The Continuous Bernoulli Distribution: Mathematical Characterization, Fractile Regression, Computational Simulations, and Applications

Fractal and Fractional

article

Mustafa Ç. Korkmaz¹  Víctor Leiva²  Carlos Martin-Barreiro³ 

[1] Department of Measurement and Evaluation, Artvin Çoruh University;School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso;Faculty of Natural Sciences and Mathematics, Escuela Superior Politécnica del Litoral ESPOL;Faculty of Engineering, Universidad Espíritu Santo

关键词: Bernoulli distribution;    likelihood and Monte Carlo methods;    point estimation;    quantile function;    R software;    residual analysis60E05;    62J02;   

DOI  :  10.3390/fractalfract7050386

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 摘 要 】

The continuous Bernoulli distribution is defined on the unit interval and has a unique property related to fractiles. A fractile is a position on a probability density function where the corresponding surface is a fixed proportion. This article presents the derivation of properties of the continuous Bernoulli distribution and formulates a fractile or quantile regression model for a unit response using the exponentiated continuous Bernoulli distribution. Monte Carlo simulation studies evaluate the performance of point and interval estimators for both the continuous Bernoulli distribution and the fractile regression model. Real-world datasets from science and education are analyzed to illustrate the modeling abilities of the continuous Bernoulli distribution and the exponentiated continuous Bernoulli quantile regression model.

【 授权许可】

CC BY