scholarly journals Application of the Negative Binomial/Pascal Distribution in Probability Theory to Electrochemical Processes

10.5772/33946 ◽  
2012 ◽  
Author(s):  
Thomas Z.
Keyword(s):  
Probability Theory ◽  
Negative Binomial ◽  
Electrochemical Processes ◽  
Pascal Distribution

Sums of random variables having the modified geometric distribution by application to two-person games

1978 ◽  
Vol 10 (3) ◽  
pp. 647-665 ◽  
Author(s):  
M. J. Phillips
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Geometric Distribution ◽  
Random Variables ◽  
Sums Of Random Variables ◽  
Pascal Distribution ◽  
Person Game ◽  
Independent And Identically Distributed

The distribution of a fixed sum of independent and identically distributed random variables with the modified geometric distribution is the same as the distribution obtained by the compounding by a binomial distribution of either a negative binomial distribution or a Pascal distribution. This result can be used to obtain three summations for the game score probabilities of a two-person game, and leads to the consideration of various ways of dividing up the trials of the game. The game score probabilities are then used to consider the ‘fairness’ of four games and to analyse various methods of ‘setting’ (or ‘tie-breaking’) the games.

Sums of random variables having the modified geometric distribution by application to two-person games

1978 ◽  
Vol 10 (03) ◽  
pp. 647-665
Author(s):  
M. J. Phillips
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Geometric Distribution ◽  
Random Variables ◽  
Sums Of Random Variables ◽  
Pascal Distribution ◽  
Person Game ◽  
Independent And Identically Distributed

The distribution of a fixed sum of independent and identically distributed random variables with the modified geometric distribution is the same as the distribution obtained by the compounding by a binomial distribution of either a negative binomial distribution or a Pascal distribution. This result can be used to obtain three summations for the game score probabilities of a two-person game, and leads to the consideration of various ways of dividing up the trials of the game. The game score probabilities are then used to consider the ‘fairness’ of four games and to analyse various methods of ‘setting’ (or ‘tie-breaking’) the games.

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