European Journal of Statistics

Kernel Smoothing for Bounded Copula Density Functions

2025-02-08T10:58:41+08:00

Non-parametric estimation of copula density functions presents significant challenges. One issue is the unboundedness of certain copula density functions and their derivatives at the corners of the unit square. Another is the boundary bias inherent in kernel density estimation. This paper presents a kernel-based method for estimating bounded copula density functions, addressing boundary bias through the mirror reflection technique. Optimal smoothing parameters are derived via Asymptotic Mean Integrated Squared Error (AMISE) minimization and cross-validation, with theoretical guarantees of consistency and asymptotic normality. Two kernel smoothing strategies are proposed: the rule-of-thumb approach and least squares cross-validation (LSCV). Simulation studies highlight the efficacy of the rule-of-thumb method in bandwidth selection for copulas with unbounded marginal supports. The methodology is further validated through an application to the Wisconsin Breast Cancer Diagnostic Dataset (WBCDD), where LSCV is used for bandwidth selection.

Introducing a New Unit Gamma Distribution: Properties and Applications

2025-02-05T19:29:55+08:00

This article fills a gap in distribution theory and statistics by introducing a new, simple and intuitive two-parameter unit distribution derived from the gamma distribution. It serves as a complementary option to the existing unit gamma distribution. The main features are explored through both theoretical and practical approaches. Specifically, the shapes of the corresponding probability density and hazard rate functions are studied, an understandable stochastic comparison with the existing unit gamma distribution is provided, moments and incomplete moments are expressed, moment skewness and kurtosis are computed, random numbers are generated, and a new family of distributions is proposed. A statistical application demonstrates how the two parameters can be estimated quite effectively and the fit to a real data set is tested. It is also shown that the new distribution is able to outperform four well-known two-parameter unit distributions: the beta distribution, the Kumaraswamy distribution, the unit Weibull distribution and, more importantly, the existing unit gamma distribution. An appendix lists the main codes used in the application.

A New Extension of Inverted Exponential Distribution with Applications

2024-12-07T23:47:11+08:00

This article introduces the MTI inverted exponential distribution (MTIIE), a two-parameter generalization of the inverted exponential distribution, developed using the MTI technique. The MTI technique is named after (Murtiza, Tariq, Ishfaq) who pioneered this approach to enhance the flexibility and applicability of statistical models. The paper explores key properties of the distribution, including moments, the quantile function, the hazard rate, the reliability function, and the moment-generating function. The distribution parameters are estimated using the method of maximum likelihood estimation (MLE). It is applied to two real data sets to demonstrate the practical utility of the new distribution, showcasing its effectiveness in modeling real-world data.

On Poisson Sampling for Estimation in Sub-Fractional Levy Stochastic Volatility Models

2024-11-29T00:20:24+08:00

The paper studies quasi-maximum likelihood and generalized method of moments estimators of the parameter in the sub-fractional Levy inverse-Gaussian Ornstein-Uhlenbeck stochastic volatility model based on Poissonly sampled data.

Strategies to Increase Pipeline Status: A Case Study from Eclinical Data

2024-11-10T13:05:29+08:00

In this paper we perform a case study regarding Eclinical data of Intelligent Medical Objects (IMO) which currently operates with eight pipeline statuses. It has been observed that the higher the pipeline status, the fewer consumers there tend to be. In this study, we aim to identify which factors significantly influence consumer presence at these advanced pipeline stages. Logistic regression is useful for predicting binary outcomes based on one or more independent variables. It estimates the probability of a particular outcome, allowing us to understand how different factors impact the likelihood of an event occurring. This method is widely used in fields like medicine, finance, and social sciences for classification problems and determining the significance of predictors, making it valuable for identifying key factors and making informed decisions based on probabilities. We apply logistic regression, using the probability of reaching the eighth status as our primary dependent variable. Of all the independent variables considered, only a select few are significant in explaining this outcome.

Assessing the Performance of the MARFIMA Model Using Simulated and Real Life Data

2024-11-29T23:10:26+08:00

A modified autoregressive fractional integrated moving average MARFIMA (p, d, q) is presented in this study to describe time series data that are nonstationary and have a fractional difference value of 1<d<1.5. Data from ARFIMA simulations are used to assess the performance of the MARFIMA model. The autoregressive fractional integrated moving average ARFIMA model and the MARFIMA model's performance were also compared in a number of applications. Using the Akaike Information Criterion (AIC), Schwartz Bayesian Information Criterion (SBIC), root mean square error (RMSE), and normalized mean square error (NMSE), the best model was chosen, and its performance was evaluated using a variety of forecast accuracy metrics. Results indicated that across four distinct financial and economic data sets, which include the price of crude oil, the Nigerian stock market, the Nigerian all-shares index, and the Nigerian food and beverage index, the MARFIMA model performed better than the ARFIMA model. The research provides a more robust method for modeling and forecasting long memory data. The study has also contributed to existing literature on the most appropriate method for modelling long memory associated with financial and economic data.

Machine Learning Models in Predicting Failure Times Data Using a Novel Version of the Maxwell Model

2024-11-21T20:25:57+08:00

This work aims to introduce a novel statistical distribution based on Maxwell distribution that can handle both positive and negative data sets with varying failure rates, including decreasing and bathtub-shaped distributions. The novel statistical distribution can be derived via the log transformation approach with an additional exponent parameter, defining the Transformed Log Maxwell (TLMax) distribution. The numerical investigation reveals that the developed TLMax distribution can effectively fit negative and positive data sets. A data set containing failure times for Kevlar 49/epoxy at a pressure of approximately 90% was employed to compare the proposed model against the traditional Maxwell model, and the results obtained indicated that the novel distribution outperformed the comparator. Finally, for the prediction of failure times in the dataset, we employed a machine learning model, including support vector regression (SVR), K-nearest neighbors’ regression (KNN), linear regression (LR), and gradient boosting regression (XGBoost). The findings indicate that the KNN model demonstrates greater prediction robustness than the other models. Beyond practitioners and researchers, this research holds relevance for professionals in physics and chemistry, where the Maxwell distribution is commonly employed.