scholarly journals A Markov-binomial distribution

2008 ◽  
Vol 2 (1) ◽  
pp. 38-50 ◽  
Author(s):  
E. Omey ◽  
J. Santos ◽  
Gulck Van
Keyword(s):  
Binomial Distribution ◽  
Markov Binomial Distribution

Two limit theorems for Markov binomial distribution

2015 ◽  
Vol 55 (3) ◽  
pp. 451-463 ◽  
Author(s):  
Jūratė Šliogere ◽  
Vydas Čekanavičius
Keyword(s):  
Binomial Distribution ◽  
Limit Theorems ◽  
Markov Binomial Distribution

On the limit of the Markov binomial distribution

1981 ◽  
Vol 18 (04) ◽  
pp. 937-942 ◽  
Author(s):  
Y. H. Wang
Keyword(s):  
Limit Distribution ◽  
Binomial Distribution ◽  
Transition Matrix ◽  
Bernoulli Sequence ◽  
Markov Binomial Distribution

Let X 1 X 2, · ·· be a Markov Bernoulli sequence with initial probabilities p of success and q = 1 – p of failure, and probabilities 1 – (1 – π) p, (1 – π) p in the first row and (1 – π) (1 – p), (1 – π) p + πin the second row of the transition matrix. If we define Sn = Σ i=1 n Xi , then the limit distribution P{Sn = k} is obtained when n →∞, np →λ.

scholarly journals Multimodality of the Markov Binomial Distribution

2011 ◽  
Vol 48 (04) ◽  
pp. 938-953 ◽  
Author(s):  
Michel Dekking ◽  
Derong Kong
Keyword(s):  
Binomial Distribution ◽  
Reactive Transport ◽  
Transport Model ◽  
Sufficient Conditions ◽  
Mass Function ◽  
Closed Form Expression ◽  
Probability Mass Function ◽  
Markov Binomial Distribution ◽  
Probability Mass ◽  
Necessary And Sufficient

We study the shape of the probability mass function of the Markov binomial distribution, and give necessary and sufficient conditions for the probability mass function to be unimodal, bimodal, or trimodal. These are useful to analyze the double-peaking results of a reactive transport model from the engineering literature. Moreover, we give a closed-form expression for the variance of the Markov binomial distribution, and expressions for the mean and the variance conditioned on the state at time n.

scholarly journals Multimodality of the Markov Binomial Distribution

2011 ◽  
Vol 48 (4) ◽  
pp. 938-953 ◽  
Author(s):  
Michel Dekking ◽  
Derong Kong
Keyword(s):  
Binomial Distribution ◽  
Reactive Transport ◽  
Transport Model ◽  
Sufficient Conditions ◽  
Mass Function ◽  
Closed Form Expression ◽  
Probability Mass Function ◽  
Markov Binomial Distribution ◽  
Probability Mass ◽  
Necessary And Sufficient

We study the shape of the probability mass function of the Markov binomial distribution, and give necessary and sufficient conditions for the probability mass function to be unimodal, bimodal, or trimodal. These are useful to analyze the double-peaking results of a reactive transport model from the engineering literature. Moreover, we give a closed-form expression for the variance of the Markov binomial distribution, and expressions for the mean and the variance conditioned on the state at time n.

On the limit of the Markov binomial distribution

1981 ◽  
Vol 18 (4) ◽  
pp. 937-942 ◽  
Author(s):  
Y. H. Wang
Keyword(s):  
Limit Distribution ◽  
Binomial Distribution ◽  
Transition Matrix ◽  
Bernoulli Sequence ◽  
Markov Binomial Distribution

Let X1X2, · ·· be a Markov Bernoulli sequence with initial probabilities p of success and q = 1 – p of failure, and probabilities 1 – (1 – π) p, (1 – π) p in the first row and (1 – π) (1 – p), (1 – π) p + πin the second row of the transition matrix. If we define Sn = Σi=1nXi, then the limit distribution P{Sn = k} is obtained when n →∞, np →λ.

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