A new approach for moments estimator and percentages method for estimating the parameters of truncated exponential Marshall-Olkin exponential distribution

In this study, a new distribution was presented, called Marshall-Olkin truncated exponential distribution based on a generalization formula, which is one of the statistical distributions to describe the continuous variables for many real life and physical experiments. The proposed distribution is consists of three parameters (α, θ, λ) and the it derivation of some important statistical properties of the Marshall-Olkin exponential distribution such as the cumulative distribution function (CDF), the probability density function (PDF), the survival function, and the risk function, as well as the derivation of some of mathematical properties such as the mean, variance, flatness, skewness, and the use of an estimation method for the parameters of the Marshall-Olkin distribution, which is (the method of moments and the method of proportions). Monte Carlo simulation method was utilized and three sample sizes (10, 50, 100) were taken to compare the parameters of the proposed distribution by using the comparison criterion of the mean square error (MSE). The results are the method of moment is superiority over the other method because it had the least mean square error.