raylpdf

Rayleigh probability density function

Syntax

p = raylpdf(x,b)

Description

p = raylpdf(x,b) returns the Rayleigh probability density function (pdf) with the scale parameter b, evaluated at the values in x.

Examples

Compute and Plot Rayleigh Probability Density Function

Compute the Rayleigh probability density function (pdf) with the scale parameter b=0.5 for values between x=0 and x=2.

x = 0:0.01:2;
p = raylpdf(x,0.5);

Plot the pdf.

figure;
plot(x,p)
grid on
xlabel("x")
ylabel("p")

Input Arguments

x — Values at which to evaluate Rayleigh pdf

nonnegative scalar value | array of nonnegative scalar values

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

To evaluate the pdf at multiple values, specify x as an array. To evaluate the pdfs of multiple distributions, specify b as an array. If x and b are both arrays, they must have the same size. If only x or b is an array, raylpdf expands the other input argument into a constant array of the same size as the array input. Each element in p is the pdf value of the distribution specified by the corresponding element in b, evaluated at the corresponding element in x.

Data Types: single | double

b — Scale parameter

1 (default) | positive scalar value | array of positive scalar values

Scale parameter, specified as a positive scalar value or an array of positive scalar values.

To evaluate the pdf at multiple values, specify x as an array. To evaluate the pdfs of multiple distributions, specify b as an array. If x and b are both arrays, they must have the same size. If only x or b is an array, raylpdf expands the other input argument into a constant array of the same size as the array input. Each element in p is the pdf value of the distribution specified by the corresponding element in b, evaluated at the corresponding element in x.

Data Types: single | double

Output Arguments

p — Rayleigh pdf values

scalar value | array of scalar values

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

More About

Rayleigh pdf

The Rayleigh pdf is

$$y=f(x|b)=\frac{x}{b^2}{e}^{\left(\frac{-x^2}{2b^2}\right)}$$

for x ≥ 0. For more information, see Rayleigh Distribution.

Alternative Functionality

• raylpdf is a function specific to the Rayleigh distribution. Statistics and Machine Learning Toolbox™ also offers the generic function pdf, which supports various probability distributions. To use pdf, create a RayleighDistribution 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 raylpdf 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