This paper establishes that every random utility discrete choice model (RUM) has a representation that can be characterized by a choice-probability generating function (CPGF) with speci c properties, and that every function with these speci c properties is consistent with a RUM. The choice probabilities from the RUM are obtained from the gradient of the CPGF. Mixtures of RUM are characterized b...

From the integration of nonsymmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. Motivated by the mathematical curiosity, we show that these generalized functions are suitable to generalize some probability density functions pdfs . A very reliable rank distribution can be conveni...

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...