Background In general, truncated distributions provide a flexible framework that allows for more realistic and accurate representation of constrained data compared to using non-truncated distributions, making them a fundamental element in modern statistical models and the analysis of constrained data. Methods Right – truncated [0,1] exponential Rayleigh distribution ([0,1]-RTERD) for lifetime is presented in this paper. The new distribution contains two parameters, one of scale and another for the shape. Statistical functions of the (RTERD), such as cumulative functions (CDF), probability density (PDF), survival, and hazard functions, are presented in terms of mathematical construction and graphics. Besides, discuss the mathematical and statistical properties of the new distribution, including median, moments of the origin, coefficients of skewness and kurtosis, order statistic, moment generating function, the rėnyi entropy, quantile function. Results the parameters of this life expectancy distribution will be estimate using the maximum likelihood estimation method and compare new continuous model with other continuous distributions using statistical information criterion. Finally, apply the ([0,1]-RTERD) to actual datasets to validate the model’s practicality. The ([0,1]-RTERD) frequently produces a better fit and shows more modeling precision when handling lifespan and reliability data, according to comparisons with traditional models. Conclusions The [0,1]-RTERD provides a new framework for more accurately dealing with data restricted to the interval [0,1], where it is characterized by several important properties, including changing the shape, center, and width of the original distribution as a result of the normalization process, which is reflected in the expected value, standard deviation, and other instantaneous properties.
