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---
title: stats
---
# Descriptive statistics
[TOC]
## `corr` - Pearson correlation of array elements
### Status
Experimental
### Description
Returns the Pearson correlation of the elements of `array` along dimension `dim` if the corresponding element in `mask` is `true`.
The Pearson correlation between two rows (or columns), say `x` and `y`, of `array` is defined as:
```
corr(x, y) = cov(x, y) / sqrt( var(x) * var(y))
```
### Syntax
`result = ` [[stdlib_stats(module):corr(interface)]] `(array, dim [, mask])`
### Class
Generic subroutine
### Arguments
`array`: Shall be a rank-1 or a rank-2 array of type `integer`, `real`, or `complex`. It is an `intent(in)` argument.
`dim`: Shall be a scalar of type `integer` with a value in the range from 1 to `n`, where `n` is the rank of `array`. It is an `intent(in)` argument.
`mask` (optional): Shall be of type `logical` and either a scalar or an array of the same shape as `array`. It is an `intent(in)` argument.
### Return value
If `array` is of rank 1 and of type `real` or `complex`, the result is of type `real` and has the same kind as `array`.
If `array` is of rank 2 and of type `real` or `complex`, the result is of the same type and kind as `array`.
If `array` is of type `integer`, the result is of type `real(dp)`.
If `array` is of rank 1 and of size larger than 1, a scalar equal to 1 is returned. Otherwise, IEEE `NaN` is returned.
If `array` is of rank 2, a rank-2 array with the corresponding correlations is returned.
If `mask` is specified, the result is the Pearson correlation of all elements of `array` corresponding to `true` elements of `mask`. If every element of `mask` is `false`, the result is IEEE `NaN`.
### Example
```fortran
{!example/stats/example_corr.f90!}
```
## `cov` - covariance of array elements
### Status
Experimental
### Description
Returns the covariance of the elements of `array` along dimension `dim` if the corresponding element in `mask` is `true`.
Per default, the covariance is defined as:
```
cov(array) = 1/(n-1) sum_i (array(i) - mean(array) * (array(i) - mean(array)))
```
where `n` is the number of elements.
The scaling can be changed with the logical argument `corrected`. If `corrected` is `.false.`, then the sum is scaled with `n`, otherwise with `n-1`.
### Syntax
`result = ` [[stdlib_stats(module):cov(interface)]] `(array, dim [, mask [, corrected]])`
### Class
Generic subroutine
### Arguments
`array`: Shall be a rank-1 or a rank-2 array of type `integer`, `real`, or `complex`. It is an `intent(in)` argument.
`dim`: Shall be a scalar of type `integer` with a value in the range from 1 to `n`, where `n` is the rank of `array`. It is an `intent(in)` argument.
`mask` (optional): Shall be of type `logical` and either a scalar or an array of the same shape as `array`. It is an `intent(in)` argument.
`corrected` (optional): Shall be a scalar of type `logical`. If `corrected` is `.true.` (default value), the sum is scaled with `n-1`. If `corrected` is `.false.`, then the sum is scaled with `n`. It is an `intent(in)` argument.
### Return value
If `array` is of rank 1 and of type `real` or `complex`, the result is of type `real` corresponding to the type of `array`.
If `array` is of rank 2 and of type `real` or `complex`, the result is of the same type as `array`.
If `array` is of type `integer`, the result is of type `real(dp)`.
If `array` is of rank 1, a scalar with the covariance (that is the variance) of all elements in `array` is returned.
If `array` is of rank 2, a rank-2 array is returned.
If `mask` is specified, the result is the covariance of all elements of `array` corresponding to `true` elements of `mask`. If every element of `mask` is `false`, the result is IEEE `NaN`.
### Example
```fortran
{!example/stats/example_cov.f90!}
```
## `mean` - mean of array elements
### Status
Experimental
### Description
Returns the mean of all the elements of `array`, or of the elements of `array` along dimension `dim` if provided, and if the corresponding element in `mask` is `true`.
