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Axioms
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Probability, Statistics and Estimations, 2nd Edition
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Probability, Statistics and Estimations, 2nd Edition

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 30 September 2025 | Viewed by 4397

Special Issue Editors

Dr. Yolanda Gómez

E-Mail Website
Guest Editor
Department of Statistics, Faculty of Science, University of Bío-Bío, Concepción, Chile
Interests: survival analysis; cure rate model; regression model; distribution theory
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Inmaculada Barranco-Chamorro

E-Mail Website
Guest Editor
Department of Statistics and Operations Research, Faculty of Mathematics, University of Seville, 41012 Sevilla, Spain
Interests: statistical inference; distribution theory; Bayesian statistics; influence analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We invite you to submit your articles to this Special Issue of Axioms for works dedicated to publishing new theoretical and/or computational methodologies related to the application of the concepts in current topics of statistics and probability. We also encourage authors to submit new applications of existing models in the literature.

The scope includes, but is not limited to, the following topics:

  • Survival analysis;
  • Cure rate model;
  • Distribution theory: Univariate and multivariate new models;
  • Regression models;
  • Machine learning;
  • Applied statistics;
  • Bayesian statistics.

Dr. Yolanda Gómez
Prof. Dr. Inmaculada Barranco-Chamorro
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • survival analysis
  • cure rate model
  • distribution theory
  • regression models
  • machine learning
  • applied statistics
  • Bayesian statistics

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (6 papers)

