Beyond the lognormal distribution with properties and applications

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
E. Gómez–Déniz, Osvaldo Venegas, H. W. Gómez
{"title":"Beyond the lognormal distribution with properties and applications","authors":"E. Gómez–Déniz, Osvaldo Venegas, H. W. Gómez","doi":"10.1214/22-bjps546","DOIUrl":null,"url":null,"abstract":". In this paper, a new family of continuous random variables with positive support is introduced. Its density function has the capacity to incorporate features of uni-modality and bimodality. Special attention is paid to the lognormal distribution which is included as a particular case. Its density function is given in closed-form, allowing prob-abilities, moments and other related measures such as skewness and kurtosis coefficients to be computed easily. In addition, a stochastic representation of the family that enables us to generate random variates of this model is also presented. Some properties related with the right tail and actuarial aspects of the distribution are also shown. This new family of distributions is numerically illustrated with data taken from the Medical Expenditure Panel Survey (MEPS), conducted by the US Agency of Health Research and Quality and with a well-known data set which has been studied widely in the actuarial literature.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Brazilian Journal of Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/22-bjps546","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0

Abstract

. In this paper, a new family of continuous random variables with positive support is introduced. Its density function has the capacity to incorporate features of uni-modality and bimodality. Special attention is paid to the lognormal distribution which is included as a particular case. Its density function is given in closed-form, allowing prob-abilities, moments and other related measures such as skewness and kurtosis coefficients to be computed easily. In addition, a stochastic representation of the family that enables us to generate random variates of this model is also presented. Some properties related with the right tail and actuarial aspects of the distribution are also shown. This new family of distributions is numerically illustrated with data taken from the Medical Expenditure Panel Survey (MEPS), conducted by the US Agency of Health Research and Quality and with a well-known data set which has been studied widely in the actuarial literature.
超越对数正态分布的性质和应用
在本文中,引入了一个新的具有正支持的连续随机变量族。它的密度函数有能力结合单模态和双模态的特征。特别注意对数正态分布,它作为一个特例被包括在内。它的密度函数是以闭合形式给出的,可以很容易地计算概率、矩和其他相关度量,如偏度和峰度系数。此外,还提出了该族的随机表示,使我们能够生成该模型的随机变量。还显示了与分布的右尾和精算方面有关的一些性质。美国卫生研究与质量局进行的医疗支出小组调查(MEPS)中的数据以及精算文献中广泛研究的著名数据集对这一新的分布家族进行了数字说明。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
1.60
自引率
10.00%
发文量
30
审稿时长
>12 weeks
期刊介绍: The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes. More specifically, the following types of contributions will be considered: (i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects. (ii) Original articles developing theoretical results. (iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it. (iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信