Pakistan Journal of Statistics and Operation Research
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A New Pareto Model: Risk Application, Reliability MOOP and PORT Value-at-Risk Analysis
No full textThe paper introduces a new reliability Burr Pareto type-II model, showcasing its versatility and effectiveness in engineering applications, particularly in analyzing the failure and service times of aircraft windshields. The BUPII model's application in failure analysis offers insights into the probabilistic behavior of windshield failures, aiding in risk prediction and management. Similarly, its extension to service time analysis demonstrates its utility in optimizing maintenance schedules and operational efficiency. Moreover, the paper conducts a rigorous mean-of-order P analysis under both failure and service time datasets, validating the new model's reliability assessment capabilities. Furthermore, employing the peaks over random threshold value at risk analysis highlights the model's practical relevance in quantifying financial risks associated with extreme events. Overall, the novel probability distribution emerges as a valuable tool for engineers and researchers involved in reliability and risk analysis, promising advancements in understanding and managing the reliability of engineering systems. Future research could explore broader applications and refined methodologies to further enhance predictive capabilities and decision-making support
Statistical Inference on Process Capability Index Cpyk for Inverse Rayleigh Distribution under Progressive Censoring
No full textIn quality engineering, process capability indexes are used to determine the capability of a process. The well-known of the process capability indexes are Cp, Cpk, Cpm, and Cpmk. These indexes assume the normality of the product lifetime. \citet{maiti2010generalizing} suggested a Cpyk as a generalized process capability index without distributional assumption. In this paper, the maximum likelihood and Bayesian inference on the Cpyk are studied under progressive censoring when the underlying distribution is inverse Rayleigh distribution. Furthermore, Bayesian credible and highest posterior density intervals are discussed with the MCMC procedure. Several types of bootsrap confidence intervals are also considered. A Monte Carlo simulation is conducted in terms of the coverage probabilities and mean lengths of the proposed intervals. An illustrative example is presented to close the paper.
 
A new three-parameter discrete distribution to model over-dispersed count data
No full textA novel discrete distribution with three parameters, referred to as the PoiNB distribution, is formulated through the convolution of a Poisson variable and an independently distributed negative binomial random variable. This distribution generalizes some well known count distributions and can be used for modelling over-dispersed as well as equi-dispersed count data. Numerous essential statistical properties of this proposed count model are thoroughly examined. Characterizations of this distribution in terms of conditional expectation and reverse hazard rate function are studied in detail. The estimation of the unknown parameters of this proposed distribution is carried out using the maximum likelihood estimation approach. Additionally, we introduce a count regression model based on the PoiNB distribution through the generalized linear model approach. Through two real-life modelling applications, it is demonstrated that the suggested distribution may offer practical utility for practitioners in modelling over-dispersed count data
Estimating the Economic Burden of Family Caregivers of COVID-19 Survivors in Punjab-Pakistan
No full textThe 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
A Unified Family for Generating Probabilistic Models: Properties, Bayesian and Non-Bayesian Inference with Real-Data Applications
No full textThis 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
Nash equilibrium selection using a hybrid two-player static game with trade-off ranking method
No full textThe paper aims to suggest the ranking of an optimal solution when there exists more than one Nash equilibrium in the game theory solution concept. Many studies tend to merge the game theory with the multi criteria decision-making (MCDM) method to cater the real-situation problems. In the paper, a novel hybrid non-cooperative static game in game theory is combines with the trade-off ranking (TOR) method in MCDM. The proposed hybrid method is used to rank multiple Nash equilibria concerning some criteria. The methodology for both static game and TOR method are explained in the paper. The game theory model used is a two-player non-constant-sum static game. The proposed methodology is tested using international cooperation in Iran. The result suggests the ranking of the combined strategies using the proposed method
Process Capability Analysis for Simple Linear Profiles in Multistage Processes
No full textWhen a process is statistically under control, one may be interested in assessing the process performance based on the specification limits provided by the customer. This evaluation is referred to as process capability analysis. Manufacturing operations are often involved with multistage processes, in which the output of a stage is the input of its subsequent stage. This property is known as the cascade property. Existing methods in capability analysis studies are not applicable when a process or product is represented by profiles. This study presents a method to conduct process capability analysis in a multistage process when quality of a product or process is characterized by a simple linear profile. The performance of the proposed method for a two-stage process is evaluated by numerical simulation using an example from the literature. The results indicate that the proposed method eliminates the effect of the cascade property for different shift sizes and autocorrelations
On estimation and monitoring of population mean using systematic sampling under an exponentially weighted moving average scheme
No full textThe present study proposes a generalized ratio estimator for estimating the population mean under the systematic sampling technique by considering auxiliary information and auxiliary attribute. Its bias and Mean Square Error (MSE) expressions have been derived. Mathematical comparisons are made by comparing the proposed estimator with the usual mean estimator, Swain (1964) estimator, Bhal and Tuteja (1991) estimator, and Singh and Singh (1998) estimator, and it is shown that the proposed estimator is more efficient than the previous estimators. A numerical comparison is also performed to demonstrate the superiority of the proposed estimator over the traditional estimators. The technique of ratio estimators based on systematic sampling is used to design an Exponentially Weighted Moving Average (EWMA) control chart. The Control chart is a significant industrial tool for monitoring the process mean. To evaluate performance efficiency Average run lengths (ARL) are obtained in this study. The proposed charts are compared based on out-of-control ARLs. A chart based on the proposed estimator is superior as it detects the shifts earlier than charts based on existing estimators. Empirical work is done to support the study. The suggested efficiency is further addressed utilizing real-life examples and simulations using R-Studio
A Novel Reciprocal-Weibull Model for Extreme Reliability Data: Statistical Properties, Reliability Applications, Reliability PORT-VaR and Mean of Order P Risk Analysis
No full textPeaks 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
A Novel Robust Class of Estimators for Estimation of Finite Population Mean: A Simulation Study
No full textIn the existing survey sampling literature, the ratio-type estimators are an obvious choice to estimate the finite population mean when auxiliary information related to the study variable is readily available. Typically, auxiliary information is incorporated into ratio-type estimators by using conventional measures such as mean, range, coefficient of kurtosis, coefficient of skewness and coefficient of correlation, etc. which are less efficient when extreme observation are present in the data. This study provides a remedy and enhances the efficiency of the ratio-type estimators of population mean in the presence of extreme observations by proposing dual auxiliary variables based exponential-cum-ratio class of estimators which integrates both conventional and non-conventional measures under simple random sampling without replacement. The expression of the mean squared error and theoretical efficiency conditions for proposed class of estimators have been obtained for comparison purposes. A simulation study was carried out based on contaminated normal distribution and the robustness of the proposed estimators has been assessed in the presence of extreme observations. For practical implementation, six real data sets have been used to compare the performance of the proposed estimators with competing estimators to support the theoretical results. The theoretical and empirical results suggest that the proposed estimators are more precise than usual mean as well as existing estimators’ ratio-type considered in this study