Morad Alizadeh

In the theory of distributions, the family of exponential distributions is an important group of probability distributions that have common characteristics and are placed in a special format. This common format is useful for facilitating better understanding and generalization of problems in mathematical applications. New distributions are created by adding one or more parameters to the basic model and create more flexibility. In this thesis, we propose a new family of continuous distributions with two parameters called expanded exponential of the second type. We review some basic properties including the quantile function, the expansion for the cumulative distribution function, and the probability distribution function, and then we study the semi-logistic distribution as a special case in more detail. We estimate the parameters using maximum likelihood method and other different methods and then compare these methods with simulation. Finally, we examine the ability of this model using two real data sets.