Pakistan Journal of Statistics and Operation Research

The Flexible Nadarajah–Haghighi Distribution: Properties, Inference, and Applications

Ahmed Z. Afify, Mohammed Alqawba, Hadeel AlQadi, Ekramy A. Hussein — Tue, 02 Sep 2025 16:39:30 +0000

This article explores a flexible extension of the Nadarajah–Haghighi (NH) model, referred to as the odd inverse Pareto Nadarajah–Haghighi (OIPNH) distribution. We derive the mathematical properties of the probability density function of the OIPNH distribution, which exhibits a variety of behavior shapes, including decreasing, increasing, J-shaped, reversed J-shaped, bathtub, upside-down bathtub, and decreasing-increasing-decreasing hazard rates. Additionally, the distribution can display right-skewed, symmetrical, and concave-down densities. The parameters of the OIPNH distribution are examined using eight classical estimation approaches. We present extensive simulation results to evaluate the performance of these methods for both small and large sample sizes. Furthermore, we analyze three real-life datasets from engineering, medicine and agricultural sciences, demonstrating the flexibility of the OIPNH distribution compared to existing NH distributions.

Point and Interval Estimation Techniques for the 2S-Lindley Distribution Under Type-II Censoring

Joul Kanjo, A. Asgharzadeh, M.Z. Raqab — Tue, 02 Sep 2025 16:41:43 +0000

Recently, Chesneau et al. (2020) introduced a new distribution called the 2S-Lindley distribution, which is based on the sum of two independent Lindley random variables with the same parameter. In this paper, we employ different methods to estimate the unknown parameter of the 2S-Lindley distribution using type-II censored samples. These methods include the moment-based method, maximum likelihood estimation, the bootstrap method, and Bayesian inference. We provide both point and interval estimates for the parameter using each method. We also analyze a real data set that follows the 2S-Lindley distribution, computing and comparing various estimates. Finally, we conduct a simulation study to illustrate and compare the effectiveness of these methods.

A New Alpha Skew Normal Distribution and its Real Life Applications

Jondeep Das, Partha Jyoti Hazarika, Dimpal Pathak, G.G. Hamedani — Tue, 02 Sep 2025 16:45:05 +0000

This paper introduces a novel continuous probability distribution which extends the alpha skew normal
distribution of Elal-Olivero (2010). The newy introduced distribution is designed to model data exhibiting
tri-modal behavior. A comprehensive overview of the novel distribution is provided including various key
statistical properties like moments, moment generating function (mgf), characterization results etc. Besides,
to assess the performance of the derived parameters, a simulation study is conducted using Metropolis-
Hastings method. Furthermore, an investigation regarding the flexibility and applicability of the distribution
is conducted by analyzing two real life datasets. During applications it is found that for the datasets
considered, the newly proposed distribution outperforms the existing models in terms of some model selection
criterion like AIC and BIC, highlighting its potential in practical applications. Finally, likelihood ratio (LR)
test is conducted to differentiate between various nested models

A New Version of the Compound Quasi-Lomax Model: Properties, Characterizations and Risk Analysis under the U.K. Motor Insurance Claims Data

Tue, 02 Sep 2025 16:47:17 +0000

This paper introduces a new lifetime distribution, the Compound Quasi-Lomax (CQLx) model, designed to enhance the modeling of heavy-tailed data in actuarial and financial risk analysis. The CQLx distribution is developed through a novel extension of the Lomax family, offering increased flexibility in capturing extreme values and complex data behaviors. Key mathematical properties are derived. Characterization of the model is achieved via truncated moments and the reverse hazard function. Several estimation methods are employed including the Maximum Likelihood Estimation (MLE), Cramér–von Mises (CVM), Anderson–Darling Estimation (ADE), Right-Tail Anderson-Darling Estimation (RTADE), and Left-Tail Anderson-Darling Estimation (LTADE). A comprehensive simulation study evaluates the performance of these methods in terms of bias and root mean square error (RMSE) across various sample sizes. Risk measures such as Value-at-Risk (VaR), Tail Value-at-Risk (TVaR), Tail Variance (TV), Tail Mean Variance (TMV), and Expected Loss (EL) are computed under artificial and real financial insurance claims data. The results demonstrate that MLE generally provides the most accurate and stable estimates, particularly for larger samples, while CVM and ADE tend to overestimate risk, especially at higher quantiles. The CQLx model shows superior performance in fitting extreme claim-size data, making it a robust tool for risk management.

