Characteristic functions provide a useful method for analyzing probability distributions. In most instances, the domain is taken to be euclidean space and although the integral transforms may not have a simple expression, some qualitative features about the underlying probability distribution can often be extracted. Although there is some research eeorts in spaces more complicated then the eucl...

Suppose that m drivers each choose a preferred parking space in linear car park with n spots. In order, driver goes to their chosen spot and parks there if possible, otherwise takes the next available it exists. If all successfully, sequence of choices is called function. Classical functions correspond case $$m=n$$ ; we study here combinatorial probabilistic aspects this generalized case. We co...

The COS method was introduced in Fang & Oosterlee (2008) and then applied to pricing a variety of stock options for continuous random variables. This paper adapts the Fourier-cosine series (COS) recover discrete probability mass functions. We approximate mixture compound distributions with cosine series. Enormous precision computational speed are qualities function estimates here obtained. also...