring schemes. To show how the schemes work in practice; we analyze a strength data for single carbon fibers as a case of real data.</p>Ehab Mohamed AlmetwallyHisham Mohamed AlmongyAmaal El sayed Mubarak2018-12-252018-12-2514485386810.18187/pjsor.v14i4.2600Bayesian Skew Normal Seemingly Unrelated Regression Modelling of Gross Regional Domestic Product
http://www.pjsor.com/index.php/pjsor/article/view/2359
<a name="OLE_LINK91"></a><a name="OLE_LINK68"></a><a name="OLE_LINK2"></a><a name="OLE_LINK1"></a><a name="OLE_LINK80"></a><a name="OLE_LINK79"></a><a name="OLE_LINK67"></a><a name="OLE_LINK66"></a><a name="OLE_LINK65"></a><a name="OLE_LINK64"></a><span lang="IN">The assumption of the error normality in the regression model was often questioned especially in cases where there was an outlier, which causes the behavior of asymmetric data.</span><span lang="IN"> To overcome this, without data transformation, we could use skew distribution. This distribution was very important and applicable in various fields of science such as finance, economics, actuarial science, medicine, biology, investment. Skew Normal distributions had been proven to have a convenient for calculating bias in data with asymmetric behavior</span><span lang="IN">. This study aims to model SUR with Skew Normal error using Bayesian approach applied to East Java GRDP data. This study would compared two types of models, namely models with Normal distributed errors and models with Skew Normal distributed errors. The result of parameter estimation with Bayesian approach shows that SUR Skew Normal model was more suitable for East Java GRDP modeling rather than using normal error model. This was based on their smaller Root of Mean Square Error (RMSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) value.</span><span lang="IN"> </span>Agus Budi SantosaNur IriawanSetiawan SetiawanMohammad Dokhi2018-12-252018-12-2514486987910.18187/pjsor.v14i4.2359A New Flexible Lifetime Model with Statistical Properties and Applications
http://www.pjsor.com/index.php/pjsor/article/view/2384
<p>In this article, we introduce a new lifetime model which exhibits the increasing, the decreasing and the bathtub hazard rates. The considerable justification for the practicality of the new lifetime model is depended on the wider use of the exponentiated Weibull and Weibull lifetime models. The new lifetime model can be viewed as a mixture of the exponentiated Weibull distribution. It can also be viewed as a appropriate model for fitting the right skewed, the symmetric, the left skewed and the unimodal data. We prove empirically the importance and flexibility of the new model in modeling two types of lifetime data. The new lifetime model is a superior on the Marshall Olkin extended-Weibull, the Poisson Topp Leone-Weibull, the Burr X Exponentiated-Weibull, the Kumaraswamy-Weibull, the Gamma-Weibull, the Transmuted modified-Weibull, the Weibull-Fréchet, the Beta-Weibull, the Mcdonald-Weibull, the transmuted exponentiated generalized-Weibull, the Kumaraswamy transmuted-Weibull, and the Modified beta-Weibull models so the new model is a good substitutional to these models in modeling the aircraft windshield data. The new lifetime model is much better than the Mcdonald-Weibull, the transmuted linear exponential, the Weibull, the transmuted modified-Weibull, the Modified beta-Weibull,the transmuted additive-Weibull, the exponentiated transmuted generalized Rayleig models in modeling cancer patient data. In modeling the survival times of Guinea pigs data we deduced that the proposed model is much better than the Odd Weibull-Weibull, the Weibull Logarithmic-Weibull and the gamma exponentiated-exponential models. Finally, the new model is a preferable model than the exponentiated-Weibull, the transmuted-Weibull, the Odd Log Logistic-Weibull models, and a good alternate to these models in modeling Glass fibres data.</p>Mohamed Abo Raya2018-12-252018-12-2514488190110.18187/pjsor.v14i4.2384Stochastic Restricted Liu Type estimator for SUR model
http://www.pjsor.com/index.php/pjsor/article/view/2302
<p>In this paper, we introduce new Stochastic Restricted Estimator for SUR model, defined by Stochastic Restricted Liu Type SUR estimator (SRLTSE) . The propose estimator has deal with multicollinearity in SUR model if there is a degree of uncertainty in the parameters restriction. Moreover, the superiority of (SRLTSE) estimator was derived with respect to mean squared error matrix (MSEM) criteria. Finally, a simulation study was conducted. This simulation used standard mean squares error (MSE) criterion to illustrate the advantage between Stochastic Restricted SUR estimator (SRSE), Stochastic Restricted Ridge SUR estimator (SRRSE), and Stochastic Restricted Liu Type SUR estimator (SRLTSE) at several factors. </p>Tarek Mahmoud Omara2018-12-252018-12-2514490391110.18187/pjsor.v14i4.2302Improved generalized family of estimators of population mean using information on transformed auxiliary variables
http://www.pjsor.com/index.php/pjsor/article/view/2338
<p>This paper addresses the problem of estimating the population mean of the study variable using information on transformed auxiliary variables. In addition to many, Yasmeen et al (2015) estimator shown to the members of the suggested classes of estimators. We have derived the bias and mean squared error (<em>MSE</em>) of the suggested classes of estimators to the first degree of approximation. We have obtained the optimum conditions for which the suggested classes of estimators have minimum mean squared errors. It has been shown that the proposed classes of estimators are more efficient than the estimators recently envisaged by Yasmeen et al (2015) and other existing estimators.</p>Housila P. SinghAnita Yadav2018-12-252018-12-2514491393410.18187/pjsor.v14i4.2338Construct validity and factor structure of the Pittsburgh Sleep Quality Index (PSQI) among physicians in Jeddah, Kingdom of Saudi Arabia
http://www.pjsor.com/index.php/pjsor/article/view/2729
