Pakistan Journal of Statistics and Operation Research

A comparison of the discrimination performance of lasso and maximum likelihood estimation in logistic regression models

2026-09-22T11:49:21+00:00

Logistic regression is widely used in many areas of knowledge. Several works compare the performance of lasso and maximum likelihood estimation in logistic regression. However, part of these works do not perform simulation studies and the remaining ones do not consider scenarios in which the ratio of the number of covariates to sample size is high. In this work, we compare the discrimination performance of lasso and maximum likelihood estimation in logistic regression using simulation studies and applications. Variable selection is done both by lasso and by stepwise when maximum likelihood estimation is used. We consider a wide range of values for the ratio of the number of covariates to sample size. The main conclusion of the work is that lasso has a better discrimination performance than maximum likelihood estimation when the ratio of the number of covariates to sample size is high.

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

2026-09-22T15:39:09+00:00

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

Item response model proposal under a uniform latent variable assumption: Application to school bullying data

2026-09-22T11:48:15+00:00

School bullying victimization is a variable that cannot be directly measured. Taking into account that this variable has a lower bound given by the absence of bullying victimization, we propose the use of Item Response Theory (IRT) logistic models, where the latent parameter ranges from $0$ to a positive real number $R$, adequately defining the IRT parameters and also including an empirical anchor estimation procedure. As academic abilities and school bullying victimization can be explained by associated factors such as habits, sex, socioeconomic level and education level of parents, IRT regression models are proposed to be able to perform joint inferences about individual and school characteristic effects.

Almost sure convergence with rate of a robust regression estimator for twice-censored data

2026-09-22T11:48:14+00:00

In this paper, we propose a new kernel M-estimator of the regression function using nonparametric methods for twice-censored data. The almost sure (a.s.) convergence with rate over a compact set of the estimator is established under appropriate conditions using an unbounded score function. As a by-product, we build a Nadaraya-Watson-type estimator in case of the twice-censoring and derive its strong uniform consistency with rate. Furthermore, knowing that the choice of the smoothing parameter is a difficult and important question, and based on cross-validation ideas, we construct some data-driven criterion for choosing a reasonable bandwidth. In the presence of censoring and/or outliers, a simulation study is carried out to illustrate the finite-sample behavior of the proposed estimator and to evaluate the effectiveness of the proposed cross-validation criterion through comparisons with the classical cross-validation criterion. Numerical comparisons with classical estimators are also presented. Finally, a real-data application is provided to demonstrate the practical value of the proposed estimator.

A New Mixed Distribution with Properties, Applications and Hydrological Engineering Risk Analysis under the Flood Peaks of the Canadian Wheaton River

2026-09-22T11:49:08+00:00

This article introduces the mixed Gamma Lindley (GL) distribution, combining Lindley’s failure-time modeling with Gamma’s heavy-tailed flexibility via a novel mixing method. We establish its corrected mathematical foundation, proving three key theoretical results: a Modality Theorem governing density shape, Mean Residual Life convergence to a finite bound, and classification within the Gumbel maximum domain of attraction. Global identifiability ensures consistent Maximum Likelihood Estimation. Applied to Canadian Wheaton River flood peaks (n=72), GL outperforms ten competitive models. Comprehensive risk analysis using Value-at-Risk (VaR), Tail-VaR (T-VaR), Tail Variance (TV_c), Tail Mean Variance (TMV_c), Mean of Order-P (MOO-P), and Peaks-Over-Random-Threshold VaR (PORT-VaR) confirms heavy-tailed behavior (Hill index ≈ 0.18) and provides coherent, actionable engineering thresholds for flood infrastructure design under climate uncertainty. This work bridges advanced statistical theory with practical hydrological engineering, offering a robust tool for managing extreme environmental risks under climate uncertainty.

