The Log-Odd Normal Generalized Family of Distributions with Application

Muhammad Zubair; Tibor K Pogány; Gauss M Cordeiro; Muhammad H Tahir

doi:10.1590/0001-3765201920180207

The Log-Odd Normal Generalized Family of Distributions with Application

An Acad Bras Cienc. 2019 Jul 1;91(2):e20180207. doi: 10.1590/0001-3765201920180207.

Authors

Muhammad Zubair¹, Tibor K Pogány², Gauss M Cordeiro³, Muhammad H Tahir⁴

Affiliations

¹ Department of Statistics, Government S.E. College, Bahawalpur, 63100, Pakistan.
² Faculty of Maritime Studies, University of Rijeka, HR-51000 Rijeka, Croatia & Applied Mathematics Institute, Óbuda University, H-1034 Budapest, Hungary.
³ Departamento de Estatística, Universidade Federal de Pernambuco, Av. Prof. Moraes Rego, 1235, Cidade Universitária, 50740-540 Recife, PE, Brazil.
⁴ Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan.

PMID: 31269102
DOI: 10.1590/0001-3765201920180207

Abstract

The normal distribution has a central place in distribution theory and statistics. We propose the log-odd normal generalized (LONG) family of distributions based on log-odds and obtain some of its mathematical properties including a useful linear representation for the new family. We investigate, as a special model, the log-odd normal power-Cauchy (LONPC) distribution. Some structural properties of LONPC distribution are obtained including quantile function, ordinary and incomplete moments, generating function and some asymptotics. We estimate the model parameters using the maximum likelihood method. The usefulness of the proposed family is proved empirically by means of a real air pollution data set.