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# MultivariatePoissonDistribution

 MultivariatePoissonDistributionrepresents a multivariate Poisson distribution with mean vector .
• The multivariate Poisson distribution corresponds to the distribution of where is Poisson distributed with mean .
• The parameters can be any positive numbers.
Probability density function:
Cumulative distribution function:
Mean and variance:
Covariance matrix:
Probability density function:
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Cumulative distribution function:
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Mean and variance:
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Covariance matrix:
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 Scope   (8)
Generate a set of pseudorandom vectors that are Poisson distributed:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Goodness-of-fit test:
Skewness for each component depends on and :
Kurtosis for each component depends on and :
Correlation:
Different mixed moments for a bivariate Poisson distribution:
Mixed central moments:
Mixed factorial moments:
Mixed cumulants:
Closed form for a symbolic order:
Hazard function:
Marginal distributions:
 Applications   (2)
In clinical studies, medicine A on average caused an adverse reaction in 12 people per 100000 and medicine B in 9 people per 100000. It has also been determined that while some people will show no adverse reaction to medicine A or B alone, the combination of both caused an adverse reaction on average in 1 person per 500000. Assuming a Poisson model, find the adverse reaction distribution in the population of 10000:
Find the probability that there are at most 3 adverse reactions to medicine A and at most 4 adverse reactions to medicine B:
A university campus lies completely within twin cities A and B. On a given day there are, on average, 10 car accidents on campus; outside of campus there are 5 more in city A, and 10 more in city B. Find the joint distribution of the number of accidents in the twin cities:
Probability density function:
Find the average number of accidents in each city:
Find the average total number of accidents in the twin cities:
Find the probability that on a given day there are more accidents in city A than in city B:
Use a random sample to find the probability that there are at least 12 accidents per day in the twin cities:
Multivariate Poisson distribution is closed under addition:
One-dimensional multivariate Poisson distribution is a PoissonDistribution:
The components are correlated for all allowed values of parameters:
Multivariate Poisson cannot be represented as a product of its marginal distributions:
Find marginal distributions:
Find ProductDistribution of marginal distributions:
Compare covariance matrices:
Compare PDFs:
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