In this article we introduce an extension of the Akash distribution. We use the slash 1 methodology to make the kurtosis of the Akash distribution more flexible. We study the general 2 density of this new distribution, some properties, moments, coefficients of asymmetry and kurtosis. 3 Statistical inference is performed using the methods of moments and maximum likelihood via the 4 EM algorithm. A simulation study is carried out to observe the behavior of the maximum likelihood 5 estimator. An application to a real data set with high kurtosis is considered, where it is shown that 6 the new distribution fits better than other extensions of the Akash distribution.

In statistics and probability theory, one of the most important statistics is the sums of random variables. After introducing a probability distribution, determining the sum of n independent and identically distributed random variables is one of the interesting topics for authors. This paper presents the probability density functions for the sum of n independent and identically distributed random variables such as Shanker, Akash, Ishita, Pranav, Rani, and Ram Awadh. In order to determine all aforementioned distributions, the problem-solving methods are applied which is based on the change-of-variables technique.