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8.4.6 The Poisson distribution

The probability density function for the Poisson distribution: poisson

Recall that for the Poisson distribution with parameter λ, the probability of a non-negative integer k is e−λλk/k!. This distribution has mean λ and variance λ.

The poisson command gives the density function for the Poisson distribution.

Example

Input:

poisson(10.0,9)

Output:

0.125110035721

The cumulative distribution function for the Poisson distribution: poisson_cdf

The poisson_cdf command computes the cumulative distribution function for the Poisson distribution.

Examples

The inverse distribution function for the Poisson distribution: poisson_icdf

The poisson_icdf command finds the inverse distribution function for the Poisson distribution.

Example

Input:

poisson_icdf(10.0,0.975)

Output:

17

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