# histcounts

Histogram bin counts

## Syntax

``````[N,edges] = histcounts(X)``````
``````[N,edges] = histcounts(X,nbins)``````
``````[N,edges] = histcounts(X,edges)``````
``````[N,edges,bin] = histcounts(___)``````
``N = histcounts(C)``
``N = histcounts(C,Categories)``
``````[N,Categories] = histcounts(___)``````
``[___] = histcounts(___,Name,Value)``

## Description

example

``````[N,edges] = histcounts(X)``` partitions the `X` values into bins, and returns the count in each bin, as well as the bin edges. The `histcounts` function uses an automatic binning algorithm that returns bins with a uniform width, chosen to cover the range of elements in `X` and reveal the underlying shape of the distribution.```

example

``````[N,edges] = histcounts(X,nbins)``` uses a number of bins specified by the scalar, `nbins`.```

example

``````[N,edges] = histcounts(X,edges)``` sorts `X` into bins with the bin edges specified by the vector, `edges`. The value `X(i)` is in the `k`th bin if `edges(k)` ≤ `X(i)` < `edges(k+1)`. The last bin also includes the right bin edge, so that it contains `X(i)` if `edges(end-1)` ≤ `X(i)` ≤ `edges(end)`.```

example

``````[N,edges,bin] = histcounts(___)``` also returns an index array, `bin`, using any of the previous syntaxes. `bin` is an array of the same size as `X` whose elements are the bin indices for the corresponding elements in `X`. The number of elements in the `k`th bin is `nnz(bin==k)`, which is the same as `N(k)`.```

example

````N = histcounts(C)`, where `C` is a categorical array, returns a vector, `N`, that indicates the number of elements in `C` whose value is equal to each of `C`’s categories. `N` has one element for each category in `C`.```
````N = histcounts(C,Categories)` counts only the elements in `C` whose value is equal to the subset of categories specified by `Categories`.```

example

``````[N,Categories] = histcounts(___)``` also returns the categories that correspond to each count in `N` using either of the previous syntaxes for categorical arrays.```

example

````[___] = histcounts(___,Name,Value)` uses additional options specified by one or more `Name,Value` pair arguments using any of the input or output argument combinations in previous syntaxes. For example, you can specify `'BinWidth'` and a scalar to adjust the width of the bins for numeric data. For categorical data, you can specify `'Normalization'` and either `'count'`, `'countdensity'`, `'probability'`, `'pdf'`, `'cumcount'`, or `'cdf'`.```

## Examples

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Distribute 100 random values into bins. `histcounts` automatically chooses an appropriate bin width to reveal the underlying distribution of the data.

```X = randn(100,1); [N,edges] = histcounts(X)```
```N = 1×7 2 17 28 32 16 3 2 ```
```edges = 1×8 -3 -2 -1 0 1 2 3 4 ```

Distribute 10 numbers into 6 equally spaced bins.

```X = [2 3 5 7 11 13 17 19 23 29]; [N,edges] = histcounts(X,6)```
```N = 1×6 2 2 2 2 1 1 ```
```edges = 1×7 0 4.9000 9.8000 14.7000 19.6000 24.5000 29.4000 ```

Distribute 1,000 random numbers into bins. Define the bin edges with a vector, where the first element is the left edge of the first bin, and the last element is the right edge of the last bin.

```X = randn(1000,1); edges = [-5 -4 -2 -1 -0.5 0 0.5 1 2 4 5]; N = histcounts(X,edges)```
```N = 1×10 0 24 149 142 195 200 154 111 25 0 ```

Distribute all of the prime numbers less than 100 into bins. Specify `'Normalization'` as `'probability'` to normalize the bin counts so that `sum(N)` is `1`. That is, each bin count represents the probability that an observation falls within that bin.

```X = primes(100); [N,edges] = histcounts(X, 'Normalization', 'probability')```
```N = 1×4 0.4000 0.2800 0.2800 0.0400 ```
```edges = 1×5 0 30 60 90 120 ```

Distribute 100 random integers between -5 and 5 into bins, and specify `'BinMethod'` as `'integers'` to use unit-width bins centered on integers. Specify a third output for `histcounts` to return a vector representing the bin indices of the data.

```X = randi([-5,5],100,1); [N,edges,bin] = histcounts(X,'BinMethod','integers');```

Find the bin count for the third bin by counting the occurrences of the number `3` in the bin index vector, `bin`. The result is the same as `N(3)`.

`count = nnz(bin==3)`
```count = 8 ```

Create a categorical vector that represents votes. The categories in the vector are `'yes'`, `'no'`, or `'undecided'`.

```A = [0 0 1 1 1 0 0 0 0 NaN NaN 1 0 0 0 1 0 1 0 1 0 0 0 1 1 1 1]; C = categorical(A,[1 0 NaN],{'yes','no','undecided'})```
```C = 1x27 categorical Columns 1 through 9 no no yes yes yes no no no no Columns 10 through 16 undecided undecided yes no no no yes Columns 17 through 25 no yes no yes no no no yes yes Columns 26 through 27 yes yes ```

Determine the number of elements that fall into each category.

`[N,Categories] = histcounts(C)`
```N = 1×3 11 14 2 ```
```Categories = 1x3 cell {'yes'} {'no'} {'undecided'} ```

## Input Arguments

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Data to distribute among bins, specified as a vector, matrix, or multidimensional array. If `X` is not a vector, then `histcounts` treats it as a single column vector, `X(:)`.

