The Poisson exponential-G family of distributions with properties and applications

Reyad H., Jamal F., Ozel G., Othman S.

JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS, vol.23, no.8, pp.1391-1414, 2020 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 8
  • Publication Date: 2020
  • Doi Number: 10.1080/09720510.2020.1714896
  • Journal Name: JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.1391-1414
  • Keywords: Entropy, Maximum Likelihood, Poisson Exponential Distribution, Probability Weighted Moments, Stress Strength Model, T-X Family
  • Hacettepe University Affiliated: Yes

Abstract

We introduce a new family of continuous distributions called the Poisson-exponential-G family based on the Poisson-exponential distribution of Cancho et al. (2011). The shapes of the density and hazard functions corresponding to new family are studied. Two sub-models are also discussed. We study some properties of the proposed family such as moments, generating functions, entropy measures, stress-strength model and order statistics. The model parameters are estimated via maximum likelihood approach. A Monte-Carlo simulation study is designed and used to show the performances of obtained estimators of parameters. Two real applications are introduced to show the importance of the new family.