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See the recommended documentation of this function

# cdfpoi

cumulative distribution function poisson distribution

### Syntax

```[P,Q]=cdfpoi("PQ",S,Xlam)
[S]=cdfpoi("S",Xlam,P,Q)
[Xlam]=cdfpoi("Xlam",P,Q,S);```

### Arguments

P,Q,S,Xlam

four real vectors of the same size.

P,Q (Q=1-P)

The cumulation from 0 to S of the poisson density. Input range: [0,1].

S

Matrix of integers. Upper limit of cumulation of the Poisson. Input range: [0, +infinity). Search range: [0,1E300]

Xlam

Mean of the Poisson distribution. Input range: [0, +infinity). Search range: [0,1E300]

### Description

Calculates any one parameter of the Poisson distribution given values for the others.

Formula 26.4.21 of Abramowitz and Stegun, Handbook of Mathematical Functions (1966) is used to reduce the computation of the cumulative distribution function to that of computing a chi-square, hence an incomplete gamma function.

Cumulative distribution function (P) is calculated directly. Computation of other parameters involve a search for a value that produces the desired value of P. The search relies on the monotonicity of P with the other parameter.

From DCDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters (February, 1994) Barry W. Brown, James Lovato and Kathy Russell. The University of Texas.

### Examples

In the following example, we compute the probability of the event `S=2` for the Poisson distribution function with `Xlam=3`.

```S = 2;
Xlam = 3;
// Expected : P = 0.4231901 and Q = 1-P
[P, Q] = cdfpoi("PQ", S, Xlam)```

• cdfbet — cumulative distribution function Beta distribution
• cdfbin — cumulative distribution function Binomial distribution
• cdfchi — cumulative distribution function chi-square distribution
• cdfchn — cumulative distribution function non-central chi-square distribution
• cdff — cumulative distribution function Fisher distribution
• cdffnc — cumulative distribution function non-central f-distribution
• cdfgam — cumulative distribution function gamma distribution
• cdfnbn — cumulative distribution function negative binomial distribution
• cdfnor — cumulative distribution function normal distribution
• cdft — cumulative distribution function Student's T distribution
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