A novel method of generating distributions on the unit interval with applications

A novel approach to the construction of absolutely continuous distributions over the unit interval is proposed. Considering two absolutely continuous random variables with positive support, this method conditions on their convolution to generate a new random variable in the unit interval. This approach is demonstrated using some popular choices of positive random variables, such as the exponential, Lindley, and gamma. Some existing distributions, like the uniform, the beta, and the Kummer-beta, are formulated with this method. Several new structures of density functions having potential for future applications in real-life problems are also provided. One of the new distributions, namely the LCG, is considered for detailed study along with a related distribution, namely the GCL. The moments, hazard rate, cumulative distribution function, stress-strength reliability, random sample generation using the quantile function, method of moments along with maximum likelihood estimation, and regression modeling are discussed for both the distributions. Real-life applications of the proposed models and the corresponding regression models show promising results.