Marshall-Olkin generalized exponential distribution

Abstract

Marshall and Olkin (Biometrika 641-652, 1997) introduced a new way of incorporating a parameter to expand a family of distributions. In this paper we adopt the MarshallOlkin approach to introduce an extra shape parameter to the two-parameter generalized exponential distribution. It is observed that the new three-parameter distribution is very flexible. The probability density functions can be either a decreasing or an unimodal function. The hazard function of the proposed model, can have all the four major shapes, namely increasing, decreasing, bathtub or inverted bathtub types. Different properties of the proposed distribution have been established. The new family of distributions is analytically quite tractable, and it can be used quite effectively, to analyze censored data also. Maximum likelihood method is used to compute the estimators of the unknown parameters. Two data sets have been analyzed, and the results are quite satisfactory.

A New Extended Uniform Distribution

“…In this paper, we introduced the Discrete Mittag-Leffler truncated distribution as a generalization of Marshall-Olkin family of distributions and studied its properties. This class is a rich class in the sense that some of the recently investigated distributions are members of this family; see Ristic and Kundu (2015), and Bidram et al (2015). As a particular case, a three parameter generalization of Uniform distribution was given special attention.…”

“…In (7), when F(x) is exponential, G(x) becomes the Marshall-Olkin generalized exponential distribution studied in Ristic and Kundu (2015). When F(x) in (7) is Weibull, G(x) reduces to Marshall-Olkin exponentiated Weibull distribution studied in Bidram et al (2015).…”

A New Generalized Exponential Distribution: Properties and Applications

“…[17] reviewed the several important characteristics of the EE distribution and derived simple explicit expressions for some properties. [24] generalized the exponential distribution by the Marshall-Olkin family. [19] generalized the gamma and Weibull distributions in similar way the EE distribution [16].…”

On Burr III Marshal Olkin family: development, properties, characterizations and applications

“…where G(x, ψ) is the baseline cumulative distribution function(cdf) which may depend on the vector parameter ψ. Many famous MO-G families and its special distributions are available in literature such as Marshall-Olkin-G (Marshall and Olkin;1997), the MO extended Lomax (Ghitany et al;2007), MO semi-Burr and MO Burr (Jayakumar and Mathew;2008), MO q-Weibull (Jose et al;2010), MO extended Lindley (Ghitany et al;2012), the generalized MO-G (Nadarajah et al (2013), the MO Fréchet (Krishna et al;, the MO family (Cordeiro and Lemonte;, MO extended Weibull (Santos-Neto et al;, the beta MO-G (Alizadeh et al 2015), the MO generalized exponential (Ristić, & Kundu;, MO gamma-Weibull (Saboor and Pogány;, MO generalized-G (Yousof et al;, MO additive Weibull (Afify et al; and Weibull MO family (Korkmaz et al;2019). This paper is sketched into the following sections.…”