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| Meta Title | betapdf - Beta probability density function - MATLAB |
| Meta Description | This MATLAB function 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. |
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| Boilerpipe Text | Beta probability density function
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]
.
example
Examples
collapse all
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
collapse all
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
.
Example:
[-1,0,3,4]
Data Types:
single
|
double
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
.
Example:
[0.75,0.5;10,100]
Data Types:
single
|
double
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
.
Example:
[0.2,100;4,7]
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
The beta probability density function for a given value
x
and given
pair of parameters
a
and
b
is
where
B
( · ) is the Beta function. The uniform distribution on
(0 1) is a degenerate case of the beta pdf where
a
= 1 and
b
= 1.
Version History
Introduced before R2006a
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- betapdf
- On this page
- [Syntax](https://www.mathworks.com/help/stats/betapdf.html#d126e173221)
- [Description](https://www.mathworks.com/help/stats/betapdf.html#description)
- [Examples](https://www.mathworks.com/help/stats/betapdf.html#brx09qc-125)
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- [x](https://www.mathworks.com/help/stats/betapdf.html#mw_946f7fea-787c-4cbe-9877-29b1e3d65758)
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- [y](https://www.mathworks.com/help/stats/betapdf.html#mw_eed23927-a4f8-45c7-a0b4-d66c54620230)
- [More About](https://www.mathworks.com/help/stats/betapdf.html#mw_93fdebdc-87a4-4cc2-b1d6-ef10714fa0f7)
- [Beta Distribution](https://www.mathworks.com/help/stats/betapdf.html#mw_0b432020-af36-44a6-9f6b-57fc781b98b3)
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Main Content
# betapdf
Beta probability density function
[collapse all in page]()
## 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]`.
[example](https://www.mathworks.com/help/stats/betapdf.html#mw_4f99fcd9-a671-494c-9879-fbd62aa18ee7)
## Examples
[collapse all]()
### Beta Distribution pdf
[Open Live Script](matlab:openExample\('stats/BetaDistributionPdfExample'\))
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
[collapse all]()
### `x` — Values at which to evaluate pdf scalar value \| array of scalar values
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`](https://www.mathworks.com/help/stats/betapdf.html#mw_96f62ccf-4145-473e-ae3f-4d61a7400a00) and [`b`](https://www.mathworks.com/help/stats/betapdf.html#mw_d87df24d-335b-4a8d-a7ef-e73ceaa6526b) 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`](https://www.mathworks.com/help/stats/betapdf.html#mw_eed23927-a4f8-45c7-a0b4-d66c54620230) is the pdf value of the distribution specified by the corresponding elements in `a` and `b`, evaluated at the corresponding element in `x`.
**Example:** `[-1,0,3,4]`
**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`](https://www.mathworks.com/help/stats/betapdf.html#mw_946f7fea-787c-4cbe-9877-29b1e3d65758) using an array. To evaluate the pdfs of multiple distributions, specify `a` and [`b`](https://www.mathworks.com/help/stats/betapdf.html#mw_d87df24d-335b-4a8d-a7ef-e73ceaa6526b) 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`](https://www.mathworks.com/help/stats/betapdf.html#mw_eed23927-a4f8-45c7-a0b4-d66c54620230) is the pdf value of the distribution specified by the corresponding elements in `a` and `b`, evaluated at the corresponding element in `x`.
**Example:** `[0.75,0.5;10,100]`
**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`](https://www.mathworks.com/help/stats/betapdf.html#mw_946f7fea-787c-4cbe-9877-29b1e3d65758) using an array. To evaluate the pdfs of multiple distributions, specify [`a`](https://www.mathworks.com/help/stats/betapdf.html#mw_96f62ccf-4145-473e-ae3f-4d61a7400a00) 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`](https://www.mathworks.com/help/stats/betapdf.html#mw_eed23927-a4f8-45c7-a0b4-d66c54620230) is the pdf value of the distribution specified by the corresponding elements in `a` and `b`, evaluated at the corresponding element in `x`.
**Example:** `[0.2,100;4,7]`
**Data Types:** `single` \| `double`
## Output Arguments
[collapse all]()
### `y` — pdf values scalar value \| array of scalar values
pdf values, evaluated at the values in [`x`](https://www.mathworks.com/help/stats/betapdf.html#mw_946f7fea-787c-4cbe-9877-29b1e3d65758), returned as a scalar value or an array of scalar values. `y` is the same size as `x`, [`a`](https://www.mathworks.com/help/stats/betapdf.html#mw_96f62ccf-4145-473e-ae3f-4d61a7400a00), and [`b`](https://www.mathworks.com/help/stats/betapdf.html#mw_d87df24d-335b-4a8d-a7ef-e73ceaa6526b) 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]()
### Beta Distribution
The beta probability density function for a given value *x* and given pair of parameters *a* and *b* is
y \= f ( x \| a , b ) \= 1 B ( a , b ) x a − 1 ( 1 − x ) b − 1 I \[ 0 , 1 \] ( x )
where *B*( · ) is the Beta function. The uniform distribution on (0 1) is a degenerate case of the beta pdf where *a* = 1 and *b* = 1.
