https://jsm.yazd.ac.ir/ Journal of Statistical Modelling: Theory and Applications en daily 1 Fri, 01 Aug 2025 00:00:00 +0430 Fri, 01 Aug 2025 00:00:00 +0430 https://jsm.yazd.ac.ir/article_4109.html The probability density function is a fundamental concept in statistics‎. ‎This study focuses on estimating the probability density function using nonparametric kernel methods. ‎Initially‎, ‎the usual kernel method is introduced‎. ‎Subsequently‎, ‎we present the two new estimates of the probability density function‎, ‎termed the biased reduced kernel estimate‎, ‎the repeat of the biased reduced kernel estimate, and the proposed biased reduced kernel estimate obtained by subtracting the bias value from the kernel estimator‎. ‎The paper explores theoretical properties, including the selection of the smoothness parameter, bias, variance, and mean squared error of the proposed estimator. ‎The accuracy of the biased reduced kernel estimate is scrutinized through Monte Carlo simulations‎. ‎Moreover‎, ‎the mentioned methods were employed using the five real datasets‎. ‎The findings reveal that the proposed biased reduced kernel method exhibits a further reduction in bias compared to the usual kernel‎, ‎biased reduced kernel, and repeated biased reduced kernel methods. https://jsm.yazd.ac.ir/article_4110.html The prediction of missing order statistics for the Generalized Extreme Value distribution is investigated‎, ‎with a focus on the Fréchet‎, ‎Gumbel‎, ‎and Weibull subtypes governed by the shape parameter γ‎. ‎This paper first establishes a necessary and sufficient condition for the existence of conditional moments of order statistics based on the domain of γ‎‎. ‎We then derive predictors using three distinct methods‎: ‎the best unbiased predictor‎, ‎the conditional median predictor‎, ‎and the conditional average predictor‎. ‎A comprehensive simulation study reveals that the optimal method is distribution-dependent‎. ‎For the Gumbel distribution‎, ‎the best unbiased predictor provides superior accuracy and robustness‎. ‎For the Fréchet distribution‎, ‎the best unbiased predictor is unequivocally superior‎, ‎while the conditional average predictor and the conditional median predictor demonstrate significant bias and instability‎. ‎For the Weibull distribution‎, ‎the choice is critically sensitive to γ‎, ‎best unbiased predictor is preferred for milder shapes‎, ‎whereas the conditional average predictor is more robust for stronger shapes‎. ‎These findings provide a clear‎, ‎evidence-based framework for selecting the appropriate prediction method in extreme value analysis‎. ‎To demonstrate the performance of the proposed methods‎, ‎a numerical example utilizing a real-world data set is provided. https://jsm.yazd.ac.ir/article_4120.html This study conducts statistical inference on a Multicomponent reliability stress-strength system with non-identical component strengths, using the exponentiated Kumaraswamy distribution for progressively censored samples. We investigate estimation of the system reliability parameter via both classical and Bayesian inference frameworks, including maximum likelihood estimation, approximate Bayesian estimation, and highest posterior density interval construction. We compare the performance of different estimators using Monte Carlo simulation, with evaluation metrics including mean squared error and coverage probability. A real-data example is also provided to demonstrate the effectiveness of the proposed model, highlighting its practical utility and relevance for both reliability engineering and statistical analysis. https://jsm.yazd.ac.ir/article_4127.html The lifetime performance index is a widely accepted measure for evaluating a process capability in terms of both its actual and expected performance‎. ‎In manufacturing contexts‎, ‎a product is typically considered acceptable if its lifetime exceeds a specified minimum threshold‎. ‎This study investigates statistical inference for the nonconforming rate of a two-component system‎, ‎in which the dependence between the two lifetime characteristics is modeled using the Farlie-Gumbel-Morgenstern copula‎. ‎The marginal distributions of both components are assumed to follow Weibull distributions‎. ‎A numerical example is presented to illustrate the practical application of the proposed approaches‎. https://jsm.yazd.ac.ir/article_4199.html This paper proposes a novel adaptive circular watermarking framework based on the human visual system that resolves this fundamental trade-off through methodological synthesis. We integrate a pre-trained backpropagation neural network, used to calculate the localized just noticeable difference in the discrete cosine transform domain, with a geometric circular constraint embedding strategy. Our core contribution is the dynamic modulation of the circular detection radius; instead of using a fixed parameter, we set the circular detection radius