International Journal of Statistics and Applied Mathematics
  • Printed Journal
  • Indexed Journal
  • Refereed Journal
  • Peer Reviewed Journal

International Journal of Statistics and Applied Mathematics

2020, Vol. 5, Issue 6, Part A

Extended exponential and Weibull families of distributions using generalized Marshall-Olkin scheme


Author(s): Thomas Mathew and Ravikumar K

Abstract: A three-parameter family of exponential distributions that may serve as an alternative to two-parameter extensions of exponential distributions is introduced and studied. This family contains the Marshall-Olkin exponential distribution introduced in Marshall and Olkin (1997) [26]. This family can be used as an alternative to exponential distribution. The reliability properties of this class of distributions are studied. A four-parameter Weibull distribution is introduced and studied. This family contains the Weibull distribution and possesses many nice characteristics. The reliability properties of this family of distributions are studied. As a generalization of the four parameter Weibull family, the general semi-Weibull family of distributions are introduced and studied. The semi-Weibull/ generalized semi-Weibull family is useful to model data that exhibit periodic movements. The applications of these distributions in time series contexts are discussed. First-order autoregressive Marshall-Olkin minification process is developed. The methods we discuss are useful to develop autoregressive models with any Marshall-Olkin distribution as marginal. Particularly, the study focuses on the time series properties of the exponential and Weibull families.

DOI: 10.22271/maths.2020.v5.i6a.621

Pages: 68-86 | Views: 34 | Downloads: 6

Download Full Article: Click Here
How to cite this article:
Thomas Mathew, Ravikumar K. Extended exponential and Weibull families of distributions using generalized Marshall-Olkin scheme. Int J Stat Appl Math 2020;5(6):68-86. DOI: 10.22271/maths.2020.v5.i6a.621
Call for book chapter
International Journal of Statistics and Applied Mathematics