# geoinv

Geometric inverse cumulative distribution function

## Syntax

```x = geoinv(y,p) ```

## Description

`x = geoinv(y,p)` returns the inverse cumulative distribution function (icdf) of the geometric distribution at each value in `y` using the corresponding probabilities in `p`.

`geoinv` returns the smallest positive integer `x` such that the geometric cdf evaluated at `x` is equal to or exceeds `y`. You can think of `y` as the probability of observing `x` successes in a row in independent trials, where `p` is the probability of success in each trial.

`y` and `p` can be vectors, matrices, or multidimensional arrays that all have the same size. A scalar input for `p` or `y` is expanded to a constant array with the same dimensions as the other input. The values in `p` and `y` must lie on the interval `[0,1]`.

## Examples

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Suppose the probability of a five-year-old car battery not starting in cold weather is 0.03. If we want no more than a ten percent chance that the car does not start, what is the maximum number of days in a row that we should try to start the car?

To solve, compute the inverse cdf of the geometric distribution. In this example, a "success" means the car does not start, while a "failure" means the car does start. The probability of success for each trial p equals 0.03, while the probability of observing x failures in a row before observing a success y equals 0.1.

```y = 0.1; p = 0.03; x = geoinv(y,p)```
```x = 3 ```

The returned result indicates that if we start the car three times, there is at least a ten percent chance that it will not start on one of those tries. Therefore, if we want no greater than a ten percent chance that the car will not start, we should only attempt to start it for a maximum of two days in a row.

We can confirm this result by evaluating the cdf at values of x equal to 2 and 3, given the probability of success for each trial p equal to 0.03.

`y2 = geocdf(2,p) % cdf for x = 2`
```y2 = 0.0873 ```
`y3 = geocdf(3,p) % cdf for x = 3`
```y3 = 0.1147 ```

The returned results indicate an 8.7% chance of the car not starting if we try two days in a row, and an 11.5% chance of not starting if we try three days in a row.