Pakistan Journal of Statistics and Operation Research
http://pjsor.com/index.php/pjsor
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 (Editor PJSOR)assoc.editor@pjsor.com (Support Team)Sun, 24 Mar 2019 17:28:03 +0500OJS 2.4.5.0http://blogs.law.harvard.edu/tech/rss60The Exponentiated Generalized Topp Leone-G Family of Distributions: Properties and Applications
http://pjsor.com/index.php/pjsor/article/view/2166
<p>In this paper, we propose a new class of continuous distributions called the exponentiated generalized Topp Leone-G family that extends the Topp Leone-G family introduced by Al-Shomrani et al. (2016). We derive explicit expressions for certain mathematical properties of the new family such as; ordinary and incomplete moments, generating functions, reliability analysis, Lorenz and Bonferroni curves, Rényi entropy, stress strength model, moment of residual and<strong> </strong>reversed residual life, order statistics and extreme values. We discuss the maximum likelihood estimates and the observed information matrix for the model parameters. Two real data sets are used to illustrate the flexibility of the new family.</p>Hesham Mohamed Reyad, Morad Alizadeh, Farrukh Jamal, Soha Othman, G G Hamedanihttp://pjsor.com/index.php/pjsor/article/view/2166Fri, 22 Mar 2019 00:00:00 +0500Weighted Analogue of Inverse Gamma Distribution: Statistical Properties, Estimation and Simulation Study
http://pjsor.com/index.php/pjsor/article/view/2238
<p>In this article we propose a new weighted version of inverse Gamma distribution known as Weighted Inverse Gamma distribution (WIGD). We examine the Length biased and Area biased versions of Weighted Inverse Gamma distribution. Basic structural properties viz moments, mode, moment generating function (mgf), characteristic function (cf), hazard rate function and measures of uncertainty. The parameters of this model are estimated from both classical (namely, maximum likelihood estimator and method of moments, and compare them by using extensive numerical simulations) and Bayesian point of view. The Bayes estimates are estimated by using non-informative Jeffrey’s prior and informative Inverse Chi square prior under different types of loss function (symmetric and asymmetric loss functions). Finally, a simulation study has been conducted for comparing weighted inverse gamma distribution with other competing distributions.</p>Afaq Ahmad, S P Ahmadhttp://pjsor.com/index.php/pjsor/article/view/2238Fri, 22 Mar 2019 00:00:00 +0500A Two-Parameter Quasi Lindley Distribution in Acceptance Sampling Plans from Truncated Life Tests
http://pjsor.com/index.php/pjsor/article/view/1618
<p>In this paper, acceptance sampling plans are developed when the life test is truncated at a pre-assigned time. For different acceptance numbers, confidence levels and values of the ratio of the fixed experiment time to the specified average life time, the minimum sample sizes required to ensure the specified average life are calculate assuming that the life time variate of the test units follows a two-parameter Quasi Lindley distribution (<em>QLD</em>(2)). The operating characteristic function values of the new sampling plans and the corresponding producer's risk are presented.</p>Amer Ibrahim Al-Omari, Amjad Al-Nasserhttp://pjsor.com/index.php/pjsor/article/view/1618Fri, 22 Mar 2019 00:00:00 +0500An Improved Exponential Type Estimator Of Population Mean of Sensitive Variable Using Optional Randomized Response Technique
http://pjsor.com/index.php/pjsor/article/view/2588
<p>In this paper, we improve the efficiency of Koyuncu et al (2014)’s estimator of population mean of sensitive variable by replacing Traditional Randomized response technique with Optional Randomized response technique as suggested by Gupta et al (2014). The mean square error of proposed estimator is obtained, up to first order of approximation, and is compared with mean square error of various existing estimators theoretically as well as numerically.</p>Lovleen Kumar Grover, Amanpreet Kaurhttp://pjsor.com/index.php/pjsor/article/view/2588Fri, 22 Mar 2019 14:46:01 +0500On The Modified Burr XII-Power Distribution: Development, Properties, Characterizations and Applications
http://pjsor.com/index.php/pjsor/article/view/2314
<p>In this paper, a flexible lifetime distribution with increasing, decreasing and bathtub hazard rate called the Modified Burr XII-Power (MBXII-Power) is developed on the basis of the T-X family technique. The density function of the MBXII-Power is arc, exponential, left-skewed, right-skewed, J, reverse-J and symmetrical shaped. Descriptive measures such as moments, moments of order statistics, incomplete moments, inequality measures, residual life functions and reliability measures are theoretically established. The MBXII-Power distribution is characterized via different techniques. Parameters of the MBXII-Power distribution are estimated using maximum likelihood method. The simulation study is performed on the basis of graphical results to see the performance of maximum likelihood estimates (MLEs) of the MBXII-Power distribution. The potentiality of the MBXII-Power distribution is demonstrated by its application to real data sets: survival times of pigs, survival times of patients and quarterly earnings</p>Fiaz Ahmad Bhatti, G. G. Hamedani, Mustafa Ç. Korkmaz, Munir Ahmadhttp://pjsor.com/index.php/pjsor/article/view/2314Fri, 22 Mar 2019 14:47:58 +0500Recent Developments in Distribution Theory: A Brief Survey and Some New Generalized Classes of distributions