### Syntax
`result = ` [[stdlib_stats(module):mean(interface)]] `(array [, mask])`
`result = ` [[stdlib_stats(module):mean(interface)]] `(array, dim [, mask])`
### Class
Generic subroutine
### Arguments
`array`: Shall be an array of type `integer`, `real`, or `complex`. It is an `intent(in)` argument.
`dim`: Shall be a scalar of type `integer` with a value in the range from 1 to `n`, where `n` is the rank of `array`. It is an `intent(in)` argument.
`mask` (optional): Shall be of type `logical` and either a scalar or an array of the same shape as `array`. It is an `intent(in)` argument.
### Return value
If `array` is of type `real` or `complex`, the result is of the same type as `array`.
If `array` is of type `integer`, the result is of type `real(dp)`.
If `dim` is absent, a scalar with the mean of all elements in `array` is returned. Otherwise, an array of rank `n-1`, where `n` equals the rank of `array`, and a shape similar to that of `array` with dimension `dim` dropped is returned.
If `mask` is specified, the result is the mean of all elements of `array` corresponding to `true` elements of `mask`. If every element of `mask` is `false`, the result is IEEE `NaN`.
### Example
```fortran
{!example/stats/example_mean.f90!}
```
## `median` - median of array elements
### Status
Experimental
### Description
Returns the median of all the elements of `array`, or of the elements of `array`
along dimension `dim` if provided, and if the corresponding element in `mask` is
`true`.
The median of the elements of `array` is defined as the "middle"
element, after that the elements are sorted in an increasing order, e.g. `array_sorted =
sort(array)`. If `n = size(array)` is an even number, the median is:
```
median(array) = array_sorted( floor( (n + 1) / 2.))
```
and if `n` is an odd number, the median is:
```
median(array) = mean( array_sorted( floor( (n + 1) / 2.):floor( (n + 1) / 2.) + 1 ) )
```
The current implementation relies on a selection algorithm applied on a copy of
the whole array, using the subroutine [[stdlib_selection(module):select(interface)]]
provided by the [[stdlib_selection(module)]] module.
### Syntax
`result = ` [[stdlib_stats(module):median(interface)]] `(array [, mask])`
`result = ` [[stdlib_stats(module):median(interface)]] `(array, dim [, mask])`
### Class
Generic subroutine
### Arguments
`array`: Shall be an array of type `integer` or `real`. It is an `intent(in)` argument.
`dim`: Shall be a scalar of type `integer` with a value in the range from 1 to `n`, where `n` is the rank of `array`. It is an `intent(in)` argument.
`mask` (optional): Shall be of type `logical` and either a scalar or an array of the same shape as `array`. It is an `intent(in)` argument.
### Return value
If `array` is of type `real`, the result is of type `real` with the same kind as `array`.
If `array` is of type `real` and contains IEEE `NaN`, the result is IEEE `NaN`.
If `array` is of type `integer`, the result is of type `real(dp)`.
If `dim` is absent, a scalar with the median of all elements in `array` is returned. Otherwise, an array of rank `n-1`, where `n` equals the rank of `array`, and a shape similar to that of `array` with dimension `dim` dropped is returned.
If `mask` is specified, the result is the median of all elements of `array` corresponding to `true` elements of `mask`. If every element of `mask` is `false`, the result is IEEE `NaN`.
### Example
```fortran
{!example/stats/example_median.f90!}
```
## `moment` - central moments of array elements
### Status
Experimental
### Description
Returns the _k_-th order central moment of all the elements of `array`, or of the elements of `array` along dimension `dim` if provided, and if the corresponding element in `mask` is `true`.
If a scalar or an array `center` is provided, the function returns the _k_-th order moment about 'center', of all the elements of `array`, or of the elements of `array` along dimension `dim` if provided, and if the corresponding element in `mask` is `true`.
The _k_-th order central moment is defined as :
```
moment(array) = 1/n sum_i (array(i) - mean(array))^k
```
where `n` is the number of elements.
