tA New Class of Skew Normal Distribution : Tanh- Skew Normal Distribution and its Properties

In this article we suggest a new class of skew normal distribution. It will be referred to as Tanh skew-normal distribution, where (Tanh) is a hyperbolic tangent function; a class of skew-normal distribution is proposed by considering a new skew function, It is not a probability distribution function, some properties of this new class distribution have been investigated. Several properties of this distribution have been discussed; parameters estimation using moments, moment generating function, maximum likelihood method, and Fisher information matrix are obtained. A numerical experiment was performed to see the behavior of MLEs. Finally, we apply this model to a real data-set to show that the new class distribution can produce a better fit than other classical Skew normal.