http://pjsor.com/index.php/pjsor/article/view/2803
<p>The generalization of the classical distributions is an old practice and has been considered as precious as many other practical problems in statistics. These generalizations started with the introduction of the additional location, scale or shape parameters. In the last couple of years, this branch of statistics has received a great deal of attention and quite a few new generalized class of distributions have been introduced. We present a brief survey of this branch and introduce several new families as well.</p>Zubair Ahmad, G. G. Hamedani, Nadeem Shafique Butthttp://pjsor.com/index.php/pjsor/article/view/2803Sat, 23 Mar 2019 14:12:47 +0500The Odd Log-Logistic Generalized Half-Normal Lifetime Poisson Model
http://pjsor.com/index.php/pjsor/article/view/2349
<p>Recently, Corderio et al. (2016) applied a model called odd-logistic generalized half-normal distribution for describing fatigue lifetime data, based on this model, we propose a new wider model with a strong physical motivation called the odd-log-logistic generalized half-normal poisson distribution which is commonly used in reliability studies and modeling maximum of a random number of lifetime variables. Various of its structural properties are derived. The method of maximum likelihood is adapted to estimate the model parameters and its potentiality is illustrated with applications to two real fatigue data sets. For different parameter settings and sample sizes, some simulation studies compare the performance of the new lifetime model.</p>Fazlollah Lak, Mehdi Basikhasteh, Morad Alizadeh, Haitham M. Yousofhttp://pjsor.com/index.php/pjsor/article/view/2349Sat, 23 Mar 2019 14:18:00 +0500Selection of Tightened-Normal-Tightened sampling scheme under the implications of intervened Poisson distribution
http://pjsor.com/index.php/pjsor/article/view/2351
<p>Tightened-normal-tightened (TNT) sampling scheme is one of the most frequently used sampling schemes for making decisions about the finished product lots by examining certain samples from the lots. TNT sampling scheme includes two attribute sampling plans, one for tightened inspection and other for normal inspection along with switching rules. This paper introduces a procedure for TNT by incorporating two single sampling plans (SSP) under the conditions of intervened Poisson distribution (IPD) for the lots which may have a possibility of some intervention during the production process. The paper also assesses the performance of the proposed scheme procedure through its operating characteristic curves. Also, the unity value table is provided for certain parameters of specified producer’s risk and consumer’s risk for shop floor conditions. Further, the efficiency of proposed TNT scheme over the individual SSP under the conditions of IPD is demonstrated with illustrations.</p>Azarudheen Shahabudheen, Pradeepa Veerakumarihttp://pjsor.com/index.php/pjsor/article/view/2351Sat, 23 Mar 2019 14:22:16 +0500The Burr X Exponentiated Weibull Model: Characterizations,Mathematical Properties and Applications to Failure and Survival Times Data
http://pjsor.com/index.php/pjsor/article/view/2824
<p>In this article, we introduce a new three-parameter lifetime model called the Burr X exponentiated Weibull model. The major justification for the practicality of the new lifetime model is based on the wider use of the exponentiated Weibull and Weibull models. We are motivated to propose this new lifetime model because it exhibits increasing, decreasing, bathtub, J shaped and constant hazard rates. The new lifetime model can be viewed as a mixture of the exponentiated Weibull distribution. It can also be viewed as a suitable model for fitting the right skewed, symmetric, left skewed and unimodal data. We provide a comprehensive account of some of its statistical properties. Some useful characterization results are presented. The maximum likelihood method is used to estimate the model parameters. We prove empirically the importance and flexibility of the new model in modeling two types of lifetime data. The proposed model is a better fit than the Poisson Topp Leone-Weibull, the Marshall Olkin extended-Weibull, gamma-Weibull , Kumaraswamy-Weibull , Weibull-Fréchet, beta-Weibull, transmuted modified-Weibull, Kumaraswamy transmuted- Weibull, modified beta-Weibull, Mcdonald-Weibull and transmuted exponentiated generalized-Weibull models so it is a good alternative to these models in modeling aircraft windshield data as well as the new lifetime model is much better than the Weibull-Weibull, odd Weibull-Weibull, Weibull Log-Weibull, the gamma exponentiated-exponential and exponential exponential-geometric models so it is a good alternative to these models in modeling the survival times of Guinea pigs. We hope that the new distribution will attract wider applications in reliability, engineering and other areas of research.</p>Mohamed G. Khalil, G. G. Hamedani, Haitham M. Yousofhttp://pjsor.com/index.php/pjsor/article/view/2824Sun, 24 Mar 2019 00:00:00 +0500A New Generalized Weighted Weibull Distribution
http://pjsor.com/index.php/pjsor/article/view/2782
