Pakistan Journal of Statistics and Operation Research

Flexible Group Service MAP/ PH/ 1 Queueing Model with Working Breakdown, Repair and Balking

2024-12-16T00:08:03+05:00

In reality, there are many uses of queues where services are provided in groups and these type of queues are widely studied in the literature. In this paper we examine a particular queueing model, wherein the services are provided in groups ranging from 1 to a pre defined constant, denoted as K, and the arrival follows a Markovian arrival process. The service time of each individual customer follows phase type distribution. The maximum of each customers individual service time within a group is defined as the group's service time. At the service completion moment if there are fewer customers than K, the server won't begin the subsequent service until the system's customer size reaches K or a randomly assigned admission period expires, whichever happens first. The phase type representation of the service times depends on the group's size. Anytime a server breakdowns and it will not proceed to repair, instead it will serve the affected customer group at a slower pace. After that specific customer group's service is finished, the server will immediately undergo repair to fix any issues. The process of repair and breakdown occurs at exponential rate. When the server breakdowns, the customer might balk. The Markov chain's stability condition is determined and stationary probability vector is computed. Formulas for the primary system performance measures are given. Numerical and graphical representations of the proposed model are illustrated.

A Unified Family for Generating Probabilistic Models: Properties, Bayesian and Non-Bayesian Inference with Real-Data Applications

2024-12-16T00:08:01+05:00

This paper introduces a new generator called the inverse-power Burr–Hatke-G (IPBH-G) family. The special models of the IPBH-G family accommodate different monotone and nonmonotone failure rates, so it turns out to be quite flexible family for analyzing non-negative real-life data. We provide three special sub-models of the family and derive its key mathematical properties. The parameters of the special IPBH-exponential model are explored from using eleven frequentist and Bayesian estimation approaches. The Bayes estimators for the unknown parameters are obtained under three different loss functions. Numerical simulations are performed to compare and rank the proposed methods based on partial and overall ranks. Furthermore, the superiority of the IPBH-exponential model over other distributions are illustrated empirically by means of three real-life data sets from applied sciences including industry, medicine and agriculture.

Characterizations of Certain (2023-2024) Introduced Univariate Continuous Distributions

2024-12-16T00:07:59+05:00

This paper deals with various characterizations of certain univariate continuous distributions proposed in (2023-2024). These characterizations are based on: (i) a simple relationship between two truncated moments; (ii) the hazard function; (iii) reverse hazard function and (iv) conditional expectation of a single function of the random variable. It should be mentioned that for the characterization (i) the cumulative distribution function need not have a closed form and depends on the solution of a first order differential equation, which provides a bridge between
probability and differential equation.

A Novel Reciprocal-Weibull Model for Extreme Reliability Data: Statistical Properties, Reliability Applications, Reliability PORT-VaR and Mean of Order P Risk Analysis

2024-12-16T00:28:37+05:00

Peaks over a random threshold value-at-risk (PORT-VaR) analysis is a powerful tool for evaluating extreme value reliability data, particularly for materials like carbon and glass fibers. By incorporating random thresholds into traditional value at risk (VaR) and tail value at risk (TVaR) frameworks, it provides a more nuanced understanding of how materials behave under extreme conditions, making it invaluable for applications where failure is costly or dangerous, such as aerospace, automotive, and civil engineering. The combination of Mean of Order P (MO-P), VaR and PORT-VaR analyses in medical data offers important insights into risk evaluation and patient management. By examining both average and extreme strength of glass fibers, healthcare professionals can create more effective treatment plans, enhance patient outcomes, and improve overall care quality. This comprehensive approach enables more sophisticated decision-making and targeted interventions in clinical settings. To illustrate our main objective and conduct a medical analysis, we introduced a new extreme value model called the generalized Rayleigh reciprocal-Weibull (GR-RW) and presented its key mathematical results. Additionally, we conducted a simulation study and analyzed two real datasets to compare the competing models.

Evaluating the Efficiency of Turkish Banking Sector Using Data Envelopment Analysis and Malmquist Productivity Index: Covid-19 Pandemic and After

2024-12-16T00:07:57+05:00

Covid-19 pandemic has created a deep crisis with social, cultural, economic, and political consequences all over the world. In this study, we used the Malmquist Total Factor Productivity Change Index (TFPCH) and Data Envelopment Analysis (DEA) methods to assess the efficiency and performance of banks during the Covid-19 pandemic and in the post-pandemic era. We performed the application for 17 banks in Türkiye of which data structure is suitable for analysis. For the analysis, data from 2019, the beginning of the Covid-19 epidemic, to 2022, when the epidemic almost ended, were used. The highest value of the general efficiency average of banks is 0.943 in 2020. 2020 is also the year with the highest number of effective banks with a total of 9 effective banks. The highest value of the TFPCH general average is 1.543 in the 2021-2022 period. It was determined that the state banks had the highest average efficiency percentage and the highest TFPCH average for the entire period of 2019-2022.

