African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 257

Full Length Research Paper

The weighted Monsef distribution

Alshrani Mustafa
  • Alshrani Mustafa
  • Faculty of Science, Tanta University, Tanta, Egypt.
  • Google Scholar
M. M. E. Abd El-Monsef
  • M. M. E. Abd El-Monsef
  • Faculty of Science, Tanta University, Tanta, Egypt.
  • Google Scholar

  •  Received: 15 February 2020
  •  Accepted: 06 August 2020
  •  Published: 31 August 2020


A two-parameter weighted Monsef distribution (WM) is proposed in this paper. WM is flexible and has the property that the hazard rate function can accommodate both increasing and bathtub shapes. Most of its mathematical properties, such as probability density function, hazard function, moments and mean residual life function, are derived. The maximum likelihood method is used to estimate the distribution parameters. A simulation study is performed to examine the bias and mean square error of the maximum likelihood estimators of the parameters. Two real data sets are presented to illustrate the model flexibility in fitting some data against some other known distributions.

Key words: Weighted Monsef distribution, hazard rate function, maximum likelihood, mean residual life function.