Pakistan Journal of Statistics and Operation Research

A Novel Insurance Claims (Revenues) Xgamma Extension: Distributional Risk Analysis Utilizing Left-Skewed Insurance Claims and Right-Skewed Reinsurance Revenues Data with Financial PORT-VaR Analysis

Haitham Yousof — 2025-06-03

The continuous probability distributions can be successfully utilized to characterize and evaluate the risk exposure in applied actuarial analysis. Actuaries often prefer to convey the level of exposure to a certain hazard using merely a numerical value, or at the very least, a small number of numbers. In this paper, a new applied probability model was presented and used to model six different sets of data. About estimating the risks that insurance companies are exposed to and the revenues of the reinsurance process, we have analyzed and studied data on insurance claims and data on reinsurance revenues as an actuarial example. These actuarial risk exposure functions, sometimes referred to as main risk actuarial indicators, are unquestionably a result of a particular model that can be explained. Five crucial actuarial indicators are used in this study to identify the risk exposure in insurance claims and reinsurance revenues. The parameters are estimated using techniques like the maximum product spacing, maximum-likelihood, and least square estimation. Monte Carlo simulation research is conducted under a specific set of conditions and controls. Additionally, five actuarial risk indicators including the value-at-risk, tail-variance, tail value-at-risk, tail mean-variance, and mean of the excess loss function, were utilized to explain the risk exposure in the context of data on insurance claims and reinsurance revenue. The peak over a random threshold value-at-risk (PORT-VaR) approach and value-at-risk estimate are taken into account and contrasted for detecting the extreme financial insurance peaks.

New highly accurate improvements for single-term approximations of the standard normal distribution function

Mohammed Obeidat — 2025-06-03

This paper proposed new, highly accurate, single-term, and explicitly invertible approximations for the standard normal distribution function and its related functions, such as the error function and the quantile function. The proposed approximations are built based on some existing approximations, however, the proposed ones are much more accurate. The accuracy of the proposed approximations is measured via maximum absolute error and mean absolute error. Some of the proposed approximations are at least five times more accurate than the original ones and two of them have maximum absolute error lower than 1.8×10^-4, which is quite sufficient for most of real-world applications. Two real applications are studied to show the applicability of the proposed improvements. These applications showed the superiority of one of the proposed approximations over some of the available single-term approximations even though the latter have smaller maximum absolute error.

Predictive Accuracy of Logistic Regression and Support Vector Machine for Short Interpregnancy Interval

Asif Hanif — 2025-06-03

Support vector machine (SVM) is considered a robust machine learning (ML) algorithm. In contrast, Logistic regression (LR) is the most preferred statistical model especially in healthcare and medical field due to its interpretability and mathematical foundations. Considering the competitive characteristics of these models, the predictive and discriminative strength of these models have been tested in this study. Short interpregnancy interval (SIPI) is a global public health issue and is associated with several feto-maternal complications. This study aims to identify the risk factors of SIPI and compare the predictive accuracy of LR vs SVM. Further, feature importance of both models will also be computed and compared. This study was conducted on 528 Pakistani pregnant females and their status of SIPI was predicted through number of risk factors. Various evaluation matrices have been computed to assess the superiority of model. Results have shown that the overall accuracy for LR was 83.14, while Sensitivity, Specificity, PPV, and NPV were 81.6%, 85.23%, 84.58% and 81.82%, respectively. The discriminating strength of this model is 92.1% and examined through receiver operating characteristic (ROC) curve. SVM yielded 94.70% accuracy, with Sensitivity, Specificity, PPV, and NPV as 95.08%, 94.32%, 94.36% and 95.04%, respectively. Further, ROC value was 98.83%. These findings suggests that SVM is better algorithm in predicting SIPI. All measures of predictive analysis as well as model fit indices were better in SVM. Hence, SVM is a comprehensive, interactive, flexible and accurate ML tool that can be used for better predictions of risk factors of SIPI compared to LR. Further, this ML algorithm is free from certain statistical assumptions like linearity of logits, model specification and weak multicollinearity as required in LR models.

