Open AccessThe extended odd family of probability distributions with practice to a submodel
Author(s) -
Hassan S. Bakouch,
Christophe Chesneau,
Muhammad Nauman Khan
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1912855b
Subject(s) - kurtosis , mathematics , bathtub , skewness , order statistic , transformation (genetics) , k distribution , probability density function , hazard , distribution (mathematics) , statistics , moment generating function , exponential family , maximum likelihood , statistical physics , generating function , probability distribution , mathematical analysis , history , biochemistry , chemistry , physics , archaeology , organic chemistry , gene
In this paper, we introduce a new family of distributions extending the odd family of distributions. A new tuning parameter is introduced, with some connections to the well-known transmuted transformation. Some mathematical results are obtained, including moments, generating function and order statistics. Then, we study a special case dealing with the standard loglogistic distribution and the modifiedWeibull distribution. Its main features are to have densities with flexible shapes where skewness, kurtosis, heavy tails and modality can be observed, and increasing-decreasing-increasing, unimodal and bathtub shaped hazard rate functions. Estimation of the related parameters is investigated by the maximum likelihood method. We illustrate the usefulness of our extended odd family of distributions with applications to two practical data sets.