Two-parameter family of distributions: Properties, estimation, and applications
Mohamed Cherif Belili, Arwa M. Alshangiti, Ahmed M. Gemeay, Halim Zeghdoudi, Kadir Karakaya, M. E. Bakr, Oluwafemi Samson Balogun, Mintodê Nicodème Atchadé, Eslam Hussam
Abstract
In this paper, a new flexible two-parameter family of distributions is introduced. Some mathematical properties, such as asymptotic behavior, moments, stochastic order, entropy, and quantile function, are examined. A special case of this family is introduced called Gemeay–Zeghdoudi distribution. The unknown parameters of the Gemeay–Zeghdoudi distribution are estimated via many estimators. The efficiency of the estimators is compared with a Monte Carlo simulation. The applicability of the new distribution is illustrated by the annual maximum flood and survival times of patients with breast cancer real data analyses.