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> A New Heavy-Tailed Exponential Distribution: Inference, Regression Model and Applications <p><span class="fontstyle0">A new weighted exponentiated-exponential distribution is proposed to model financial data. It has heavy-tailed behavior which is suitable for data with right tails. Some actuarial measures for the new model are determined, and simulations are reported. Its parameters are estimated using nine approaches including a Bayesian method. A new Log-WEx-Exponential regression model is defined for right censored data. The importance of the new models is proved by applications to financial data.</span></p> Ahmed Z. Afify Rodrigo R. Pescim Gauss M. Cordeiro Hisham A. Mahran Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-09-03 2023-09-03 395 411 10.18187/pjsor.v19i3.4230 Mixed Poisson Transmuted New Weighted Exponential Distribution with Applications on Skewed and Dispersed Count Data <p>In this study, a new three-parameter mixed Poisson Cubic Rank Transmuted New Weighted Exponential Distribution is proposed. The new discrete distribution is obtained by mixing the Poisson distribution with a newly obtained Cubic Rank Transmuted New Weighted Exponential Distribution. Various shapes and mathematical properties of both mixing distribution and the new count distribution are examined. Special cases of the new proposition are also identified. The distribution along with its special cases and other count distributions are assumed for skewed and dispersed count observations. The maximum likelihood estimation is used to provide estimates for the parameters of all examined distributions. Results show that the new proposition along with some of its special cases provide good fit for all the examined data.</p> Ademola Abiodun ADETUNJI Shamsul Rijal Muhammad Sabri Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-09-03 2023-09-03 413 424 10.18187/pjsor.v19i3.4113 Modeling the Asymmetric Reinsurance Revenues Data using the Partially Autoregressive Time Series Model: Statistical Forecasting and Residuals Analysis <p>The autoregressive model is a representation of a certain kind of random process in statistics, insurance, signal processing, and econometrics; as such, it is used to describe some time-varying processes in nature, economics and insurance, etc. In this article, a novel version of the autoregressive model is proposed, in the so-called the partially autoregressive (PAR(1)) model. The results of the new approach depended on a new algorithm that we formulated to facilitate the process of statistical prediction in light of the rapid developments in time series models. The new algorithm is based on the values of the autocorrelation and partial autocorrelation functions. The new technique is assessed via re-estimating the actual time series values. Finally, the results of the PAR(1) model is compared with the Holt-Winters model under the Ljung-Box test and its corresponding p-value. A comprehensive analysis for the model residuals is presented. The matrix of the autocorrelation analysis for both points forecasting and interval forecasting are given with its relevant plots.</p> Salwa L. Alkhayyat Heba Soltan Mohamed Nadeem Shafique Butt Haitham M. Yousof Emadeldin I. A. Ali Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-09-02 2023-09-02 425 446 10.18187/pjsor.v19i3.4123 The Construction of Unemployment Rate Model Using SAR, Quantile Regression, and SARQR Model <p>The Open Unemployment Level (OUL) is the percentage of the unemployed to the total labor force. One of the provinces with the highest OUL score in Indonesia is West Java Province. If an object of observation is affected by spatial effects, namely spatial dependence and spatial diversity, then the regression model used is the Spatial Autoregressive (SAR) model. Quantile regression minimizes absolute weighted residuals that are not symmetrical. It is perfect for use on data distribution that is not normally distributed, dense at the ends of the data distribution, or there are outliers. The Spatial Autoregressive Quantile Regression (SARQR) is a model that combines spatial autoregressive models with quantile regression. This research used the data regarding OUR in West Java in 2020 from the Central Bureau of Statistics. This study compares the estimation results based on SAR and SARQR models to obtain an acceptable model. In this study, it was found that the SARQR model is better than SAR at dealing with the problems of dependency and diversity in spatial data modeling and is not easily affected by the presence of outlier data.</p> Ferra Yanuar Tasya Abrari Izzati Rahmi HG Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-09-03 2023-09-03 447 458 10.18187/pjsor.v19i3.4241 Assessing the Effect of Non-response in Stratified Random Sampling using Enhanced Ratio Type Estimators under Double Sampling Strategy. <p>In this paper, separate and combined ratio type estimators have been proposed in presence of non-response for estimating the population mean under stratified random sampling when the non-response occurs both on study and the auxiliary variables and the population mean of the auxiliary variable is unknown. The expressions for the biases and mean square errors (MSEs) of the proposed estimators have been derived to the first order of approximation. The proposed estimators have been compared with the other existing estimators using MSE criterion, and the condition under which the proposed estimators perform better than existing estimators have been obtained. In addition to the theoretical research, an empirical study was conducted.</p> Zakir Hussain Wani jana S.E.H.Rizvi Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-09-03 2023-09-03 459 473 10.18187/pjsor.v19i3.4063 An EPQ Model for Delayed Deteriorating Items with Reliability Consideration, Quadratic Demand and Shortages <p>In this paper, an EPQ model for items that exhibit delay in deterioration is developed. It is assumed that there is no demand and no deterioration during production buildup period. Demand starts immediately after production but no deterioration. Then a period of deterioration sets in until the stock finishes. It is also supposed that the cost of a unit product is inversely related to the rate of demand and directly related to the process reliability (as assumed by Tripathy et al. (2015) and modified by Dari and Sani (2015)). The demand before deterioration sets in is quadratic time dependent while demand after deterioration sets in is a constant. Shortages are allowed and partially backordered.&nbsp; A numerical model is given to compare the simulation model and the statistical analysis conducted on the model to see the effect of measurement changes in other system parameters.