Main Content

# wblpdf

Weibull probability density function

## Syntax

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

## Description

example

````y = wblpdf(x)` returns the probability density function (pdf) of the Weibull distribution with unit parameters, evaluated at the values in `x`.```

example

````y = wblpdf(x,a)` returns the pdf of the Weibull distribution with scale parameter `a` and unit shape, evaluated at the values in `x`. This is equivalent to the pdf of the exponential distribution.```

example

````y = wblpdf(x,a,b)` returns the pdf of the Weibull distribution with scale parameter `a` and shape parameter `b`, evaluated at the values in `x`.```

## Examples

collapse all

Compute the density of the observed value `3` in the Weibull distribution unit scale and shape.

`y1 = wblpdf(3)`
```y1 = 0.0498 ```

Compute the density of the observed value `3` in the Weibull distributions with scale parameter `2` and shape parameters `1` through `5`.

`y2 = wblpdf(3,2,1:5)`
```y2 = 1×5 0.1116 0.1581 0.1155 0.0427 0.0064 ```

The exponential distribution with parameter `mu` is a special case of the Weibull distribution, where `a = mu` and `b = 1`.

Compute the density of sample observations in the exponential distributions with means `1` through `5` using `expcdf`.

```x = 0.2:0.2:1; mu = 1:5; y1 = exppdf(x,mu)```
```y1 = 1×5 0.8187 0.4094 0.2729 0.2047 0.1637 ```

Compute the density of the same sample observations using `wblpdf` where the scale parameter is equal to `mu` and the shape parameter is `1`.

`y2 = wblpdf(x,mu)`
```y2 = 1×5 0.8187 0.4094 0.2729 0.2047 0.1637 ```

The two functions return the same values.

## Input Arguments

collapse all

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, `wblpdf` 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`

Scale parameter of the Weibull distribution, specified as a positive scalar value or an array of positive 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, `wblpdf` 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 2 3 5]`

Data Types: `single` | `double`

Shape parameter of the Weibull distribution, specified as a positive scalar value or an array of positive 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, `wblpdf` 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 2 2]`

Data Types: `single` | `double`

## Output Arguments

collapse all

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

collapse all

### Weibull pdf

The Weibull distribution is a two-parameter family of curves. The parameters a and b are scale and shape, respectively.

The Weibull pdf is

`$f\left(x|a,b\right)=\frac{b}{a}{\left(\frac{x}{a}\right)}^{b-1}{e}^{-{\left(x/a\right)}^{b}}.$`

Some instances refer to the Weibull distribution with a single parameter, which corresponds to `wblpdf` with a = 1.

For more information, see Weibull Distribution.

## Alternative Functionality

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

## See Also

### Topics

Introduced before R2006a

Download ebook