betapdf

Beta probability density function

Syntax

y = betapdf(x,a,b)

Description

y = betapdf(x,a,b) returns the probability density function (pdf) of the beta distribution at each of the values in x using the corresponding parameters in a and b. Values in x must be between [0,1].

Examples

Beta Distribution pdf

Compute the pdf values evaluated at the values in x for the beta distribution with first shape parameter a and second shape parameter b.

x = 0.2:0.2:1;
a = 2;
b = 1;
y = betapdf(x,a,b)

y = 1×5

    0.4000    0.8000    1.2000    1.6000    2.0000

Compute the pdf values evaluated at 0.1 for various beta distributions with different first shape parameter values.

a = [1,2,3];
b = 1;
y = betapdf(0.1,a,b)

y = 1×3

    1.0000    0.2000    0.0300

Input Arguments

x — Values at which to evaluate pdf

scalar value in the range [0,1] | array of scalar values in the range [0,1]

Values at which to evaluate the pdf, specified as a scalar value or an array of scalar values in the range [0,1].

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, betapdf 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.

Data Types: single | double

a — First shape parameter

positive scalar value | numeric array of positive values

First shape parameter, specified as a positive scalar value or a numeric array of positive 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, betapdf 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.

Data Types: single | double

b — Second shape parameter

positive scalar value | numeric array of positive values

Second shape parameter, specified as a positive scalar value or a numeric array of positive 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, betapdf 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.

Data Types: single | double

Output Arguments

y — pdf values

scalar value | array of scalar values

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.

More About

Beta Distribution

The beta probability density function for a given value x and a given pair of parameters a and b is

$$y=f(x|a,b)=\frac{1}{B(a,b)}{x}^{a-1}{(1-x)}^{b-1}{I}_{\left[0,1\right]}(x)$$

where B( · ) is the Beta function. The indicator function I_[0,1](x) ensures that only values of x in the range [0,1] have nonzero probability. The uniform distribution on (0 1) is a degenerate case of the beta pdf where a=1 and b=1.

Alternative Functionality

• betapdf is a function specific to the beta distribution. Statistics and Machine Learning Toolbox™ also offers the generic function pdf, which supports various probability distributions. To use pdf, create a BetaDistribution 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 betapdf is faster than the generic function pdf.

• 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