Enhancing Food Security Analysis in South Sulawesi Using Robust Mixed Geographically and Temporally Weighted Regression with M-Estimator

Nur Aulia, Siswanto Siswanto — Tue, 02 Sep 2025 16:48:40 +0000

MGTWR (Mixed Geographically and Temporally Weighted Regression) combines a global linear regression model with GTWR by incorporating spatial and temporal dimensions. However, it remains sensitive to outliers, which can reduce accuracy. To address this limitation, a robust regression approach with the M-Estimator was applied to model the food security index in South Sulawesi Province from 2018 to 2022. The resulting Robust MGTWR (RMGTWR) model demonstrated improved performance, with a lower AIC ( ) and a high explanatory power ( ). Key factors influencing food security include the ratio of normative consumption per capita to net production, the percentage of households with a proportion of expenditure on food more significant than 65% of total spending, the percentage of households without access to electricity, the percentage of households without access to clean water, and the percentage of stunting toddlers. These findings highlight the effectiveness of RMGTWR with M-Estimator in addressing data irregularities and provide valuable insights for policymakers in designing targeted strategies to strengthen food security in South Sulawesi Province.

A New Odd-Burr Pareto Distribution: Statistical Properties, Estimation, and Applications

Yeliz MERT KANTAR, İbrahim ARIK — Tue, 02 Sep 2025 16:55:53 +0000

This study introduces the Odd-Burr Pareto (OBu-P) distribution as a novel and flexible model, which is developed by combining the Burr and Pareto distributions using the T-X generator approach (Alizadeh et al. 2017). The OBu-P distribution can be used for modelling complex phenomenon characterized by heavy tails.

The paper provides the OBu-P distribution’s statistical properties, including its moments, incomplete moments, quantile functions, and limiting behaviours, as well as its generating functions and order statistics. Maximum likelihood estimation is applied to facilitate efficient parameter estimation of the OBu-P. The flexibility of distribution is shown in a real-life example versus its alternatives.

A Generalized Exponential Regression Model for Predicting High-Grade Glioma Growth in Paediatric Patients

Md Shohel Rana, Mohana Sundaram Muthuvalu — Tue, 02 Sep 2025 17:01:16 +0000

High-grade gliomas (HGG) are invasive brain tumours characterized by abnormal growth patterns and poor prognoses. Aware and precise prediction of tumour growth helps improve both treatment protocols and patient medical outcome. The quick replicating and diverse nature of HGGs in children makes their predictive progression highly difficult to determine. This research utilized a generalized exponential regression approach to study glioma progression in children's brains with predicted accuracy reaching 73.68% for all tumours but elevating to 77.7% for small tumours under 100 mm³. Statistical analyses revealed significant negative correlations between tumour growth and tumour size, along with pre-radiotherapy performance status (PS Before RT), as determined by Kendall’s Tau test. The Mann-Whitney U and Kruskal-Wallis H tests were employed for bivariate analysis of categorical data, demonstrating a significant association (p < .05) among tumour growth rate, the extent of surgical resection, and survival status. The child's age, the occurrence of headaches, and edema were independently associated with the progression of tumour growth. These findings enhance the understanding of paediatric HGGs development, facilitating more accurate prognostic evaluations and improving personalized treatment strategies.

A Flexible Discrete Rayleigh-G Family for Engineering and Reliability Modeling: Properties, Characterizations, Bayesian and Non-Bayesian Inference

Tue, 02 Sep 2025 17:09:55 +0000

A novel flexible probability tool for modeling extreme and zero-inflated count data with various hazard rate shapes is introduced in this work. Numerous pertinent statistical and mathematical features are developed and examined. Some important mathematical features are obtained, including, ordinary moments, central moment, dispersion index, L-moments, cumulant generating function and moment generating function. A specific example is investigated numerically and visually examined. The new class of hazard rate function offers a broad range of flexibility, including "monotonically decreasing," "upside down," "monotonically increasing," "constant," "decreasing-constant," and "decreasing-constant-increasing (U-hazard rate function)". Furthermore, the new mass function accommodates many useful forms in the field of modeling, including the "right skewed with one peak", "right skewed with two peaks (right skewed and bimodal)", "symmetric mass function" "left skewed with one peak". The conditional expectation of a certain function of the random variable as well as the hazard function are used to provide relevant characterization results. For the estimation process, evaluating and comparing inferential effectiveness, Bayesian and non-Bayesian estimation approaches are taken into consideration. We propose and explain the Bayesian estimation method for the squared error loss function. For comparing non-Bayesian versus Bayesian estimates, Markov chain Monte Carlo simulation experiments are carried out using the Metropolis Hastings algorithm and the Gibbs sampler. The Bayesian and non-Bayesian approaches are compared using four real-life applications of count data sets. By using four additional real count data applications, the significance and adaptability of the new discrete class are demonstrated.