[0,1] Truncated Lomax - Uniform distribution with properties

In this paper, we produce a new of continuous distribution based on [0,1] Truncated Lomax distribution, is railed [0,1] liuncated Lomax - Uniform distribution. The cumulative distribution function, the rth moment, the mean, the variance, the skewness, the kurtosis, the median, the characteristic function, the reliability function,the hazared rate function, the quantile function, the Shannon entropy function and Relative entropy function has been derived for the distribution.we know that the an element fails when it exceeds the stress of the corresponding strength. therefor, the [0,1] Truncated Lomax- Uniform strength stress model with different parameters has also been derived here. Finally, we proposed a study in Estimation for parameters of [0,1] Truncated Lomax - Uniform distribution by using maximum likelihood estimation method and we used simulation to generate random variables to take four experiments for the default values of three real parameters with samples sizes (n = 30, 60, 90,120) and sample iteration (S = 1000).