Maximization of Likelihood Estimations for Some Exponential Distributions Family

In this paper, we attempt to diagnosis of some of exponential distributions, represent by the normal distribution as a criteria with two others distributions (Gamma & Exponential) distributions we attempt to analyze the effect of the number of parameter(s) two or one parameter(s) in the distribution on the maximize likelihood estimation for the three distributions. That proved the maximum likelihood estimates (MLE’s) of the parameters; it's obtained by using some packages (e.g. fitdistrplus) insides some algorithms in (R) that based on behavior of the simulated data like parameter and sample size. A comparison is carried out between the mentioned distributions based on the classical kolmogrov-smirnov distance to minimize distance estimation test statistic and Grammer von misses distance, to emphasize that which distribution fitted to the data better than the other models. After completing this, A good preface to some distributions is to summarize the relationships between observations. How to calculate and Plot Probability and Density Functions the normal distribution.