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 a 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 a variety of disciplines. Because of the increasing submission rate, the editorial board of PJSOR decided to publish it on a quarterly basis from 2012. Brief chronicles are overseen by an <a title="PJSOR Editorial Board" href="">Editorial Board</a> comprised of academicians and scholars. We welcome you to <a title="Submissions" href="">submit</a> your research for possible publication in PJSOR through our online submission system. <strong>Publishing in PJSOR is absolutely free of charge (No Article Processing Charges)</strong>.<br><a href=""><strong>ISSN : 1816 2711</strong></a>&nbsp; &nbsp;<strong>|&nbsp; &nbsp;<a href="">E- ISSN : 2220 5810</a></strong></p> College of Statistical and Actuarial Sciences en-US Pakistan Journal of Statistics and Operation Research 1816-2711 <p><strong>Authors who publish with this journal agree to the following License</strong></p> <p><strong><a href=""><img class="alignleft" src="" width="118" height="41"></a><a href="">CC BY</a>:&nbsp;</strong>This license allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use.</p> <p>&nbsp;</p> Bayesian Inference for a Weighted Bilal Distribution: Regression Model <p>In this paper, a new lifetime distribution is proposed. Various statistical properties of the proposed distribution such as survival function, hazard rate function, mean residual life function, moments, moment generating function, Bonferroni curve, Lorenz curve, and order statistic are presented. The Bayesian estimator of the distribution parameter is derived. The behavior of the Bayesian estimator is assessed by a simulation study. Furthermore, a regression model is developed based on the proposed distribution. Some real data applications are analyzed to show the potentiality of the proposed<br>models.</p> Yupapin Atikankul Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-03-04 2023-03-04 1 13 10.18187/pjsor.v19i1.4140 Approximate MLEs for the location and scale parameters of the Poisson-half-logistic distribution <p>Recently, the application of compound distributions has increased due to the flexibility in fitting to actual data in various fields such as economics, insurance, etc. Poisson-half-logistic distribution is one of these distributions with an increasing-constant hazard rate that can be used in parallel systems and complementary risk models. Because of the complexity of the form of this distribution, it is not possible to obtain classical parameter estimates (such as MLE) by the analytical method for the location and scale parameters. We present a simple way of deriving explicit estimators by approximating the likelihood equations appropriately. This paper presents AMLE (Approximate MLE) method to obtain the location and scale parameters estimation. Using simulation, we show that this method is as efficient as the maximum likelihood estimators (MLEs), we obtain the variance of estimators from the inverse of the observed Fisher information matrix, and we see that when sample size increases bias and variance of these estimators, MSEs of parameters decrease. Finally, we present a numerical example to illustrate the methods of inference developed here.</p> Mehrdad Niaparast Leila Esmaeili Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-03-04 2023-03-04 15 26 10.18187/pjsor.v19i1.4018 Bayesian estimation for the type-I hybrid xgamma distribution using asymmetric loss function <p>This article proposes the Bayes estimation of the parameter and reliability function for xgamma distribution in the presence of type-I hybrid censored observations. The Bayes estimate of the parameter has been obtained by assuming informative and non-informative priors using general entropy loss function. Obviously, censoring adds difficulties in estimation procedure; hence the Bayes estimators computed with type-I hybrid censored observation under the mentioned prior often do not assume any standard form. Therefore, Bayes estimates are computed using Tierney-Kadane approximation and Markov Chain Monte Carlo numerical technique. Further, different interval estimates namely asymptotic confidence interval, bootstrap confidence interval and highest posterior density interval along with the width of the interval and coverage probability are also discussed. The maximum likelihood estimate for the same has also been computed using non- linear maximization iterative procedure and compared with corresponding Bayes estimates using Monte Carlo simulations. The comparison of the estimators are made in terms of average loss over whole sample space and corresponding length of the interval. lastly, one medical data set has been considered for the real application of the proposed study.