*Article* **The Generalized Odd Linear Exponential Family of Distributions with Applications to Reliability Theory**

**Farrukh Jamal 1,\*, Laba Handique 2, Abdul Hadi N. Ahmed 3, Sadaf Khan 1, Shakaiba Shafiq <sup>1</sup> and Waleed Marzouk <sup>3</sup>**


**Abstract:** A new family of continuous distributions called the generalized odd linear exponential family is proposed. The probability density and cumulative distribution function are expressed as infinite linear mixtures of exponentiated-F distribution. Important statistical properties such as quantile function, moment generating function, distribution of order statistics, moments, mean deviations, asymptotes and the stress–strength model of the proposed family are investigated. The maximum likelihood estimation of the parameters is presented. Simulation is carried out for two of the mentioned sub-models to check the asymptotic behavior of the maximum likelihood estimates. Two real-life data sets are used to establish the credibility of the proposed model. This is achieved by conducting data fitting of two of its sub-models and then comparing the results with suitable competitive lifetime models to generate conclusive evidence.

**Keywords:** generalized odd linear distribution; hazard rate function; moments; residual analysis; maximum likelihood estimation; Monte Carlo simulation