</p> Dari Sani Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-09-03 2023-09-03 475 489 10.18187/pjsor.v19i3.4157 A Novel Version of the Exponentiated Weibull Distribution: Copulas, Mathematical Properties and Statistical Modeling <p>In this study, the authors of the current work describe a novel exponentiated Weibull distribution that they have invented. The study was written by the writers of the current work. It is required to analyze those properties once the pertinent mathematical properties have been derived. In addition to the dispersion index, the anticipated value, variance, skewness, and kurtosis are also statistically examined. The dispersion index is likewise examined. Other beneficial shapes that the new density can assume include "bathtub," "right skewed," "bimodal and left skewed," "unimodal and left skewed," and "bimodal and right skewed." Additionally, these forms can be merged to create a "bathtub." The term "bathtub (U-HRF)," "constant," "monotonically increasing," "upside down-increasing (reversed U-increasing)," "J-HRF," "upside down-constant," "increasing-constant," or "upside down (reversed U)" may be used to describe the new rate of failure. The greatest likelihood method's efficiency is assessed via graphical analysis. The main measures for this procedure’s evaluation are biases and mean squared errors. The reader is given a scenario that graphically displays the adaptability and value of the innovative distribution through the use of three separate sets of actual data.</p> Mohamed K. A. Refaie Asmaa Ayoob Yaqoob Mahmoud Ali Selim Emadeldin I. A. Ali Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-09-03 2023-09-03 491 519 10.18187/pjsor.v19i3.4089 Marginal and Conditional both Extreme Value Distributions: A Case of Stochastic Regression Model <p>A mathematical model is a mathematical connection that describes some real-life scenario. To handle real-world problems securely and effectively, simulation modelling is required. In this article, the author investigates the stochastic regression model scenario in which the dependent and independent variables in a linear regression model follow a distribution. We assume that the dependent and independent variables both exhibit Type I Extreme Value Distribution. The estimators are then derived using the Modified Maximum Likelihood (MML) estimation method. In accordance with this, a hypothesis testing technique is developed.</p> Sulaxana Bharali Jiten Hazarika Kuldeep Goswami Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-09-03 2023-09-03 521 536 10.18187/pjsor.v19i3.4143 An Improved Class of Estimators Of Population Mean of Sensitive Variable Using Optional Randomized Response Technique <p>In this paper we have suggested a class of estimators of population mean of sensitive variable under optional randomized response technique as reported in Gupta et alÂ&nbsp;Â&nbsp;(2014).Â&nbsp;We have obtained the mean squared errorÂ&nbsp; (MSE) of the suggested class of estimators up to theÂ&nbsp; first order of approximation. The optimum conditions are obtained at which the (MSE)Â&nbsp;of theÂ&nbsp; proposed class of estimators is minimum. AnÂ&nbsp; empirical study is carried out to show the performance of the suggested class of estimators over existing estimators .It is found that the performance of proposed class of estimators is better than the existing estimators including Grover and Kaur (2019).</p> Preeti Patidar Housila Prasad Singh Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-09-03 2023-09-03 537 550 10.18187/pjsor.v19i3.2877 A modified weighting system for combined forecasting methods based on the correlation coefficients of the individual forecasting models <p>Herein, a modified weighting for combined forecasting methods is established. These weights are used to adjust the correlation coefficient between the actual and predicted values from five individual forecasting models based on their correlation coefficient values and ranking. Time-series datasets with three patterns (stationary, trend, or both trend and seasonal) were analyzed by using the five individual forecasting models and three combined forecasting methods: simple-average, Bates-Granger, and the proposed approach. The MAPE and RMSE results indicate that the proposed method outperformed the others, especially when the time-series pattern was stationary and improved the forecasting accuracy of the worst and best individual forecasting models by 35–37% and 7–10%, respectively. Moreover, the proposed method showed improvements in MAPE and RMSE of around 18–20% and 9–11% compared to the simple-average and Bates-Granger methods, respectively. In addition, the combined forecasting methods outperformed the individual forecasting models when analyzing non-stationary data. Remarkably, the performances of the proposed and Bates-Granger methods were almost the same, with improvements in MAPE and RMSE in the range of 1–2% on average. Therefore, the proposed method for creating weights based on the correlation coefficients of the individual forecasting models greatly improves combined forecasting methods.</p> Chantha Wongoutong Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-09-03 2023-09-03 551 568 10.18187/pjsor.v19i3.4247 A Class of Methods Using Interval Arithmetic Operations for Solving Multi–Objective Interval Transportation Problems <p>The objective of this article is studying on cost and time minimization of interval transportation problem (ITP) by using Best Candidate Method (BCM), Improved ASM method (IASM), ASM method, Zero Suffix Method (ZSM) and Zero Point Method (ZPM) with new interval arithmetic operations. We have obtained a better optimum result campared with existing methods available in the literature. The problems considered in this article are solved by the above listed methods without converting them into classical transportation problems. A comparative results are also given.</p> Ramesh Ganesan Mathavan N Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-09-03 2023-09-03 569 583 10.18187/pjsor.v19i3.3983 Modeling Tri-Model Data With a New Skew Logistic Distribution <p>This paper considers a new family of the trimodal skew logistic distributions. Some properties of this distribution, including moments, moments generating function, entropy, maximum likelihood estimates of parameters and some other properties, are presented. A simulation study is conducted to examine the performance of the parameters. Numerical optimization is carried out via two real-life datasets. Results show that the new distribution is better fitted in terms of these datasets among logistic, skew logistic and alpha skew logistic distributions based on the value of AIC and BIC.</p> Dimpal Pathak Partha Jyoti Hazarika Subrata Chakraborty Jondeep Das G. G. Hamedani Copyright (c) 2023 Pakistan Journal of Statistics and Operation Research 2023-09-03 2023-09-03 585 602 10.18187/pjsor.v19i3.3885