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) . 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.
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