Exact probability distribution functions for Parrondo's games

Exact Probability Distribution versus Entropy

The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both firstand second-order approximations to a natural language are considered. The guessing strategy used is guessing words in decreasing order of probability. When word and alphabet sizes are large, a...

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 ...

Stationary probability density functions: An exact result

An exact expression is obtained for the probability density function (pdf) of any quantity measured in a general stationary process, in terms of conditional expectations of time derivatives of the signal. This expression indicates that the conditional expectations of both the time derivative squared and of the second time derivative influence the shape of the pdf, including its tails. A previou...

Evaluation of estimation methods for parameters of the probability functions in tree diameter distribution modeling

One of the most commonly used statistical models for characterizing the variations of tree diameter at breast height is Weibull distribution. The usual approach for estimating parameters of a statistical model is the maximum likelihood estimation (likelihood method). Usually, this works based on iterative algorithms such as Newton-Raphson. However, the efficiency of the likelihood method is not...

Inferring Trading Strategies from Probability Distribution Functions Inferring Trading Strategies from Probability Distribution Functions