Pakistan Journal of Statistics and Operation Research

On The Efficiency of Receiving a Stepwise Gaussian Random Disturbance With an Unknown Moment of Appearance and Central Frequency

2025-12-08T06:19:56+00:00

The synthesis of the computationally simple maximum likelihood algorithms for detecting and measuring the moment of appearance and the central frequency of a fast-fluctuating Gaussian random disturbance is carried out. Using the method of multiplicative and additive local Markov approximation of the decision-determining statistics or its increment, the closed analytical expressions are found for the false alarm and missing probabilities (the detection task), as well as for the conditional biases and variances of the desired estimates (the measurement task). By statistical simulation methods, it is established that the proposed detector and measurer are operable, and the analytical formulas describing their performance are in good agreement with the corresponding experimental data in a wide range of parameter values of the random process being analyzed.

The Burr Inverse Weibull Model for Risk Analysis Under US Social Security Administration Disability Data Using Peaks Over Random Threshold Method with A Case Study in KSA

2025-12-08T06:19:48+00:00

This study assesses and analyzes real disability insurance data to evaluate extreme risks using advanced statistical tools and metrics. The primary objective is to identify significant events or anomalies in the data and propose actionable strategies for managing financial risks associated with disability insurance claims. To achieve this, we utilize a range of indicators, including Value-at-Risk (VaR), Tail-VaR (TVaR), Tail-Mean-Variance (TMV), Tail-Variance (TV), Mean Excess Loss (MXL), Mean of Order P (MOO-P), Optimal Order of P (O-P), and Peaks Over a Random Threshold Value-at-Risk (PORT-VaR), are applied to identify and describe significant events or anomalies in the data. To address these risks effectively, the research explores the application of the Burr inverse Weibull (BIW) model, a well-regarded framework within extreme value theory (EVT). The study provides a structured approach for disability insurance institutions to better manage unexpected and potentially severe financial losses. Our dataset comprises n=2000 anonymized records from the Social Security Administration (SSA) disability insurance system. By analyzing the asymmetric, right-skewed nature of SSA disability insurance data through these advanced indicators, the research offers insights into the behavior of extreme events and long-tail distributions. Moreover, the percentage distribution of disability reasons in KSA for 2023 is considered. Based on this comprehensive risk analysis, practical recommendations are proposed.

E-Bayesian estimation and prediction of insurance premium in Poisson model

2025-12-09T06:20:15+00:00

Premium estimation and prediction are widely applied in insurance, healthcare, and finance to improve risk management, pricing accuracy, and customer personalization. They help insurers balance profitability with fairness, while giving customers more transparent and tailored options. In this paper, the E-Bayesian estimation of premium and predicting the number of claims is considered when the number of claims follows a Poisson distribution. The Escher premium principle is used to obtain the estimators and predictors. The Bayesian and E-Bayesian estimators of premium are derived under three densities for hyperparameters of prior distribution and compared by using a simulation study. A real data analysis is given to illustrate the results. The method of E-Bayesian estimation is extended to E-Bayesian predicting the number of claims. Performance of the proposed predictors are evaluated conducting a prequential analysis within a simulation.

The Beta-Weibull-X Family of Distributions with some Properties and Applications to Engineering and Health Data when X ∼ Rayleigh Distribution

2025-12-09T06:20:07+00:00

Generating new statistical distributions that provide sufficient characterization for real-life phenomena such as those in reliability engineering, meteorology, and the health sciences is an important area of concern for the researchers. Many complex real-life phenomena are yet to be optimally characterized by some of the existing methods and this study proposed the Beta Weibull-X (BWei-X) family. The Beta Weibull-Rayleigh (BWR), developed as a family member, has notable distributions in the literature as special cases, moments, and some basic statistical properties were investigated. The parameters of the distribution were estimated by the method of maximum likelihood estimation. Graphical reports show that the failure rates can be declining or increasing, J-shape, bathtub, and inverted bathtub shapes, making it an exciting tool in diverse areas of applications for modeling noisy phenomena with left-skewed, right-skewed, and approximately symmetric features. A systolic blood pressure and engineering dataset was applied to investigate the performance of the model, and the results from data analysis using the R-software justify the significance of the research

A Novel Generated G Family for Risk Analysis and Assessment under Different Non-Bayesian Methods: Properties, Characterizations and Applications to USA House Prices and UK Insurance Claims Data