## Extended Capabilities
[expand all]()
### 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](https://www.mathworks.com/help/parallel-computing/run-matlab-functions-on-a-gpu.html) (Parallel Computing Toolbox).
## Version History
**Introduced before R2006a**
## See Also
[`pdf`](https://www.mathworks.com/help/stats/prob.normaldistribution.pdf.html) \| [`betafit`](https://www.mathworks.com/help/stats/betafit.html) \| [`betainv`](https://www.mathworks.com/help/stats/betainv.html) \| [`betastat`](https://www.mathworks.com/help/stats/betastat.html) \| [`betalike`](https://www.mathworks.com/help/stats/betalike.html) \| [`betarnd`](https://www.mathworks.com/help/stats/betarnd.html) \| [`betacdf`](https://www.mathworks.com/help/stats/betacdf.html)
### Topics
- [Beta Distribution](https://www.mathworks.com/help/stats/beta-distribution.html)
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| Readable Markdown | Beta probability density function
## 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]`.
[example](https://www.mathworks.com/help/stats/betapdf.html#mw_4f99fcd9-a671-494c-9879-fbd62aa18ee7)
## Examples
collapse all
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
collapse all
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`](https://www.mathworks.com/help/stats/betapdf.html#mw_96f62ccf-4145-473e-ae3f-4d61a7400a00) and [`b`](https://www.mathworks.com/help/stats/betapdf.html#mw_d87df24d-335b-4a8d-a7ef-e73ceaa6526b) 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`](https://www.mathworks.com/help/stats/betapdf.html#mw_eed23927-a4f8-45c7-a0b4-d66c54620230) is the pdf value of the distribution specified by the corresponding elements in `a` and `b`, evaluated at the corresponding element in `x`.
**Example:** `[-1,0,3,4]`
**Data Types:** `single` \| `double`
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`](https://www.mathworks.com/help/stats/betapdf.html#mw_946f7fea-787c-4cbe-9877-29b1e3d65758) using an array. To evaluate the pdfs of multiple distributions, specify `a` and [`b`](https://www.mathworks.com/help/stats/betapdf.html#mw_d87df24d-335b-4a8d-a7ef-e73ceaa6526b) 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`](https://www.mathworks.com/help/stats/betapdf.html#mw_eed23927-a4f8-45c7-a0b4-d66c54620230) is the pdf value of the distribution specified by the corresponding elements in `a` and `b`, evaluated at the corresponding element in `x`.
**Example:** `[0.75,0.5;10,100]`
**Data Types:** `single` \| `double`
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`](https://www.mathworks.com/help/stats/betapdf.html#mw_946f7fea-787c-4cbe-9877-29b1e3d65758) using an array. To evaluate the pdfs of multiple distributions, specify [`a`](https://www.mathworks.com/help/stats/betapdf.html#mw_96f62ccf-4145-473e-ae3f-4d61a7400a00) 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`](https://www.mathworks.com/help/stats/betapdf.html#mw_eed23927-a4f8-45c7-a0b4-d66c54620230) is the pdf value of the distribution specified by the corresponding elements in `a` and `b`, evaluated at the corresponding element in `x`.
**Example:** `[0.2,100;4,7]`
**Data Types:** `single` \| `double`
## Output Arguments
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pdf values, evaluated at the values in [`x`](https://www.mathworks.com/help/stats/betapdf.html#mw_946f7fea-787c-4cbe-9877-29b1e3d65758), returned as a scalar value or an array of scalar values. `y` is the same size as `x`, [`a`](https://www.mathworks.com/help/stats/betapdf.html#mw_96f62ccf-4145-473e-ae3f-4d61a7400a00), and [`b`](https://www.mathworks.com/help/stats/betapdf.html#mw_d87df24d-335b-4a8d-a7ef-e73ceaa6526b) 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
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The beta probability density function for a given value *x* and given pair of parameters *a* and *b* is
where *B*( · ) is the Beta function. The uniform distribution on (0 1) is a degenerate case of the beta pdf where *a* = 1 and *b* = 1.
## Version History
**Introduced before R2006a**
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