Random Variables and Discrete Probability Distributions—Uniform, Binomial, Hypergeometric, and Geometric Distributions

2009 ◽  
pp. 58-74
Keyword(s):  
Probability Distributions ◽  
Random Variables ◽  
Discrete Probability ◽  
Discrete Probability Distributions

scholarly journals GENERATION OF VALUES FROM DISCRETE PROBABILITY DISTRIBUTIONS WITH THE USE OF CHAOTIC MAPS

2020 ◽  
pp. 49-54
Author(s):  
Marcin Lawnik ◽  
Arkadiusz Banasik ◽  
Adrian Kapczyński
Keyword(s):  
Chaotic Maps ◽  
Chaotic Behavior ◽  
Probability Distributions ◽  
Discrete Dynamical System ◽  
Chaotic Map ◽  
Random Variables ◽  
Discrete Distribution ◽  
Random Variable ◽  
Discrete Probability ◽  
Discrete Probability Distributions

The values of random variables are commonly used in the field of artificial intelligence. The literature shows plenty of methods, which allows us to generate them, for example, inverse cumulative density function method. Some of the ways are based on chaotic projection. The chaotic methods of generating random variables are concerned with mainly continuous random variables. This article presents the method of generating values from discrete probability distributions with the use of properly constructed piece-wise linear chaotic map. This method is based on a properly constructed discrete dynamical system with chaotic behavior. Successive probability values cover the unit interval and the corresponding random variable values are assigned to the determined subintervals. In the next step, a piece-wise linear map on the subintervals is constructed. In the course of iterations of the chaotic map, consecutive values from a given discrete distribution are derived. The method is presented on the example of Bernoulli distribution. Furthermore, an analysis of the discussed example is conducted and shows that the presented method is the fastest of all analyzed methods.

scholarly journals Classroom note: An inductive derivation of Stirling numbers of the second kind and their applications in statistics

1997 ◽  
Vol 1 (2) ◽  
pp. 151-157 ◽  
Author(s):  
Anwar H. Joarder ◽  
Munir Mahmood
Keyword(s):  
Probability Distributions ◽  
Stirling Numbers ◽  
Higher Order ◽  
Inductive Method ◽  
Higher Order Moments ◽  
Discrete Probability ◽  
Discrete Probability Distributions

An inductive method has been presented for finding Stirling numbers of the second kind. Applications to some discrete probability distributions for finding higher order moments have been discussed.

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