unifcdf

Continuous uniform cumulative distribution function

Syntax

p = unifcdf(x,a,b)

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

Description

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.

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

Calculate Uniform Distribution CDF

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 Complement of Uniform CDF

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

x — Values at which to evaluate cdf

numeric scalar | numeric vector | numeric array

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

a — Lower endpoint

numeric scalar | numeric vector | numeric array

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

b — Upper endpoint

numeric scalar | numeric vector | numeric array

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

p — Cdf values

nonnegative scalar | nonnegative vector | nonnegative array

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

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

The indicator function $$I_{[a.b]}(x)$$ ensures that x only adopts values in the range [a, b].

Data Types: single | double

Alternative Functionality

• unifcdf is a function specific to the continuous uniform distribution. Statistics and Machine Learning Toolbox™ also offers the generic function cdf, which supports various probability distributions. To use cdf, 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 unifcdf is faster than the generic function cdf.

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced before R2006a