# unifcdf

Continuous uniform cumulative distribution function

## Syntax

``p = unifcdf(x,a,b)``
``p = unifcdf(x,a,b,"upper")``

## Description

example

````p = unifcdf(x,a,b)` returns the continuous uniform cumulative distribution function (cdf) at each value in `x` using the corresponding lower endpoint `a` and upper endpoint `b`.```

example

````p = unifcdf(x,a,b,"upper")` returns the complement of the continuous uniform cdf using an algorithm that more accurately computes the extreme upper tail probabilities.```

## Examples

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Calculate the probability that an observation from the standard uniform distribution will be less than 0.75. The standard uniform distribution corresponds to `a = 0` and `b = 1`.

`p = unifcdf(0.75)`
```p = 0.7500 ```

The probability of an observation being less than 0.75 is 0.75.

Calculate the probability that an observation from a uniform distribution with `a` = `-1` and `b` = `1` will be less than 0.5.

`p = unifcdf(0.5,-1,1)`
```p = 0.7500 ```

The probability of an observation being less than 0.5 is 0.75.

Calculate the probability of an observation from the standard uniform distribution being greater than 0.75.

`p = unifcdf(0.75,"upper")`
```p = 0.2500 ```

The probability of an observation being greater than 0.75 is 0.25.

## Input Arguments

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Values at which to evaluate the continuous uniform cdf, specified as a numeric scalar, vector, or array.

To evaluate the cdf at multiple values, specify `x` with an array.

If `x` is a vector or an array it must have the same size as `a` and `b`. If `x` is a scalar, the function expands `x` to a constant matrix that has the same dimensions as `a` and `b`.

Example: `[0.5 0.75 1]`

Data Types: `single` | `double`

Lower endpoint of the continuous uniform cdf, specified as a numeric scalar, vector, or array.

To evaluate the cdfs of multiple distributions specify `a` with an array.

If `a` is a vector or an array it must have the same size as `x` and `b`. If `a` is a scalar, the function expands `a` to a constant matrix that has the same dimensions as `x` and `b`.

Example: `[0 -1 7 9]`

Data Types: `single` | `double`

Upper endpoint of the continuous uniform cdf, specified as a numeric scalar, vector, or array.

To evaluate the cdfs of multiple distributions specify `b` with an array.

If `b` is a vector or an array it must have the same size as `x` and `a`. If `b` is a scalar, the function expands `b` to a constant matrix that has the same dimensions as `x` and `a`.

Example: `[1 1 10 12]`

Data Types: `single` | `double`

## Output Arguments

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Cdf values evaluated at each point in `x`, returned as a nonnegative scalar, vector, or array with elements in the range [0,1]. The output `p` is the same size as `x`, `a`, and `b` after any necessary scalar expansion. Each element in `p` is the cdf value of the distribution specified by the corresponding elements in `a` and `b`, evaluated at the corresponding element in `x`.

The uniform cdf is

`$p=F\left(x|a,b\right)=\frac{x-a}{b-a}{I}_{\left[a,b\right]}\left(x\right)$`

Data Types: `single` | `double`

## Version History

Introduced before R2006a