Statistical Advancement of a Flexible Unitary Distribution and Its Applications

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-14 DOI:10.3390/axioms13060397

Hugo S. Salinas, H. Bakouch, Fatimah E. Almuhayfith, Wilson E. Caimanque, Leonardo Barrios-Blanco, Olayan Albalawi

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Abstract

A flexible distribution has been introduced to handle random variables in the unit interval. This distribution is based on an exponential transformation of the truncated positive normal distribution with two parameters and can effectively fit data with varying degrees of skewness and kurtosis. Therefore, it presents an alternative for modeling this type of data. Several mathematical and statistical properties of this distribution have been derived, such as moments, hazard function, the Bonferroni curve, and entropy. Moreover, we investigate the characterizations of the proposed distribution based on its hazard function. Parameter estimation has been performed using both the maximum likelihood method and method of the moments. Because of this, we were able to determine the best critical region and the information matrix, facilitating the calculation of asymptotic confidence intervals. A simulation study is presented to analyze the behavior of the obtained estimators for different sample sizes. To demonstrate the suitability of the proposed distribution, applications and goodness-of-fit tests have been performed on two practical data sets.

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灵活单元分布的统计进步及其应用

我们引入了一种灵活的分布来处理单位区间内的随机变量。该分布基于截断正态分布的指数变换，有两个参数，能有效拟合不同偏度和峰度的数据。因此，它为这类数据建模提供了另一种选择。我们已经推导出该分布的一些数学和统计性质，如矩、危险函数、Bonferroni 曲线和熵。此外，我们还根据危险函数研究了拟议分布的特征。我们使用最大似然法和矩法进行了参数估计。因此，我们能够确定最佳临界区和信息矩阵，从而便于计算渐近置信区间。我们还进行了模拟研究，分析了所获得的估计值在不同样本量下的表现。为了证明所提议的分布的适用性，我们在两个实际数据集上进行了应用和拟合优度测试。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.