  A novel approach towards 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 the positive random
variables such as the exponential, Lindley, gamma. Some existing distributions
like the uniform and the beta are formulated with this method. Several new
structures of density functions having potential for future application in real
life problems are also provided. One of the new distributions having one
parameter is considered for parameter estimation and real life modelling
application and shown to provide better fit than the popular one parameter
Topp-Leone model.