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Research

19 pages, 929 KiB  
Article
Simulation-Based Evaluation of Robust Transformation Techniques for Median Estimation Under Simple Random Sampling
by Fatimah A. Almulhim and Abdulaziz S. Alghamdi
Axioms 2025, 14(4), 301; https://doi.org/10.3390/axioms14040301 - 16 Apr 2025
Viewed by 215
Abstract
An efficient estimator can reduce both bias and mean squared error to provide more accurate results by using the transformation strategy. In this paper, an enhanced class of ratio–product types of estimators is introduced, which employs the transformation technique by linearly combining two [...] Read more.
An efficient estimator can reduce both bias and mean squared error to provide more accurate results by using the transformation strategy. In this paper, an enhanced class of ratio–product types of estimators is introduced, which employs the transformation technique by linearly combining two robust measures, the trimean and decile mean, and five non-conventional measures, the range, inter-quartile range, mid-range, quartile average, and quartile deviation, on auxiliary variables with a simple random sampling method to estimate the finite population median. This transformation approach improves efficiency and enables estimators to manage data variability better. Using these estimators, we investigate their bias and mean squared error up to the first order of approximation. A comparison of the proposed estimators and existing methods is conducted through five simulated populations generated through different suitable distributions and three real datasets. By improving the precision and efficiency of median estimation, the proposed estimators ensure accurate and reliable results. Comparing the new estimators to traditional estimators, the findings show superior performance for new estimators in terms of mean squared errors (MSEs). Full article
(This article belongs to the Special Issue Probability, Statistics and Estimations, 2nd Edition)
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14 pages, 455 KiB  
Article
On a Sum of Two Akash Distributions: Inference and Applications
by Luis Firinguetti-Limone, Neveka M. Olmos, Osvaldo Venegas and Héctor W. Gómez
Axioms 2025, 14(3), 158; https://doi.org/10.3390/axioms14030158 - 22 Feb 2025
Viewed by 339
Abstract
We propose a new distribution which is the sum of two independent Akash (AK) random variables with the same parameter. We refer to this distribution as the AKS distribution. We study the density and some of its properties. We derive the method of [...] Read more.
We propose a new distribution which is the sum of two independent Akash (AK) random variables with the same parameter. We refer to this distribution as the AKS distribution. We study the density and some of its properties. We derive the method of moments (MM) and the maximum likelihood (ML) estimator, along with the Fisher information. The performance of the ML estimator is evaluated through a simulation study. In addition, we present two real data applications, demonstrating in these cases the superiority of the AKS distribution compared to two other distributions. Full article
(This article belongs to the Special Issue Probability, Statistics and Estimations, 2nd Edition)
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20 pages, 672 KiB  
Article
EM Algorithm in the Slash 2S-Lindley Distribution with Applications
by Héctor A. Muñoz, Jaime S. Castillo, Diego I. Gallardo, Osvaldo Venegas and Héctor W. Gómez
Axioms 2025, 14(2), 101; https://doi.org/10.3390/axioms14020101 - 29 Jan 2025
Viewed by 461
Abstract
In this work, we present a new distribution, which is a slash extension of the distribution of the sum of two independent Lindley random variables. This new distribution is developed using the slash methodology, resulting in a distribution with more flexible kurtosis, i.e., [...] Read more.
In this work, we present a new distribution, which is a slash extension of the distribution of the sum of two independent Lindley random variables. This new distribution is developed using the slash methodology, resulting in a distribution with more flexible kurtosis, i.e., the ability to model atypical data. We study the density function of the new model and some of its properties, such as the cumulative distribution function, moments, and its asymmetry and kurtosis coefficients. The parameters are estimated by the maximum likelihood method with the EM algorithm. Finally, we apply the proposed model to two real datasets with high kurtosis, showing that it provides a better fit than two distributions known in the literature. Full article
(This article belongs to the Special Issue Probability, Statistics and Estimations, 2nd Edition)
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27 pages, 436 KiB  
Article
On the Conflation of Negative Binomial and Logarithmic Distributions
by Anfal A. Alqefari, Abdulhamid A. Alzaid and Najla Qarmalah
Axioms 2024, 13(10), 707; https://doi.org/10.3390/axioms13100707 - 13 Oct 2024
Viewed by 949
Abstract
In recent decades, the study of discrete distributions has received increasing attention in the field of statistics, mainly because discrete distributions can model a wide range of count data. One common distribution used for modeling count data, for instance, is the negative binomial [...] Read more.
In recent decades, the study of discrete distributions has received increasing attention in the field of statistics, mainly because discrete distributions can model a wide range of count data. One common distribution used for modeling count data, for instance, is the negative binomial distribution (NBD), which performs well with over-dispersed data. In this paper, a new count distribution is introduced, called the conflation of negative binomial and logarithmic distributions, which is formed by conflating the negative binomial and logarithmic distributions, resulting in a distribution that possesses some of the properties of negative binomial and logarithmic distributions. The distribution has two parameters and is verified by a positive integer. Two modifications are proposed to the distribution, which includes zero as a support point. The new distribution is valuable from a theoretical perspective since it is a member of the weighted negative binomial distribution family. In addition, the distribution differs from the NBD in the sense that the probability of lower counts is inflated. This study discusses the characteristics of the proposed distribution and its modified versions, such as moments, probability generating functions, likelihood stochastic ordering, log-concavity, and unimodality properties. Real-world data are used to evaluate the performance of the proposed models against other models. All computations shown in this paper were produced using the R programming language. Full article
(This article belongs to the Special Issue Probability, Statistics and Estimations, 2nd Edition)
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23 pages, 1980 KiB  
Article
Unit-Power Half-Normal Distribution Including Quantile Regression with Applications to Medical Data
by Karol I. Santoro, Yolanda M. Gómez, Darlin Soto and Inmaculada Barranco-Chamorro
Axioms 2024, 13(9), 599; https://doi.org/10.3390/axioms13090599 - 2 Sep 2024
Viewed by 1169
Abstract
In this paper, we present the unit-power half-normal distribution, derived from the power half-normal distribution, for data analysis in the open unit interval. The statistical properties of the unit-power half-normal model are described in detail. Simulation studies are carried out to evaluate the [...] Read more.
In this paper, we present the unit-power half-normal distribution, derived from the power half-normal distribution, for data analysis in the open unit interval. The statistical properties of the unit-power half-normal model are described in detail. Simulation studies are carried out to evaluate the performance of the parameter estimators. Additionally, we implement the quantile regression for this model, which is applied to two real healthcare data sets. Our findings suggest that the unit power half-normal distribution provides a robust and flexible alternative for existing models for proportion data. Full article
(This article belongs to the Special Issue Probability, Statistics and Estimations, 2nd Edition)
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32 pages, 519 KiB  
Article
New Flexible Asymmetric Log-Birnbaum–Saunders Nonlinear Regression Model with Diagnostic Analysis
by Guillermo Martínez-Flórez, Inmaculada Barranco-Chamorro and Héctor W. Gómez
Axioms 2024, 13(9), 576; https://doi.org/10.3390/axioms13090576 - 23 Aug 2024
Viewed by 712
Abstract
A nonlinear log-Birnbaum–Saunders regression model with additive errors is introduced. It is assumed that the error term follows a flexible sinh-normal distribution, and therefore it can be used to describe a variety of asymmetric, unimodal, and bimodal situations. This is a novelty since [...] Read more.
A nonlinear log-Birnbaum–Saunders regression model with additive errors is introduced. It is assumed that the error term follows a flexible sinh-normal distribution, and therefore it can be used to describe a variety of asymmetric, unimodal, and bimodal situations. This is a novelty since there are few papers dealing with nonlinear models with asymmetric errors and, even more, there are few able to fit a bimodal behavior. Influence diagnostics and martingale-type residuals are proposed to assess the effect of minor perturbations on the parameter estimates, check the fitted model, and detect possible outliers. A simulation study for the Michaelis–Menten model is carried out, covering a wide range of situations for the parameters. Two real applications are included, where the use of influence diagnostics and residual analysis is illustrated. Full article
(This article belongs to the Special Issue Probability, Statistics and Estimations, 2nd Edition)
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