A Wrapped New Polynomial One-Parameter Distribution with Applications to Ecological and Wind Direction Data

2026-09-22T15:39:08+00:00

Observations recorded as angles or directions appear across a wide range of scientific fields, from ecology and en- vironmental to atmospheric science and materials research. Because such circular data follow a periodic structure, standard statistical tools fail to capture their geometry, and purpose-built circular distributions are required. This study proposes the Wrapped New Polynomial Single-Parameter (WNPS) distribution, a novel one-parameter circular model constructed by wrapping the New Polynomial Single-Parameter distribution onto the unit circle. A systematic study of its mathematical structure gives the closed-form expressions for the survival function, hazard rate, modality condi- tions, characteristic function, trigonometric moments,invariance behavior and Renyi entropy measures. Also, various ´ characterizations of the proposed distribution are presented. Parameter estimation is addressed through ten frequen- tist procedures alongside a Bayesian framework employing five loss functions from both symmetric and asymmetric penalization. Monte Carlo simulation experiment compares the finite-sample behavior of all estimators across vary- ing sample sizes and parameter configurations. The usefulness of the WNPS distribution in practice is illustrated via two real-life datasets consisting of angular measurements from an ecological study and another on wind direction. Goodness-of-fit comparisons against the wrapped Lindley, wrapped modified Lindley, wrapped XLindley, and related competitors confirm the WNPS distribution as a competitive and parsimonious choice for circular data modeling.

Theory to Prediction: Hybrid Models for Binary Endogenous Variables in PLS-SEM Using Supervised Machine Learning

2026-09-22T11:48:11+00:00

Theoretical explanation and out-of-sample prediction are both important in applied structural modeling. Partial least squares structural equation modeling (PLS-SEM) estimates relationships among latent-variable scores, but its ordinary least squares structural regressions are not directly suited to a binary endogenous outcome. We evaluate a hybrid workflow in which PLS-SEM latent scores are supplied to logistic regression (LR), linear and radial-kernel support vector machines (SVMs), and random forests (RFs). Eight open-source datasets were analyzed after the focal continuous endogenous score was dichotomized at the mean or median. Models were compared using 5-, 7-, and 10-fold cross-validation and 90:10, 80:20, and 70:30 train-test splits. Performance was assessed with sensitivity, specificity, accuracy, area under the receiver operating characteristic curve, Cohen's kappa, and the Matthews correlation coefficient. RF most frequently produced the highest cross-validation values, whereas held-out test performance varied across datasets and split ratios. Radial-kernel SVM was competitive in several datasets. The results show that supervised classifiers can extend a PLS-SEM workflow for constructed binary outcomes, but no classifier was uniformly superior. Model selection should therefore rely on prespecified tuning and rigorous out-of-sample validation.

A New Light-tailed Weighted Model for Reliability Risk Analysis: Theory, Properties and Case Study

2026-09-22T15:39:06+00:00

This paper introduces the new weighted distribution, an exponential‑type, flexible, right‑skewed, and provably light‑tailed probability model for reliability risk analysis. It is motivated by the fact that failure‑time data are strongly right‑skewed in the body yet exhibit exponential‑type upper tails, so heavy‑tailed models inflate extreme quantiles while simple laws lack body flexibility. It is further motivated by the absence of any weighted extension, unified mathematical theory, or rigorous tail analysis for the Bilal baseline, i.e. the median of three exponential lifetimes (a two‑out‑of‑three system). A third motivation is the literature’s routine advertisement of “heavy‑tailed” constructions without extreme‑value validation, which this paper counters with an honest, mathematically verified tail classification. A consolidated tail theory establishes the Gumbel extreme‑value behavior of the model and explains the drifting, non‑stabilizing patterns of the Hill estimator. A comprehensive risk analysis using Value‑at‑Risk (VaR), Tail Value‑at‑Risk (T‑VaR), Tail Variance (TVc), Tail Mean Variance (TMVc), Peaks Over a Random VaR (PORT‑VaR), and Mean of Order P ( ), validated by tail‑index and extreme value theory (EVT) diagnostics. The results yield a confidence‑level planning ladder for routine maintenance, warranty limits, and redundancy against catastrophic failures, offering engineers a verified light‑tailed alternative to routinely advertised heavy‑tailed constructions.