# unifpdf

Continuous uniform probability density function

## Syntax

``y = unifpdf(x)``
``y = unifpdf(x,a,b)``

## Description

example

````y = unifpdf(x)` returns the probability density function (pdf) of the standard uniform distribution, evaluated at the values in `x`.```

example

````y = unifpdf(x,a,b)` returns the pdf of the continuous uniform distribution on the interval [`a`, `b`], evaluated at the values in `x`.```

## Examples

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The pdf of the standard uniform distribution is constant on the interval `[0,1]`.

Compute the pdf of 0.2, 0.4,...,1 in the standard uniform distribution.

```x = 0.2:0.2:1; y = unifpdf(x)```
```y = 1×5 1 1 1 1 1 ```

If `x` is not between `a` and `b`, `unifpdf` returns `0`.

Compute the pdf of `1` through `5` in the continuous uniform distribution on the interval `[2,4]`.

```x2 = 1:5; unifpdf(x2,2,4)```
```ans = 1×5 0 0.5000 0.5000 0.5000 0 ```

If the parameter `a` is larger than `b`, `unifpdf` returns `NaN` regardless of the `x` input.

`unifpdf(5,10,1)`
```ans = NaN ```

## Input Arguments

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Values at which to evaluate the pdf, specified as a nonnegative scalar value or an array of nonnegative scalar values.

• To evaluate the pdf at multiple values, specify `x` using an array.

• To evaluate the pdfs of multiple distributions, specify `a` and `b` using arrays.

If one or more of the input arguments `x`, `a`, and `b` are arrays, then the array sizes must be the same. In this case, `unifpdf` expands each scalar input into a constant array of the same size as the array inputs. Each element in `y` is the pdf value of the distribution specified by the corresponding elements in `a` and `b`, evaluated at the corresponding element in `x`.

Example: `[3 4 7 9]`

Data Types: `single` | `double`

Lower endpoint of the uniform distribution, specified as a scalar value or an array of scalar values.

• To evaluate the pdf at multiple values, specify `x` using an array.

• To evaluate the pdfs of multiple distributions, specify `a` and `b` using arrays.

If one or more of the input arguments `x`, `a`, and `b` are arrays, then the array sizes must be the same. In this case, `unifpdf` expands each scalar input into a constant array of the same size as the array inputs. Each element in `y` is the pdf value of the distribution specified by the corresponding elements in `a` and `b`, evaluated at the corresponding element in `x`.

Example: `[0 -1 7 9]`

Data Types: `single` | `double`

Upper endpoint of the uniform distribution, specified as a scalar value or an array of scalar values.

• To evaluate the pdf at multiple values, specify `x` using an array.

• To evaluate the pdfs of multiple distributions, specify `a` and `b` using arrays.

If one or more of the input arguments `x`, `a`, and `b` are arrays, then the array sizes must be the same. In this case, `unifpdf` expands each scalar input into a constant array of the same size as the array inputs. Each element in `y` is the pdf value of the distribution specified by the corresponding elements in `a` and `b`, evaluated at the corresponding element in `x`.

Example: `[1 1 10 10]`

Data Types: `single` | `double`

## Output Arguments

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pdf values evaluated at the values in `x`, returned as a scalar value or an array of scalar values. `y` is the same size as `x`, `a`, and `b` after any necessary scalar expansion. Each element in `y` is the pdf value of the distribution specified by the corresponding elements in `a` and `b`, evaluated at the corresponding element in `x`.

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### Continuous Uniform pdf

The continuous uniform distribution is a two-parameter family of curves with a constant pdf on its interval of support, . The parameters a and b are the endpoints of the interval.

The continuous uniform pdf is

`$y=f\left(x|a,b\right)=\frac{1}{b-a}{I}_{\left[a,b\right]}\left(x\right).$`

The standard uniform distribution occurs when a = 0 and b = 1.

## Alternative Functionality

• `unifpdf` is a function specific to the continuous uniform distribution. Statistics and Machine Learning Toolbox™ also offers the generic function `pdf`, which supports various probability distributions. To use `pdf`, create a `UniformDistribution` probability distribution object and pass the object as an input argument or specify the probability distribution name and its parameters. Note that the distribution-specific function `unifpdf` is faster than the generic function `pdf`.

• Use the Probability Distribution Function app to create an interactive plot of the cumulative distribution function (cdf) or probability density function (pdf) for a probability distribution.