Pakistan Journal of Statistics and Operation Research

Analysis of Two-Dimensional State Markovian Queuing Model with Multiple Vacation, Correlated Servers, Feedback and Catastrophes

Sharvan Kumar — 2025-03-07

This paper investigates the queuing system with multiple vacation, correlated servers, feedback and catastrophes. Inter arrival times follow an exponential distribution with parameters λ and service times follow Bivariate exponential distribution BVE (μ, μ, ν) where μ is the service time parameter and ν is the correlation parameter. Both the servers go on vacation with probability one when there are no units in the system. Laplace transform approach has been used to find the time-dependent solution. The model estimates the total expected cost, total expected profit and obtained the optimal values by varying time for cost and profit. The best optimal value at t=5 when service rate=2.75 and t=2 when feedback probability=0.55 for minimum cost and maximum profit respectively. These important key measures give a greater understanding of the model behaviour. Numerical analysis and graphical representations have been done by using Maple software.

Properties and Application of Trimodal Skew Normal Distribution

Dimpal Pathak — 2025-03-07

A new type of continuous distribution that extends the skew distribution developed by Azzalini (1985) is presented in this paper. This new distribution is designed to effectively model real-life data that may have up to three modes. The primary objective of this study is to provide a comprehensive understanding of the structural properties of this distribution, including moments, moments generating function, Fisher's information matrix, characterization, and parameter estimation through the method of maximum likelihood. Additionally, the distribution's flexibility and usefulness are evaluated by analyzing two real-life datasets. The analysis findings suggest that, as measured by AIC and BIC values, the new distribution demonstrates superior performance in fitting the datasets compared to other distributions. The lower values of AIC and BIC suggest that the new distribution better fits the datasets compared to other alternatives.

Consistency Issues in Skew Random Fields: Investigating Proposed Alternatives and Identifying Persisting Problems

Mehrdad Taghipour — 2025-03-07

Multiple researchers have proposed skew random fields derived from multivariate skew distributions, yet the consistency of these fields has been questioned. Mahmoudian (2018) and Saber et al. (2018) have put forth alternative suggestions to address these concerns. In our study, we identify that the random fields outlined by Mahmoudian (2018) continue to demonstrate consistency issues, suggesting a flaw in their definition. Finally we propose a skew random field and apply it to spatial prediction.

Addressing the Autocorrelation Problem in the Poisson Regression Model: Theory and Numerical Illustrations

Mustafa Haitham Sultan — 2025-03-07

The Poisson regression model (PRM) is usually applied in the situations where the dependent variable is in the form of count data. The purpose of this study is to compare methods of estimation for the Poisson Regression Model's first-order autocorrelation (AR(1)). The Kibria and Lukman Estimator Method (KL), Generalized Least Square Estimator Method (GLS), the Liu Estimator Method (LE), and the Reduction Liu Estimator Method (RLE) were employed. Monte Carlo simulations are used to compare these methods. The data generated follows Poisson Regression Model, however because of sample size and autocorrelation levels among other things, to create first-order autocorrelation among random errors. The Mean square Error (MSE) criterion was used for comparison. The methods are also evaluated on actual data, Moreover, the findings demonstrated that the KL approach is superior to the other estimation techniques in terms of its performance.

The Statistical Distributional Validation under a Novel Generalized Gamma Distribution with Value-at-Risk Analysis for the Historical Claims, Censored and Uncensored Real-life Applications

Haitham M. Yousof — 2025-03-07

This study introduces and examines a new probability distribution, presenting various characterizations. Key financial risk measures, including the value-at-risk (VaR), tail-value-at-risk (TVaR), also referred to as conditional tail expectation or conditional value-at-risk (CVaR), tail variance (TV), tail mean-variance (TMV), and mean excess loss (MExL) function are evaluated using maximum likelihood estimation, ordinary least squares, weighted least squares, and the Anderson-Darling estimation methods. These methods are applied for actuarial analysis in both a simulation study and an insurance claims data application. For validation of the distribution using complete data, the widely recognized Nikulin-Rao-Robson statistic is utilized and assessed through simulations and three real data sets. Two uncensored real-life data sets for failure times and remission times are used in uncensored validation. Additionally, for censored data validation, a modified version of the Nikulin-Rao-Robson statistic is proposed and evaluated through extensive simulations and three censored real data sets.

Generalized Bayesian Double Group Sampling Plan for Manufacturing Industry

Waqar Hafeez — 2025-03-07

Quality is not simply a goal or a choice for organizations, it is also a need for success in the global market. Acceptance sampling is one of two key strategies for quality assurance in manufacturing industry, along with statistical process control. After inspection the lot is either accepted or rejected based on the acceptance criteria. If historical information about the product is available, then the most effective approach for making the appropriate judgement is the Bayesian approach. To estimate quality regions, this work presents a Bayesian double group sampling plan (BDGSP). Based on acceptance criteria, the binomial distribution is used to build a likelihood function for defective and non-defective items. The beta distribution is utilized as the prior distribution to determine the average probability of acceptance. For some stated values of producer’s and consumer’s risks, four different quality regions are estimated. The suggested plan estimates variation point values based on various design parameter combinations. Producer's and consumer's risks correlate with acceptable quality levels and limiting quality levels of regions, respectively. Operating characteristic curves are used to monitor the effects of change in the values of specified parameters and for comparison with existing sampling plan. Application based on real data set proves that the proposed plan is applicable for existing manufacturing industry policies.