<p>In this article, we present a new generalization of weighted Weibull distribution using Topp Leone family of distributions. We have studied some statistical properties of the proposed distribution including quantile function, moment generating function, probability generating function, raw moments, incomplete moments, probability, weighted moments, Rayeni and q th entropy. The have obtained numerical values of the various measures to see the eect of model parameters. Distribution of of order statistics for the proposed model has also been obtained. The estimation of the model parameters has been done by using maximum likelihood method. The eectiveness of proposed model is analyzed by means of a real data sets. Finally, some concluding remarks are given.</p>Salman Abbas, Gamze Ozal, Saman Hanif Shahbaz, Muhammad Qaiser Shahbazhttp://pjsor.com/index.php/pjsor/article/view/2782Sat, 23 Mar 2019 14:26:51 +0500MSEPBurr Distribution: Properties and Parameter Estimation
http://pjsor.com/index.php/pjsor/article/view/2291
<p>MSNBurr and MSTBurr distribution have been developed as Neo-Normal distributions that represent a relaxation of normality. The difference between them is that the MSTBurr’s peak is below MSNBurr’s. In this paper, we propose a MSEPBurr distribution with its peak could be not only lower but also high-er than MSNBurr. Furthermore, we study several properties of MSEPBurr, such as mean, variance, skewness, kurtosis, and quantile. The MSEPBurr parameters are estimated by using the Bayesian approach with the BUGS language implementation for its computation. We employ simulation study and use existing data to illustrate the application of the regression model. In real data, we notice that MSEPBurr has similar performance with MSNBurr and MSTBurr that they outperform Normal and Student-<em>t </em>distribution in Australian athlete data because their skewness can accommodate long left tail excellently. However, their performance is less than the Student-<em>t</em> model in chemical reaction rate data because their skewness can not accommodate long right tail perfectly. Although in general their perfor-mance is the same, we observe that the MSEPBurr performs better than the MSNBurr and the MSTBurr in some simulated data.</p>Achmad Syahrul Choir, Nur Iriawan, Brodjol Sutijo Suprih Ulama, Mohammad Dokhihttp://pjsor.com/index.php/pjsor/article/view/2291Sat, 23 Mar 2019 14:32:19 +0500A New Extremely Flexible Version of the Exponentiated Weibull Model: Theorem and Applications to Reliability and Medical Data Sets
http://pjsor.com/index.php/pjsor/article/view/2383
<p>In this work, a new lifetime model is introduced and studied. The major justification for the practicality of the new model is based on the wider use of the exponentiated Weibull and Weibull models. We are also motivated to introduce the new lifetime model since it exhibits decreasing, upside down-increasing, constant, increasing-constant and <strong>J</strong> shaped hazard rates also the density of the new distribution exhibits various important shapes. The new model can be viewed as a mixture of the exponentiated Weibull distribution. It can also be considered as a suitable model for fitting the symmetric, left skewed, right skewed and unimodal data. The importance and flexibility of the new model is illustrated by four read data applications.</p>Mohamed Abo Rayahttp://pjsor.com/index.php/pjsor/article/view/2383Sat, 23 Mar 2019 14:35:56 +0500Bayesian Estimation for Nadarajah-Haghighi Distribution Based on Upper Record Values
http://pjsor.com/index.php/pjsor/article/view/2569
<p>This paper discusses maximum likelihood and Bayes estimation of the two unknown parameters of Nadarajah and Haghighi distribution based on record values. Different Bayes estimates are derived under squared error, balanced squared error and general entropy loss functions by using Jeffreys' prior information and extension of Jeffreys' prior information. It is observed that the associated posterior distribution appears in an intractable form. So, we have used Tierney and Kadane approximation method to compute these estimates. Finally, numerical computations are presented based on generated record values using R software.</p>MS Sana, M. Faizanhttp://pjsor.com/index.php/pjsor/article/view/2569Sat, 23 Mar 2019 14:39:38 +0500Exact reliability formula for a linear consecutive k-out-of-n: F system and relayed consecutive systems with a change point for any 𝒌≤𝒏, with stress-strength application.
http://pjsor.com/index.php/pjsor/article/view/2356
This paper presents exact formulas for the reliability of linear consecutive k-out-of-n: F, and relayed consecutive k-out-of-n: F systems, having a change point at position 𝑐, 1≤𝑐≤𝑛, for any 𝑘≤𝑛. A change point at position 𝑐, means that the components after this point have reliabilities that are different from those before or at position 𝑐. The components are assumed to be independent. Practically, the change in the components reliabilities may be due to change in the stress applied. Assuming a change in stress, exact formulas of the stress-strength reliability of the systems are derived, considering two cases. The first case assumed strength and stress having the same form of distributions, while the second case assumed strength and stress having different forms of distributions. Estimation of the stress-strength reliability for both cases is discussed. Application to both cases are considered with numerical illustration.S. M. Bakry, N. A. Mokhlishttp://pjsor.com/index.php/pjsor/article/view/2356Sat, 23 Mar 2019 14:40:28 +0500