</p> Abhimanyu Singh Yadav Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-03-04 2023-03-04 27 49 10.18187/pjsor.v19i1.2808 Kumaraswamy Esscher Transformed Laplace Distribution: Properties, Application and Extensions <p>In this article, we introduce a new generalized family of Esscher transformed Laplace distribution, namely the Kumaraswamy Esscher transformed Laplace distribution. We study the various properties of the distribution including the survival function, hazard rate function, cumulative hazard rate function and reverse hazard rate function. The parameters of the distribution are estimated using the maximum likelihood method of estimation. A real application of this distribution on breaking stress of carbon fibres is also considered. Further, we introduce and study the exponentiated and transmuted exponentiated Kumaraswamy Esscher transformed Laplace distributions.</p> Dais George Rimsha H. Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-03-06 2023-03-06 51 62 10.18187/pjsor.v19i1.3818 A Proposed Method for Finding Initial Solutions to Transportation Problems <p><span dir="ltr" style="left: 120px; top: 340.08px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.939878);" role="presentation">The Transportation Model (TM) in the application of Linear Programming (LP) is very useful in optimal distribution </span><span dir="ltr" style="left: 120px; top: 360.005px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.922755);" role="presentation">of goods. This paper focuses on finding Initial Basic Feasible Solutions (IBFS) to TMs hence, proposing a Demand-</span><span dir="ltr" style="left: 120px; top: 379.93px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.930812);" role="presentation">Based Allocation Method (DBAM) to solve the problem. This unprecedented proposal goes in contrast to the Cost-</span><span dir="ltr" style="left: 120px; top: 399.855px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.907);" role="presentation">Based Resource Allocations (CBRA) associated with existing methods (including North-west Corner Rule, Least Cost </span><span dir="ltr" style="left: 120px; top: 419.78px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.922046);" role="presentation">Method and Vogel’s Approximation Method) which make cost cell (i.e. decision variable) selections before choosing </span><span dir="ltr" style="left: 120px; top: 439.705px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.948969);" role="presentation">demand and supply constraints. The proposed ‘DBAM’ on page 4 is implemented in MATLAB and has the ability </span><span dir="ltr" style="left: 120px; top: 459.632px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.930794);" role="presentation">to solve large-scale transportation problems to meet industrial needs. A sample of five (5) examples are presented </span><span dir="ltr" style="left: 120px; top: 479.557px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.938355);" role="presentation">to evaluate efficiency of the method.</span> <span dir="ltr" style="left: 379.16px; top: 479.557px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.959965);" role="presentation">Initial Basic Feasible Solutions drawn from the study (according to DBAM) </span><span dir="ltr" style="left: 120px; top: 499.482px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.914033);" role="presentation">represent the optimal with higher accuracy, in comparison to the existing methods. Results from the study qualify the </span><span dir="ltr" style="left: 120px; top: 519.407px; font-size: 16.6043px; font-family: sans-serif; transform: scaleX(0.910531);" role="presentation">DBAM as one of the best methods to solve industrial transportation problems.</span></p> Joseph Ackora-Prah Valentine Acheson Emmanuel Owusu-Ansah Seth K. Nkrumah Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-03-06 2023-03-06 63 75 10.18187/pjsor.v19i1.4196 A Generalization of Burr Type XII Distribution with Properties, Copula and Modeling Symmetric and Skewed Real Data Sets <p>A new generalization of Burr type XII model is introduced and studied. The genesis of the new model is based on the family of Cordeiro et al. (2016). The new model generalizes at least eight important sub-models. The new density can be unimodal, symmetric and left skewed. Some useful properties related to the new model are derived. The Clayton Copula-based construction is used to generate many bivariate and multivariate type distributions. Graphically, we performed the simulation experiments to assess of the finite sample behavior of the estimations.