# geostat

Geometric mean and variance

## Syntax

```[m,v] = geostat(p) ```

## Description

`[m,v] = geostat(p)` returns the mean `m` and variance `v` of a geometric distribution with corresponding probability parameters in `p`. `p` can be a vector, a matrix, or a multidimensional array. The parameters in `p` must lie in the interval `[0,1]`.

## Examples

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Define a probability vector that contains six different parameter values.

`p = 1./(1:6)`
```p = 1×6 1.0000 0.5000 0.3333 0.2500 0.2000 0.1667 ```

Compute the mean and variance of the geometric distribution that corresponds to each value contained in probability vector.

`[m,v] = geostat(1./(1:6))`
```m = 1×6 0 1.0000 2.0000 3.0000 4.0000 5.0000 ```
```v = 1×6 0 2.0000 6.0000 12.0000 20.0000 30.0000 ```

The returned values indicate that, for example, the mean of a geometric distribution with probability parameter p equal to 1/3 is 2, and its variance is 6.

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### Geometric Distribution Mean and Variance

The mean of the geometric distribution is $\text{mean}=\frac{1-p}{p}\text{\hspace{0.17em}},$ and the variance of the geometric distribution is $\mathrm{var}=\frac{1-p}{{p}^{2}}\text{\hspace{0.17em}},$ where p is the probability of success.