# unifinv

Continuous uniform inverse cumulative distribution function

## Description

example

x = unifinv(p,a,b) computes the inverse of the continuous uniform cumulative distribution function (cdf) with lower endpoint a and upper endpoint b, at the corresponding probabilities in p.

## Examples

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Calculate the median of the standard uniform distribution.

median = unifinv(0.5)
median = 0.5000

The median (50th percentile) of the standard uniform distribution is 0.5.

Calculate the 75th and 99th percentiles of a uniform distribution with a = -1 and b = 1.

a = -1;
b =  1;
P = [0.75 0.99];
X = unifinv(P,a,b)
X = 1×2

0.5000    0.9800

The 75th percentile of the uniform distribution is 0.5 and the 99th percentile is 0.98.

## Input Arguments

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Probability for which unifinv calculates the inverse cdf, specified as a nonnegative scalar, vector, or array with elements in the range [0,1].

To evaluate the inverse cdf at multiple probabilities specify p with an array.

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

Example: [0.1 0.5 0.75 0.99]

Data Types: single | double

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

To evaluate the inverse cdf of multiple distributions, specify a with an array.

If a is a vector or an array it must have the same size as p and b. If a is a scalar, the function expands a to a constant matrix that has the same dimensions as p 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 inverse cdf of multiple distributions, specify b with an array.

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

Example: [1 1 10 12]

Data Types: single | double

## Output Arguments

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Inverse of the uniform cdf, specified as a numeric scalar, vector, or array.

Each element in x is the inverse cdf value of the distribution specified by the corresponding elements in a and b, evaluated at the corresponding probabilities in p.

The inverse of the uniform cdf is

$x={F}^{-1}\left(p|a,b\right)=a+p\left(a-b\right){I}_{\left[0,1\right]}\left(p\right)$

Data Types: single | double

## Version History

Introduced before R2006a