A New Bivariate Exponentiated Family of Distributions: Properties and Applications

Saman Hanif Shahbaz — 2025-06-03

The bivariate distributions are useful for the joint modeling of two random variables. In this paper, we have presented a bivariate version of the exponentiated family of distributions. Some desirable properties of the proposed bivariate family of distributions have been explored. These include the conditional distributions, the joint and conditional moments, dependence measures, reliability analysis, and maximum likelihood estimation of the parameters. A specific member of the proposed family has been explored for the power function baseline distribution giving rise to the bivariate exponentiated power function distribution. Some properties of the derived bivariate exponentiated power function distribution have been explored. The derived bivariate exponentiated power function distribution is fitted on some real data sets to see its suitability. It is found that the derived bivariate exponentiated power function distribution performs better than the competing distributions for modeling of the used data.

New highly efficient one and two-stage ranked set sampling variations

Mohammed Obeidat — 2025-06-05

In this paper, we proposed highly efficient ranked set sampling schemes to estimate the population mean. First, we proposed a new single-stage sampling scheme which we called new neoteric ranked set sampling. Second, we proposed a two-stage methods based on the systematic ranked set sampling and the new neoteric ranked set sampling. The performance of the proposed methods is compared with that of competitive two-stage methods through a Monte Carlo simulation study using various popular symmetric and asymmetric statistical distributions. The results show that the newly proposed methods are more efficient in estimating the population mean than the existing methods. The proposed methods are illustrated on data of the diameter and height of pine trees.

A New Model for Reliability Value-at-Risk Assessments with Applications, Different Methods for Estimation, Non-parametric Hill Estimator and PORT-VaRq Analysis

Mohamed Ibrahim — 2025-06-05

This paper introduces a new extension of the exponential distribution tailored for enhanced reliability and risk analysis. We incorporate several insurance risk indicators like the value-at-risk, tail mean-variance, tail value-at-risk, tail variance, and maximum excess loss to significantly refine reliability risk assessments. These indicators offer vital insights into the financial consequences of extreme risk events and potential for substantial losses. To assess these risk indicators, we explore various non-Bayesian estimation techniques, including maximum likelihood estimation, ordinary least squares estimation, Anderson-Darling estimation, right tail Anderson-Darling estimation, and left tail Anderson-Darling estimation of the second order. Our approach involves a comprehensive simulation study with varying sample sizes, followed by empirical risk analysis using these methods. We also evaluate the applicability of the new model on two real reliability data sets. Finally, we apply the risk indicators including the value-at-risk (VaRq), tail mean-variance (TMVq), tail value-at-risk (TVaRq), tail variance (TVq) and maximum excess loss (MELq) to analyze reliability risk using failure (relief) and survival data. Finally the peaks over a random threshold value-at-risk (PORT-VaRq) analysis under the failure and survival data is presented.

The New Topp-Leone-Heavy-Tailed Type II Exponentiated Half Logistic-G Family of Distributions: Properties, Actuarial Measures, with Applications to Censored Data

Wilbert Nkomo — 2025-06-05

The Topp-Leone heavy-tailed type II exponentiated half logistic-G (TL-HT-TIIEHL-G) is the newly proposed family
of distributions (FoDs) introduced in this research. The study thoroughly investigates the statistical properties of
this FoDs, as well as its relevance in actuarial risk assessment. The estimation of the unknown model parameters is done using the method of maximum likelihood estimation, and the consistency of these estimates is assessed through the implementation of Monte Carlo simulations. Additionally, numerical simulations are conducted to analyze the risk measures associated with the TL-HT-TIIEHL-G FoDs. The Topp-Leone heavy-tailed type II exponentiated half logistic-Weibull (TL-HT-TIIEHL-W) distribution, a particular case of the TL-HT-TIIEHL-G FoDs is compared with other contending distributions including heavy-tailed distributions to evaluate its performance. The model’s capacity, adaptability, and practicality are convincingly showcased through its application to real data.

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

G. G. Hamedani — 2025-06-05

This paper is a continuation of our previous work with the same title, which deals with various characterizations of certain univariate continuous distributions proposed in (2023-2024) after the publication of our first paper in (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.