Designing a variable control chart for a two-stage production process

2024-12-17T15:49:43+05:00

In this paper, a variable chart has been proposed to study a two-stage serial production process. Measurements of quality characteristics of products processed at each stage are assumed to be independent and follow normal distribution. In order to evaluate performance of the control chart, two cases of equal shifts in both the stages and unequal shifts were considered and results were presented accordingly. The necessary measures are given to calculate the average run length (ARL) for shifted processes. The tables of ARLs are presented for equal and different sample sizes at first- and second- stage. Performance of the proposed control chart is presented using a simulation study.

A New Discrete Generator with Mathematical Characterization, Properties, Count Statistical Modeling and Inference with Applications to Reliability, Medicine, Agriculture, and Biology Data

2024-12-16T00:26:52+05:00

In this piece of work, we examine and present a completely new discrete family of distributions that we have created. Our investigation into the relevant mathematical properties and characterizations of the system makes use of both analytical and numerical methods. We focus on a particular member of this family so that we can study its theoretical foundations as well as its graphical and numerical representations. This new model contains a few different hazard rate functions, some of which are referred to as "increasing constant", "decreasing-constant-increasing (U)", "constant", "U-constant", "decreasing", and "J-shape" In a similar vein, the model's probability mass function provides a variety of forms, all of which are helpful and practical. These forms include "asymmetric left skewed," "right skewed with wide peak," "right skewed," "bimodal," "symmetric," and "right skewed," amongst others. Each of these forms is valuable and applicable in their own way. These forms might be discovered in the probability mass function that the model generates. In this investigation, in addition to the Bayesian estimating technique under the traditional loss function of squared errors, we investigate and make use of a total of eight estimate strategies that are not founded on Bayesian theory (classical methods). Simulations employing the Markov Chain Monte-Carlo method are run for comparing the Bayesian way of estimation with the more traditional approach of estimating values. According to the findings that we've compiled, the estimation strategy that is referred to as maximum likelihood yields the most accurate results across the board and for all different types of sample sizes. In addition, we evaluate and contrast the various methods of estimation by making use of six distinct real dataset sets; this indicates the versatility of the unique model that we have developed.

Topp-Leone generalization of the Generalized Pareto distribution and its impact on Extreme value modelling

2024-12-16T00:24:34+05:00

Extreme Value theory (EVT) is a phenomenon used to model rare or extreme events and has been useful in well-known areas such as finance, economics, hydrology, insurance, etc. In this paper, we combine EVT and Bayesian statistics to estimate the extreme value index and other distribution parameters. EVT studies the behavior of the tails of the distribution, while Bayesian statistics allows us to incorporate prior knowledge of the parameters. The interdependence between these two statistical branches allows us to account for uncertainty in parameter and tail estimation. Block maxima and Peaks over Threshold are EVT divisions that are used to model observations. In this paper we use the Peaks over Threshold approach. The generalized Pareto distribution is a Peaks over Threshold distribution. Existing literature studied the generalizations and extensions of the generalized Pareto distribution. These extensions mostly focus on the positive domain of attraction. In this paper we contribute to the study of EVT by considering both the negative and positive domains of attraction. We consider the (Topp and Leone, 1955) generalization for the generalized Pareto distribution. We show, by means of a simulation study, that this distribution can effectively estimate the extreme value index and that it is less sensitive to threshold selection than the normal generalized Pareto distribution.

Estimating the Economic Burden of Family Caregivers of COVID-19 Survivors in Punjab-Pakistan

2024-12-05T17:19:47+05:00

The COVID-19 pandemic has significantly impacted healthcare systems and families worldwide, with family caregivers bearing a substantial burden. In Punjab, Pakistan, family caregivers of COVID-19 survivors face significant financial strain due to prolonged care requirements, medical expenses, and loss of income. This study aims to quantify the economic burden on these caregivers and identify socioeconomic factors contributing to financial strain for targeted support. Employing a cross-sectional design, the study surveyed 5,770 caregivers selected through convenience sampling using a self-constructed 27-item questionnaire with dichotomous responses. Data analysis included structural equation modeling, odds ratio calculations, and tree diagrams to evaluate the economic burden and identify contributing factors. The study found that 59.1% of the family caregivers were female, with a mean age of 45 years. A six-factor economic burden model was developed to quantify the financial strain on caregivers during the pandemic. Results indicated a higher burden on female caregivers over 45, married, unemployed, earning up to sixty thousand PKR, with a maximum secondary education, living in rural areas, in joint families, or away from families. Those performing household, medical, and personal tasks faced higher financial challenges, especially when caring for survivors hospitalized, in ICU, with long disease durations, permanent disabilities, or severe infections. The study highlights the substantial economic impact on family caregivers of COVID-19 survivors in Punjab, Pakistan, underscoring the urgency for governmental and community support to alleviate their financial strain.