</p> Mohamed G. Khalil Emadeldin I. A. Ali Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-03-06 2023-03-06 77 101 10.18187/pjsor.v19i1.3377 Prediction of KLCI Index Through Economic LASSO Regression Model and Model Averaging <p>The Financial Times Stock Exchange (FTSE) Bursa Malaysia KLCI Index is a key component in the development of Malaysia's economic growth and the complexity in terms of identifying the factors that have a substantial impact on the Malaysian stock market has always been a contentious issue. In this study, the macroeconomic factors of exchange rate, interest rate, gold price, consumer price index, money supply M1, M2, and M3, industrial production, and oil price were discussed by using economic LASSO regression and Bayesian Model Averaging (BMA) with monthly average and monthly end time-series data spanning from January 2015 to June 2021, with a total of 78 observations by using the R Studio. The findings demonstrate that month-end data is better suited for stock market prediction than month-average data and that the BMA model is more suitable than the LASSO model, as seen by lower Mean Square Error of Prediction, MSE(P) and Residual Mean Square Error of Prediction, RMSE(P) values. The exchange rate, gold price, and money supply have a negative association with the dependent variables, while the consumer price index has a positive relationship associated with the dependent variables. The consumer price index is the most significant contributing factor, whereas gold price is the least significant. The result depicted that the KLCI index has no significant relationship with the variables interest rate, money supply M2, M1, industrial production index, and oil price. In conclusion, investors could specifically focus on the positive contributor and put lesser attention on improving their portfolio return.</p> Khuneswari Gopal Pillay Soh Pei Lin Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-03-06 2023-03-06 103 113 10.18187/pjsor.v19i1.4214 Asymptotic Normality of the Conditional Hazard Rate Function Estimator for Right Censored Data under Association <p>In this paper, we study a smooth estimator of the conditional hazard rate function in the censorship model when the data exhibit some dependence structure. We show, under some regularity conditions, that the kernel estimator of the conditional hazard rate function suitably normalized is asymptotically normally distributed.</p> Samra Dhiabi Ourida Sadki Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-03-06 2023-03-06 115 130 10.18187/pjsor.v19i1.3740 Mean Estimation of a Sensitive Variable under Measurement Errors using Three-Stage RRT Model in Stratified Two-Phase Sampling <p>In the present study, the problem of mean estimation of a sensitive variable using three-stage RRT model under measurement errors is addressed. A generalized class of estimators is proposed using a mixture of auxiliary attribute and variable. Some members of the proposed generalized class of estimators are identified and studied. The bias and mean squared error (MSE) expressions for the proposed estimators are correctly derived up to first order Taylor's series of approximation. The proposed estimator's efficiency is investigated theoretically and numerically using real data. From the numerical study, the proposed estimators outperforms existing mean estimators. Furthermore, the efficiencies of the mean estimators’ decreases as the sensitivity level of the survey question increases.</p> Ronald O Onyango Brian Oduor Francis Odundo Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-03-06 2023-03-06 131 144 10.18187/pjsor.v19i1.3929 Multiclass Forecasting on Panel Data Using Autoregressive Multinomial Logit and C5.0 Decision Tree <p>Panel data is commonly used for the numerical response variables, while the literature for forecasting categorical variables on the panel data structure is still challenging to find. Forecasting is important because it is helpful for government policies. This study aimed to forecast multiclass or categorical variables on the panel data structure. The proposed forecasting models were autoregressive multinomial logit and autoregressive C5.0. The strategy applied so that the two models could be used for forecasting was to add autoregressive effects and fixed predictor variables such as location, time, strata, and month of observations. The autoregressive effect &nbsp;was assumed to be a fixed effect and treated as a dummy variable. The data used was the category of land conditions through The Area Sampling Frame (ASF) survey conducted by the BPS-Statistics Indonesia. The evaluation of both models was based on classification and forecasting performance. Classification performance was obtained by dividing the dataset into 75% training data for modeling and 25% test data for validation and then repeated 200 times. The classification results showed that the autoregressive C5.0 accuracy was 86.48%, while the autoregressive multinomial logit was 83.97%. A comparison of forecasting performance was obtained by dividing the data into training and testing based on the time sequence. The result showed that the forecasting performance was worse than the classification performance. Autoregressive C5.0 had an accuracy of 77.43%, while autoregressive multinomial logit had 77.77%.