Some new flexible classes of normal distribution for fitting multimodal data. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Martínez-Flórez, Guillermo; Tovar-Falón, Roger; Elal-Olivero, David
• Is Part Of: Statistics. Volume 56:Issue 1(2022)
• Page Start: 182
• Page End: 205
• Publication Date: 2022-01-02
• Subjects: Trimodal distribution -- asymmetry -- exponentiated flexible alpha-normal distribution -- maximum-likelihood estimation; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2022.2041642
• Languages: English
• ISSNs: 0233-1888

Abstract

Abstract : In this paper, we introduce two new families of distributions containing unimodal as well as bimodal and trimodal distributions. The models extend the normal model to trimodal symmetric and asymmetric situations, and typically involve fewer parameters to be estimated than the mixtures of normal distributions. Statistical properties of these new families are studied in detail. The problem of estimating parameters is addressed by considering the maximum likelihood method and Fisher information matrices are derived. A small Monte Carlo simulation study is conducted to examine the performance of the obtained estimators. The methodology developed is illustrated with three real data applications.