Perfect Hemisphere Trend Realization: A Combinatorial Modification of Probability Distributions

The paper reviews creative ways to develop continuous probability models playing around the integration method and the concept of normalization. It further projects a probability distribution realized by combining two symmetric probability models that differ in shape, to produce a perfect hemisphere or half-sun trend. Normal and arcsine distributions are the root distributions used for this development. At some values of the parameter, the distribution can be right skewed; where other moments-related measures and estimation are studied as their properties, alongside simulation.