2025-12-09T06:19:58+00:00

This study proposes a new and versatile family of continuous probability models known as the log-exponential generated (LEG) distributions, with particular emphasis on the log-exponential generated Weibull (LEGW) model as its prominent representative. By introducing an additional layer of parameterization, the family offers improved adaptability in shaping distributional forms, especially regarding skewness and heavy-tailed behavior. The LEGW formulation proves especially relevant for reliability data and for capturing rare but impactful events where asymmetry plays a major role. The work details the theoretical framework of the family through explicit expressions for its cumulative distribution function (CDF) and probability density function (PDF), alongside the corresponding hazard rate function (HRF). Several analytical characteristics are also investigated, including series representations and behavior in the extreme tail. To demonstrate practical value, the paper conducts risk evaluations employing sophisticated key risk indicators (KRIs) such as Value-at-Risk (VaR), Tail Value-at-Risk (TVaR), and tail mean-variance measure (TMVq) across multiple quantile levels. Parameter estimation is addressed using several techniques, including maximum likelihood estimation (MLE), the Cramér–von Mises approach (CVM), and the Anderson–Darling estimator (ADE), in addition to their right-tail adjusted (RTADE) and left-tail adjusted variants (LTADE) to better capture extreme behaviors. Comparative performance analyses are carried out using both controlled simulation scenarios and real data from the insurance and housing sectors to test robustness under heavy-tail conditions. The findings highlight the effectiveness of the LEGW model in applied risk assessment, supported by evidence from insurance claims and economic datasets.

Hybrid Approach Based on the CHAID Algorithm for Improving Classification Performance of Diabetes Data

2025-12-09T06:19:50+00:00

Diabetes, a chronic disease that is becoming more prevalent, presents increasing challenges, especially in low- and middle-income countries, where it is a growing burden. Egypt is the 9th most prevalent country for diabetes in the world, with estimated diabetes prevalence among adults at 15.2%, which raises urgent implications for early detection to limit complications including retinopathy, renal impairment and limb amputation. This study proposes a method to address classification of Type 2 diabetes (T2DM) through implementing and exploring the application of five machine learning algorithms: support vector machine (SVM), naïve Bayes (NB), K-Nearest Neighbor (KNN), Bayesian network (BNC) and stochastic gradient descent (SGD), along with CHAID algorithm to produce conditional segmentation variable to model non-linear interactions while improving expressivity of features used. CHAID analyses found that the best predictor of T2DM involved high levels of the hemoglobin A1c, and insulin resistance. The next best predictors were triglycerides and then followed by age, obesity, and blood pressure. Effects from the metabolic, cardiovascular, and lifestyle variables were small-to-moderate showing a significant amount of clustering. The hybrid model was developed as protection against overfitting, thus allowing robust and generalizable classification performance. The proposed hybrid models outperformed that of a single model. Specifically, SVM via CHAID and SGD via CHAID were able to obtain a perfect classification accuracy of 100% revealing the model's potential as a powerful tool for early detection and examination of risk of diabetes.

Empirical Performance of Nonparametric Regression with Heteroscedasticity

2025-12-09T06:19:41+00:00

Heteroscedasticity is a well-known violation of an assumption in parametric regression analysis. In such cases, to handle this problem, a generalized least squares method is used. In this article, we have manifested the robustness of nonparametric regression in the case of heteroscedastic errors. Nonparametric regression is a robust method that proceeds without requiring inflexible assumptions from the model. We empirically compared the performance of the generalized least squares method with multivariate nonparametric kernel regression. Multivariate nonparametric kernel regression is used with a Gaussian kernel and six bandwidths on China's per capita consumption expenditure. The performance of nonparametric regression with Bayesian bandwidth was found better on the basis of mean squared error. Simulation results are also presented, with their graphical representation, where nonparametric regression with different bandwidths at different heteroscedastic levels is observed, and we found that our proposed method performed best in both presence and absence of homoscedasticity.

Psychological Impact of COVID-19 on Families of Children with ASD and Typically Developing Children: A Case Study of Pakistan

2025-12-09T06:19:33+00:00

Children with Autism Spectrum Disorder (ASD) and their parents, being a vulnerable population, were expected to be highly affected by the pandemic and its containment response. This study aims to analyze and compare the impact of COVID-19 on behavioral and mental well-being of ASD and TD (typically developing) individuals and their parents/caregivers in Pakistan. A total of 51 primary data samples from both groups were collected from Rawalpindi and Islamabad using a comprehensively designed survey, consisting of 6 sections related to participants and children demographics, parental exposure to COVID-19, impact of COVID-19 lockdowns, behavioral problems and ASD support during lockdown, parental distress (estimated via DASS21) and 2 open response questions. The study found that ASD families reported increased difficulties and required more commitment than before in nearly all aspects of life as compared to the TD group. Additionally, ASD children showed more behavioral problems in terms of aggressive, repetitive, and transition activities during lockdowns than before. Moreover, comparison of machine learning models ranked 5 significant factors contributing in parental distress which include family income, severity of ASD symptoms, type of ASD therapy, parental exposure to COVID-19, and impact of lockdowns on daily routines. Majority of participants reported the need for financial support, awareness, and proper planning from the government during the pandemic. The findings of this study provide evidence which highlights the necessity of collaborative interventions from both healthcare professionals and government authorities aimed at assisting parents in reducing distress and developing effective coping strategies, especially for individuals with ASD.

