The Entropy Transformed Rayleigh Distribution: Properties and Applications

Abstract

Abstract In this paper, we introduce a new one-parameter continuous model, called the T-Rayleigh distribution which is obtained by applying transform of entropy, the new function was investigated and found to meet the conditions of the probability function. Some mathematical properties of this distribution, such as density function, cumulative function, moments, moment generating function, mode, median, skewness, kurtosis, Shannon and Renyi entropy are derived. The model parameter is estimated by the maximum likelihood method. Finally, we illustrated the importance of this model by the means of three different real data sets, we conclude that the new model performs better than the original Rayleigh distribution, via the three applications.