Specifying a joint space- and time-lag using a bivariate Poisson distribution

Suppose that shocks arrive and act on a system according to a Poisson distribution with mean rate of arrival equal to λ shock(s) per unit time. A δ-shock failure model is proposed in this paper, which assumes that when a system is acted on by a shock, it will recover fully in time δ(>0), and after that it will function as if no shock had occurred before. If the time lag between two successive shocks is less than δ, the second shock will cause failure of the system. Theoretical expressions related to the distribution of the failure time of the system are derived. These results can be used to optimize the design of a system from a costing point of view.

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On a characterization of Poisson distributions

Journal of Applied Probability ◽

10.2307/3212622 ◽

1972 ◽

Vol 9 (4) ◽

pp. 852-856 ◽

Cited By ~ 10

Author(s):

J. Aczél

Keyword(s):

Poisson Distribution ◽

Random Variables ◽

Mutual Dependence ◽

Binomial Distributions ◽

Destructive Process ◽

Poisson Distributions ◽

Bivariate Poisson Distribution

The conjecture pronounced at the end of the paper of Srivastava and Srivastava (1970) is proved in this paper. It gives the following characterization of (bivariate) Poisson distributions. Suppose that items of two types have been observed certain numbers of times, but these original observations have been reduced due to a destructive process which is the product of two binomial distributions and that the probabilities of these reduced numbers are the same whether damaged or undamaged. Then the original random variables had a bivariate Poisson distribution with zero mutual dependence coefficient.

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SMOOTH TESTS FOR THE BIVARIATE POISSON DISTRIBUTION

Australian Journal of Statistics ◽

10.1111/j.1467-842x.1995.tb00656.x ◽

1995 ◽

Vol 37 (2) ◽

pp. 233-245 ◽

Cited By ~ 5

Author(s):

J.C.W. Rayner ◽

D.J. Best

Keyword(s):

Poisson Distribution ◽

Smooth Tests ◽

Bivariate Poisson Distribution

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The New Bivariate Conway-Maxwell-Poisson Distribution Obtained by the Crossing Method

International Journal of Statistics and Probability ◽

10.5539/ijsp.v9n6p1 ◽

2020 ◽

Vol 9 (6) ◽

pp. 1

Author(s):

Rufin Bidounga ◽

Evrand Giles Brunel Mandangui Maloumbi ◽

Réolie Foxie Mizélé Kitoti ◽

Dominique Mizère

Keyword(s):

Probability Distribution ◽

Poisson Distribution ◽

Generalized Linear Models ◽

Generating Functions ◽

Linear Models ◽

Double Series ◽

Bivariate Distribution ◽

Probability Generating Functions ◽

Bivariate Poisson Distribution ◽

Bivariate Function

Kimberly et al. had proposed in 2016 a bivariate function as a bivariate Conway-Maxwell-Poisson distribution (COM-Poisson) using the generalized bivariate Poisson distribution and the probability generating functions of the follow distributions: bivariate bernoulli, bivariate Poisson, bivariate geometric and bivariate binomial. By examining this paper we have shown that this bivariate function is constant and it double series is divergent, when it should have been 1. To overcome this deadlock, we propose a new bivariate Conway-Maxwell-Poisson distribution which is definetely a probability distribution based on the crossing method, method highlighted by Elion et al. in 2016 and revisited by Batsindila et al. and Mandangui et al. in 2019. And this is the purpose of this paper. To this bivariate distribution is attached two generalized linear models (GLM) whose resolution allows us to highlight, not only the independence between the variables forming the couple, but also the effect of the factors (or predictors) on these variables. The resulting correlation is negative, zero or positive depending on the values of a parameter; in particular for the bivariate Poisson distribution according to Berkhout and Plug. A simulation of data will be given at the end of the article to illustrate the model.

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