The _k_-th order moment about `center` is defined as :
```
moment(array) = 1/n sum_i (array(i) - center)^k
```
### Syntax
`result = ` [[stdlib_stats(module):moment(interface)]] `(array, order [, center [, mask]])`
`result = ` [[stdlib_stats(module):moment(interface)]] `(array, order, dim [, center [, mask]])`
### Class
Generic subroutine
### Arguments
`array`: Shall be an array of type `integer`, `real`, or `complex`.
`order`: Shall be an scalar of type `integer`.
`dim`: Shall be a scalar of type `integer` with a value in the range from 1 to `n`, where `n` is the rank of `array`.
`center` (optional): Shall be a scalar of the same type of `result` if `dim` is not provided. If `dim` is provided, `center` shall be a scalar or an array (with a shape similar to that of `array` with dimension `dim` dropped) of the same type of `result`.
`mask` (optional): Shall be of type `logical` and either a scalar or an array of the same shape as `array`.
### Return value
If `array` is of type `real` or `complex`, the result is of the same type as `array`.
If `array` is of type `integer`, the result is of type `real(dp)`.
If `dim` is absent, a scalar with the _k_-th (central) moment of all elements in `array` is returned. Otherwise, an array of rank `n-1`, where `n` equals the rank of `array`, and a shape similar to that of `array` with dimension `dim` dropped is returned.
If `mask` is specified, the result is the _k_-th (central) moment of all elements of `array` corresponding to `true` elements of `mask`. If every element of `mask` is `false`, the result is IEEE `NaN`.
### Example
```fortran
{!example/stats/example_moment.f90!}
```
## `var` - variance of array elements
### Status
Experimental
### Description
Returns the variance of all the elements of `array`, or of the elements of `array` along dimension `dim` if provided, and if the corresponding element in `mask` is `true`.
Per default, the variance is defined as the best unbiased estimator and is computed as:
```
var(array) = 1/(n-1) sum_i (array(i) - mean(array))^2
```
where `n` is the number of elements.
The use of the term `n-1` for scaling is called Bessel 's correction. The scaling can be changed with the logical argument `corrected`. If `corrected` is `.false.`, then the sum is scaled with `n`, otherwise with `n-1`.
### Syntax
`result = ` [[stdlib_stats(module):var(interface)]] `(array [, mask [, corrected]])`
`result = ` [[stdlib_stats(module):var(interface)]] `(array, dim [, mask [, corrected]])`
### Class
Generic subroutine
### Arguments
`array`: Shall be an array of type `integer`, `real`, or `complex`. It is an `intent(in)` argument.
`dim`: Shall be a scalar of type `integer` with a value in the range from 1 to `n`, where `n` is the rank of `array`. It is an `intent(in)` argument.
`mask` (optional): Shall be of type `logical` and either a scalar or an array of the same shape as `array`. It is an `intent(in)` argument.
`corrected` (optional): Shall be a scalar of type `logical`. If `corrected` is `.true.` (default value), the sum is scaled with `n-1`. If `corrected` is `.false.`, then the sum is scaled with `n`. It is an `intent(in)` argument.
### Return value
If `array` is of type `real` or `complex`, the result is of type `real` corresponding to the type of `array`.
If `array` is of type `integer`, the result is of type `real(dp)`.
If `dim` is absent, a scalar with the variance of all elements in `array` is returned. Otherwise, an array of rank `n-1`, where `n` equals the rank of `array`, and a shape similar to that of `array` with dimension `dim` dropped is returned.
If `mask` is specified, the result is the variance of all elements of `array` corresponding to `true` elements of `mask`. If every element of `mask` is `false`, the result is IEEE `NaN`.
If the variance is computed with only one single element, then the result is IEEE `NaN` if `corrected` is `.true.` and is `0.` if `corrected` is `.false.`.
### Example
```fortran
{!example/stats/example_var.f90!}
```
|