as a function of the backpropagation neural network output just noticeable difference. This dynamic approach ensures that the constraint region expands where the block can perceptually mask stronger changes (textured areas), maximizing robustness, and contracts where the image is visually sensitive (smooth areas), maximizing imperceptibility. Experimental results rigorously demonstrate the superiority of the adaptive circular watermarking framework. Against both a pure artificial neural network additive baseline and a static-constraint baseline, the proposed adaptive circular watermarking method achieved significantly higher peak signal-to-noise ratio in smooth image regions proving better imperceptibility while simultaneously achieving similarity of extracted watermark values, particularly against aggressive JPEG compression, proving enhanced robustness. The adaptive circular watermarking scheme sets a new benchmark for creating structurally resilient and visually intelligent watermarks. https://jsm.yazd.ac.ir/article_4212.html The COVID-19 pandemic has unfolded in multiple waves across Iran‎, ‎presenting complex challenges for public health management‎. ‎Accurate modeling of active cases is essential for understanding transmission dynamics and guiding interventions‎. This study aims to investigate the progression of active COVID-19 cases across six epidemic waves in Iran using statistical‎, ‎machine learning‎, ‎and mathematical models to estimate key transmission rates and evaluate model performance‎. ‎‎Models including autoregressive integrated moving average‎, multilayer perceptron‎, ‎Holt-Winter‎, trigonometric seasonal‎, ‎Prophet‎, ‎and Bayesian structural time series were evaluated using root mean square, mean absolute, and mean absolute percentage errors‎. ‎Mathematical approaches were applied to estimate transmission rates‎: ‎infected to active‎, ‎active to recovered‎, ‎and active to death‎. ‎Comparative performance was assessed across all six waves‎. Model performance varied by wave and variable‎. Multilayer perceptron and Bayesian structural time series showed superior accuracy for infected and active cases‎, ‎respectively‎, ‎while autoregressive integrated moving average excelled in predicting recoveries and deaths‎. ‎Felberg consistently outperformed other models in estimating death cases‎. ‎Transmission rates revealed that ‎infected to active peaked during the third and fourth waves and declined post-vaccination‎. ‎The fifth wave showed increased ‎active to recovered and reduced active to death‎, ‎indicating improved recovery and reduced mortality‎. Combining statistical‎, ‎machine learning‎, ‎and mathematical models offers a robust framework for analyzing COVID-19 dynamics‎. ‎Transmission rate estimation provides actionable insights for epidemic control‎, ‎highlighting the impact of vaccination and public health compliance on disease progression. https://jsm.yazd.ac.ir/article_4216.html Understanding the asymptotic behavior of the sample variance is important in statistical theory and inference. While classical results provide chi-square limiting distributions for continuous populations, discrete random variables often exhibit non-classical behavior, complicating both theoretical analysis and practical applications. In this paper, we propose a decomposition of the sample variance for discrete random variables into two theoretically tractable components, enabling a finer characterization of their stochastic structure. We derive the asymptotic distributions of these components under a specific condition, revealing that certain components converge to chi-square laws - a phenomenon previously observed only in Bernoulli and binomial models with success probability one-half. Extensive Monte Carlo simulations confirm the accuracy of the theoretical approximations and demonstrate their relevance even for moderate sample sizes. These results provide new insights into the interplay between discreteness, variance decomposition, and asymptotic behavior, extending classical chi-square asymptotics to a broader class of discrete models. https://jsm.yazd.ac.ir/article_4223.html According to the δ-shock model‎, ‎a system subjected to random shocks fails when the inter-arrival time between two successive shocks is less than a critical threshold δ‎. ‎Several generalizations of the δ-shock model have been proposed to study shock-exposed systems in different scenarios‎. ‎In this paper‎, ‎we examine a recently proposed generalization of the δ-shock model within a discrete-time framework‎, ‎where inter-arrival times follow a geometric distribution‎. ‎We derive the probability generating function‎, ‎the mean time to failure‎, ‎and the variance of the system lifetime‎. ‎Furthermore‎, we present ‎an illustrative example related to crop insurance is presented to demonstrate the practical relevance and applicability of the proposed discrete-time model.