Modeling Anemia Dynamics Among Women of Reproductive Age Using Topp-Leone Exponentiated Generalized Exponential (TLEG-E) Distribution

2025-12-09T06:19:25+00:00

Anemia continues to be a significant public health issue, particularly impacting women aged 15 to 49. To improve the modeling of anemia prevalence, this study introduces the proposed distribution, offering enhanced flexibility for capturing skewed and heavy-tailed data structures. The model is applied to country-level data from Pakistan, with global trends from World Bank data serving as a comparative backdrop. The TLEG-E distribution demonstrates superior fit and interpretability compared to traditional models, effectively highlighting a declining trend in anemia among Pakistani women, potentially reflecting the impact of health policy reforms and improved nutritional access. While global prevalence varies widely across regions, the emphasis here lies in the methodological advancement and its utility for health data modeling. The proposed framework provides a robust statistical foundation for tracking anemia trends and can support more targeted policy interventions. Its adaptability makes it suitable for broader applications in epidemiological research, enabling more precise assessments of public health initiatives across diverse populations.

L−moment Based Regional Frequency Analysis of Annual Maximum Relative Humidity Across Pakistan

2025-12-09T06:19:16+00:00

Climate change has significantly impacted regional weather patterns in Pakistan, leading to an increase in the frequency and intensity of extreme weather events, such as heatwaves, droughts, and floods. This study aimed to investigate the regional frequency analysis of extreme relative humidity across Pakistan, identify potential geographically related trends, and estimate possible frequencies associated with extreme relative humidity in distinct regions. The data were collected from 24 meteorological stations. Discordance measures were used to evaluate distinct sites in the region, with GAWADAR and KARACHI exhibiting the highest discordance values. The study region was divided into three homogeneous regions based on geographic and statistical measures to verify the heterogeneity statistics. The L−moment ratio diagram and goodness−of−fit statistic identified suitable distributions for each region, with the generalized extreme value and Pearson type III distributions proving to be most effective in the first region. The second region was best represented by the generalized extreme value and Weibull distributions, whereas the third region was most accurately characterized by the generalized log-normal and polynomial density−quantile III distributions. These results offer valuable insights into the spatial patterns of humidity extremes, potentially supporting efforts in climate change adaptation and flood risk management.

Characterizations of the Recently Introduced Discrete Distributions II

2025-12-09T06:19:08+00:00

Certain characterizations of 19 recently introduced discrete distributions are presented in three directions: (i) based on an appropriate function of the random variable; (ii) in terms of the reverse hazard function and (iii) in terms of the hazard function. This is a continuation of our previous work with the same title.

The Negative Binomial-Bilal Distribution: Regression Model and Applications to Health Care Data

2025-12-09T06:18:59+00:00

In health care research, overdispersion often arises in count data. The Poisson distribution is a traditional distribution for modeling count data. However, it cannot handle overdispersed count data. This article introduces a new count distribution for overdispersed data. Statistical properties and a multivariate version of the proposed distribution are derived. Two parameter estimation methods are discussed by the maximum likelihood method and Bayesian approach. A simulation study is conducted to assess the performance of the estimators. A regression model based on the proposed distribution is constructed. Finally, two health care applications are analyzed to show the potential of the proposed distribution and its associated regression model.

Conditional quantile estimation under LTRC model with functional regressors

2025-12-09T06:18:51+00:00

In this paper, we study the kernel estimator of the conditional quantile when the interest variable Y is subject to left truncation and right censoring (LTRC) with a functional covariate variable X. We establish the consistency properties with rate of this estimator when the observations are independent and identically distributed. Simulations are made to illustrate the good behavior of our estimator.

Comparison of Metaheuristic Algorithms for Maximum Likelihood Estimation of the Transmuted Weibull Distribution with Applications

2025-12-09T06:18:43+00:00

The Weibull distribution, widely utilized due to its flexibility, often requires generalization to improve its fit to real-world data. The Transmuted Weibull Distribution offers enhanced flexibility by incorporating a transmutation parameter. Metaheuristic algorithms have emerged as robust tools for parameter estimation, particularly for probability distributions with complex likelihood functions. This study compares the performance of four metaheuristic algorithms: Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), and Artificial Bee Colony (ABC) against the traditional Newton-Raphson (NR) algorithm for estimating parameters of the Transmuted Weibull Distribution (TWD). Extensive Monte Carlo simulations evaluated the algorithms' efficiencies using metrics like log-likelihood values, bias, mean squared error (MSE), and deficiency. Additionally, the methods are applied to real-world datasets to compare their practical utility. Both simulation and real data application results revealed that metaheuristic algorithms outperformed traditional Newton-Raphson (NR) optimization.