Research Article
Marginalized Maximum Likelihood Estimation Method for the Three-parameter Lognormal Distribution
Ouedraogo Ouindllassida Jean-Etienne*
,
Katchekpele Edoh
Issue:
Volume 11, Issue 1, February 2026
Pages:
1-5
Received:
21 November 2025
Accepted:
11 December 2025
Published:
15 January 2026
DOI:
10.11648/j.mcs.20261101.11
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Views:
Abstract: This paper proposes an adjustment method to overcome the difficulties encountered by the maximum likelihood method in the case of the three-parameter lognormal distribution. Endeed, when the threshold parameter is close to the smallest order statistic, the standard likelihood function is no longer bounded. In this case, maximum likelihood estimators are no longer accessible. Our strategy is twofold: first, we construct adaptive bounds intended to contain the location and shape parameters with a probability close to one as the sample size increases. Second, we construct a marginal likelihood function, which we maximize using an optimization method available in the R software through the ”nlnimb” package. This likelihood function is based on the (n-1) largest order statistics. Finally, Monte Carlo simulation studies are used to analyze the asymptotic behavior of the constructed intervals and to study the asymptotic properties of the proposed estimators through bias and the Root Mean-Squared Error(RMSE).
Abstract: This paper proposes an adjustment method to overcome the difficulties encountered by the maximum likelihood method in the case of the three-parameter lognormal distribution. Endeed, when the threshold parameter is close to the smallest order statistic, the standard likelihood function is no longer bounded. In this case, maximum likelihood estimator...
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Review Article
A Comprehensive Analysis of Five Machine Learning Models for Predicting Heart Disease
Issue:
Volume 11, Issue 1, February 2026
Pages:
6-16
Received:
10 December 2025
Accepted:
25 December 2025
Published:
4 February 2026
DOI:
10.11648/j.mcs.20261101.12
Downloads:
Views:
Abstract: Cardiovascular disease, especially heart disease, is one of the leading causes of global mortality. Annually, approximately 17.9 million people suffer from heart disease and accounting for over 80%of the deaths. So, predicting and detecting heart disease at an early stage is very important. As a result, medical professionals need to take appropriate and necessary actions at earlier stages. By applying machine learning technology, Healthcare professionals can diagnose cardiac conditions more accurately. Many researchers are focusing on developing intelligent systems that can accurately diagnose them using electronic health data, with the aid of machine learning (ML) algorithms. This study evaluates five machine learning algorithms, including Logistic Regression (LR), Naive Bayes (NB), K-Nearest Neighbours (KNN), Decision Tree (DT), and Random Forest (RF), to predict the likelihood of heart disease using the UCI Cleveland Heart Disease dataset. Data pre-processing and feature selection steps were done before building the models. The performance of this algorithm has been evaluated using accuracy, precision, recall, and F1-score. Further, the model performance has been shown through AUC and ROC curves. It is observed from the result that Logistic Regression performs better than other considered classification models with 88.52% accuracy, 90.62% recall, and 89.23% F1-score. However, in terms of precision, Naive Bayes performs better than the other considered models. These findings highlight how machine learning-based techniques can enhance the identification of early cardiovascular risk and help clinical decision-making.
Abstract: Cardiovascular disease, especially heart disease, is one of the leading causes of global mortality. Annually, approximately 17.9 million people suffer from heart disease and accounting for over 80%of the deaths. So, predicting and detecting heart disease at an early stage is very important. As a result, medical professionals need to take appropriat...
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