</p> Muhlis Ardiansyah Hari Wijayanto Anang Kurnia Anik Djuraidah Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-03-06 2023-03-06 145 154 10.18187/pjsor.v19i1.4053 The Marshall-Olkin Pranav distribution: Theory and applications <div class="page" title="Page 1"> <div class="section"> <div class="layoutArea"> <div class="column"> <p>The current paper presented new two-parameter life processes distribution, the Marshall-Olkin Pranav (MOEP) distribution. This study combines the Marshall-Olkin method with the Pranav distribution to produce a more accessible and flexible model used to perform data survival techniques. Some of its critical statistical features are presented in this study. For instance, we mentioned its survival , hazard, reversed hazard, and cumulative hazard rate function. Then we discussed its Moment generating functions, The characteristic function, Incomplete moments, R`enyi and Entropies, and stochastic orderings. The research utilized maximization of chance in estimating parameters. These tests are done through simulations to achieve the desired results. After its attainment, real-life data was used to test the new model, which possesses the best goodness of fit.</p> </div> </div> </div> </div> Rehab Alsultan Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-03-06 2023-03-06 155 166 10.18187/pjsor.v19i1.4058 Short-Term Insurance Claims Payments Forecasting with Holt-Winter Filtering and Residual Analysis <p>Time series are essential for anticipating various claims payment applications. For insurance firms to prevent significant losses brought on by potential future claims, the future values of predicted claims are crucial. Additionally, the ideal parameter is chosen artificially. By using a genuine application, the proposed model’s utility is demonstrated. Additionally, the ideal parameter is chosen artificially. By using a genuine application, the proposed model's utility is demonstrated. Also, the single exponential smoothing model is used for prediction under the Holt-Winters’ additive algorithm.</p> Moustafa Salem Mohamed G. Khalil Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-03-06 2023-03-06 167 186 10.18187/pjsor.v19i1.4215 Comparison of Infinite Capacity FM/FEk/1 Queuing Performance Using Fuzzy Queuing Model and Intuitionistic Fuzzy Queuing Model with Erlang Service Rates <p>In this work, we suggest an analytic technique with triangular fuzzy and triangular intuitionistic fuzzy numbers to compute the membership functions of considerable state-executing proportion in Erlang service models. The inter-entry rate, which is Poisson, and the admin (service) rate, which is Erlang, are both fuzzy-natured in this case, with FEk designating the Erlang probabilistic deviation with k exponentially phase. The numeric antecedents are shown to validate the model's plausibility, FM/FEk/1. A contextual inquiry is also carried out, comparing individual fuzzy figures. Intuitionistic fuzzy queueing models that are comprehensible are more categorical than fuzzy queueing models. Expanding the fuzzy queuing model to an intuitionistic fuzzy environment can boost the implementation of the queuing model. The purpose of this study is to assess the performance of a single server Erlang queuing model with infinite capacity using fuzzy queuing theory and intuitionistic fuzzy queuing theory. The fuzzy queuing theory model's performance evaluations are reported as a range of outcomes, but the intuitionistic fuzzy queuing theory model provides a myriad of values. In this context, the arrival and the service rate are both triangular and intuitionistic triangular fuzzy numbers. An assessment is made to find evaluation criteria using a design protocol in which fuzzy values are kept as they are and not made into crisp values, and two statistical problems are solved to understand the existence of the method.</p> AARTHI S M. Shanmugasundari Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-03-06 2023-03-06 187 202 10.18187/pjsor.v19i1.4055 The Multimodal Extension of the Balakrishnan Alpha Skew Normal Distribution: Properties and Applications <p>This paper introduces a new class of Balakrishnan distribution by extending the multimodal skew-normal distribution proposed by Chakraborty&nbsp;et al.&nbsp;(2015). Statistical properties of the new family of distributions are studied in detail. In particular, explicit expressions of the density and distribution function, moments, skewness, kurtosis and the moments generating function are derived. Furthermore, estimation of the parameters using the maximum likelihood method of the new family of distributions is considered. Finally, the paper ends with an illustration of real-life data sets and then comparing the value of Akaike Information Criterion and Bayesian information criterion of the new distribution with some other known distributions.&nbsp;For the nested models, the Likelihood Ratio Test is carried out.</p> SRICHARAN SHAH Partha Jyoti Hazarika Dimpal Pathak Subrata Chakraborty M. Masoom Ali Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-03-06 2023-03-06 203 217 10.18187/pjsor.v19i1.4019