{"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":null,"pages":null},"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.
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.