Combining Two Probability Functions

Probability Generating Functions for Sattolo’s Algorithm

In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. Recently, H. Prodinger analysed two important random variables associated with the algorithm, and found their mean and variance. H. Mahmoud extended Prodinger’s analysis by finding limit laws for the same two random variables.The present article, starting from the ...

Combining Probability Forecasts

Linear pooling is by the far the most popular method for combining probability forecasts. However, any nontrivial weighted average of two or more distinct, calibrated probability forecasts is necessarily uncalibrated and lacks sharpness. In view of this, linear pooling requires recalibration, even in the ideal case in which the individual forecasts are calibrated. Toward this end, we propose a ...

Probability generating functions of absolute difference of two random variables.

Communicated by Jerzy Neyman, August 1, 1966 1. All random variables considered in this note are nonnegative and integervalued. Generically, the probability generating functions (P. G. F.) of such variables are denoted by G with subscripts identifying the random variables concerned. The argument, or arguments of the P. G. F., denoted by either u or v, will be assumed to have their moduli less t...

Probability Generating Functions

Random Probability Functions