<p>Sleep disorders continue to rise and have been estimated to affect around half of the global population. Poor sleep quality and insomnia are also linked to various health issues in different populations. The Pittsburgh Sleep Quality Index (PSQI) is one of the most commonly used tool to assess sleep quality. It has been tested in various clinical and non-clinical settings and populations but mostly in developed world. Literature is limited from Arab region and further scarcity of studies is observed among health providers from the region. This study aimed to assess the construct validity and factor structure of PSQI among physicians in Jeddah, Kingdom of Saudi Arabia. This cross-sectional study used the PSQI tool with 19 items and 7 components on 330 physicians working in Jeddah. Data was entered and analyzed in IBM SPSS and AMOS version 22. Cronbach alpha was 0.745. Construct validity showed satisfactory results. Exploration of factor structure with Confirmatory factor analysis (CFA) showed 1-factor model as better fit. Among three models, 3-factor model showed least fit indices. The study findings showed some similarities as well as differences to comparable studies using PSQI in other settings that requires further as well as continuous exploration of the dynamic issue in similar and diverse settings.</p>Ahmad Azam MalikMarwan A. BakarmanNadeem Shafique Butt2018-12-252018-12-2514493594310.18187/pjsor.v14i4.2729An Empirical Study of Error Evaluation in Trend and Seasonal Time Series Forecasting Based on SSA
http://www.pjsor.com/index.php/pjsor/article/view/2443
<p>SSA (Singular Spectrum Analysis) starts to become a popular method in decomposing time series into some separable and interpretable series. This study provides an error evaluation in the SSA-based model for trend and multiple seasonal time series forecasting. This error evaluation is obtained by means of a numerical study on the mean square error of the estimators and mean absolute percentage error of the forecast values. Four distinct types of data generating processes (DGP) with varying sample sizes are considered in this experimental study. The parameters are estimated from the component series of SSA. Each DGP is decomposed into trend, periodic and irregular components. All these components except the irregular one are fitted by appropriate deterministic function separately. Based on the numerical simulation results, the estimated parameters are closer to the true values as the sample size increases. As the illustrative example of the real data set implementation, we used the monthly atmospheric concentrations of CO2 from Moana Loa observatory for period January 1959 to June 1972. The proposed method produces better forecast values than the results of SSA-LRF (Linear Recurrent Formula) and TLSAR (Two Level Seasonal Autoregressive). The results encourage the improvement in the time series modeling on the more complex pattern.</p>Winita SulandariSubanar SubanarSuhartono SuhartonoHerni UtamiMuhammad Hisyam Lee2018-12-252018-12-2514494596010.18187/pjsor.v14i4.2443A Control Chart Based on Two-piece Normal Distribution Using Repetitive Sampling
http://www.pjsor.com/index.php/pjsor/article/view/1561
<p>In this manuscript, a control chart is designed for two-piece normal distribution using repetitive sampling. The necessary measures to determine the average run lengths for in control and out-of-control process are given. The average run lengths are presented for various specified parameters and shift constants. The efficiency of the proposed chart is compared with the existing control chart using single sampling. The application of the proposed chart is given with the help of an example.</p>Gadde Srinivasa RaoMuhammad AslamMuhammad AzamChi-Hyuck Jun2018-12-252018-12-2514496197310.18187/pjsor.v14i4.1561A Family of Bayes Estimators for the Parameters of the Generalized Gamma Distribution
http://www.pjsor.com/index.php/pjsor/article/view/1536
The paper aims to propose a family of estimators for the Bayesian analysis of three parametric generalized gamma (GG) distribution under different priors and loss functions. We have proposed the Gibbs sampler to obtain the numerical solutions for the point and interval estimators of the parameters using WinBugs. The comparison among the different estimators has been made in terms of posterior risks and the widths of the corresponding credible intervals. A simulation study has been conducted to investigate the performance of the estimators under different combinations of the parametric values and using various sample sizes. A real life data set has been analyzed to illustrate the practical applicability of the results.Navid FerozeMuhammad Aslam2018-12-252018-12-2514497599410.18187/pjsor.v14i4.1536Improved Structural Equation Models Using Factor Analysis
http://www.pjsor.com/index.php/pjsor/article/view/2474
<p>We develop an agricultural adaptive structural equation model (SEM) that incorporates a large number of factors. These factors simultaneously account for food production while uncompromising food quality and safety. Using the principal component analysis (PCA), we obtain provisional factors, which we rotate using factor analysis, thus leading to reduced number of variables. To decide on the form of the covariance structure in the estimation of the parameters of the regression model, we conduct analysis of covariance. The generated principal components are incorporated into the SEMs where testing of different inter-associations among latent variables (LV) is conducted. For simplicity of the model, we utilise J reskog linear structural equation (LSE) system throughout the investigation process. Using a comprehensive real-life example, we illustrate the concepts and effects of the outcomes. The results show that factors such as energy, transport, labour and fertilizer make a positive contribution in the increase of the quantity and quality food. In addition, we demonstrate how to determine the key factors that influence food production where some factors are not directly measured.</p>Busanga Jerome KanyamaPeter NjuhoJean-Claude Malela-Majika2018-12-262018-12-26144995101210.18187/pjsor.v14i4.2474