`histcounts` ignores all `NaN` values. Similarly, `histcounts` ignores `Inf` and `-Inf` values unless the bin edges explicitly specify `Inf` or `-Inf` as a bin edge.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `logical` | `datetime` | `duration`

Categorical data, specified as a categorical array. `histcounts` ignores undefined categorical values.

Data Types: `categorical`

Number of bins, specified as a positive integer. If you do not specify `nbins`, then `histcounts` automatically calculates how many bins to use based on the values in `X`.

Example: `[N,edges] = histcounts(X,15)` uses 15 bins.

Bin edges, specified as a vector. `edges(1)` is the left edge of the first bin, and `edges(end)` is the right edge of the last bin.

For datetime and duration data, `edges` must be a datetime or duration vector in monotonically increasing order.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `logical` | `datetime` | `duration`

Categories included in count, specified as a cell vector of character vectors or a categorical vector. By default, `histcounts` uses a bin for each category in categorical array `C`. Use `Categories` to specify a unique subset of the categories instead.

Example: `h = histcounts(C,{'Large','Small'})` counts only the categorical data in the categories `'Large'` and `'Small'`.

Data Types: `cell` | `categorical`

### Name-Value Pair Arguments

Specify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside quotes. You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.

Example: `[N,edges] = histcounts(X,'Normalization','probability')` normalizes the bin counts in `N`, such that `sum(N)` is 1.

Bin limits, specified as a two-element vector, `[bmin,bmax]`. This option bins only the values in `X` that fall between `bmin` and `bmax` inclusive; that is, `X(X>=bmin & X<=bmax)`.

This option does not apply to categorical data.

Example: `[N,edges] = histcounts(X,'BinLimits',[1,10])` bins only the values in `X` that are between `1` and `10` inclusive.

Binning algorithm, specified as one of the values in this table.

Value

Description

`'auto'`

The default `'auto'` algorithm chooses a bin width to cover the data range and reveal the shape of the underlying distribution.

`'scott'`

Scott’s rule is optimal if the data is close to being normally distributed, but is also appropriate for most other distributions. It uses a bin width of `3.5*std(X(:))*numel(X)^(-1/3)`.

`'fd'`

The Freedman-Diaconis rule is less sensitive to outliers in the data, and may be more suitable for data with heavy-tailed distributions. It uses a bin width of `2*IQR(X(:))*numel(X)^(-1/3)`, where `IQR` is the interquartile range of `X`.

`'integers'`

The integer rule is useful with integer data, as it creates a bin for each integer. It uses a bin width of 1 and places bin edges halfway between integers. To prevent from accidentally creating too many bins, a limit of 65536 bins (216) can be created with this rule. If the data range is greater than 65536, then wider bins are used instead.

Note

`'integers'` does not support datetime or duration data.

`'sturges'`

Sturges’ rule is a simple rule that is popular due to its simplicity. It chooses the number of bins to be ```ceil(1 + log2(numel(X)))```.

`'sqrt'`

The Square Root rule is another simple rule widely used in other software packages. It chooses the number of bins to be `ceil(sqrt(numel(X)))`.

`histcounts` does not always choose the number of bins using these exact formulas. Sometimes the number of bins is adjusted slightly so that the bin edges fall on "nice" numbers.

For datetime data, the bin method can be one of these units of time:

 `'second'` `'month'` `'minute'` `'quarter'` `'hour'` `'year'` `'day'` `'decade'` `'week'` `'century'`

For duration data, the bin method can be one of these units of time:

 `'second'` `'day'` `'minute'` `'year'` `'hour'`

If you specify `BinMethod` with datetime or duration data, then `histcounts` can use a maximum of 65,536 bins (or 216). If the specified bin duration requires more bins, then `histcounts` uses a larger bin width corresponding to the maximum number of bins.

This option does not apply to categorical data.

Example: `[N,edges] = histcounts(X,'BinMethod','integers')` uses bins centered on integers.

Width of bins, specified as a scalar. If you specify `BinWidth`, then `histcounts` can use a maximum of 65,536 bins (or 216). If the specified bin width requires more bins, then `histcounts` uses a larger bin width corresponding to the maximum number of bins.

For datetime and duration data, the value of `'BinWidth'` can be a scalar duration or calendar duration.

This option does not apply to categorical data.

Example: `[N,edges] = histcounts(X,'BinWidth',5)` uses bins with a width of 5.

Type of normalization, specified as one of the values in this table. For each bin `i`:

• ${v}_{i}$ is the bin value.

• ${c}_{i}$ is the number of elements in the bin.

• ${w}_{i}$ is the width of the bin.

• $N$ is the number of elements in the input data. This value can be greater than the binned data if the data contains `NaN`, `NaT`, or `<undefined>` values, or if some of the data lies outside the bin limits.

ValueBin ValuesNotes
`'count'` (default)

`${v}_{i}={c}_{i}$`

• Count or frequency of observations.

• Sum of bin values is less than or equal to `numel(X)`. The sum is less than `numel(X)` only when some of the input data is not included in the bins.

• For categorical data, sum of bin values is either `numel(X)` or `sum(ismember(X(:),Categories))`.

`'countdensity'`

`${v}_{i}=\frac{{c}_{i}}{{w}_{i}}$`

• Count or frequency scaled by width of bin.

• For categorical data, this the same as `'count'`.

Note

`'countdensity'` does not support datetime or duration data.

`'cumcount'`

`${v}_{i}=\sum _{j=1}^{i}{c}_{j}$`

• Cumulative count. Each bin value is the cumulative number of observations in that bin and all previous bins.

• The value of the last bin is less than or equal to `numel(X)`.

• For categorical data, the value of the last bin is less than or equal to `numel(X)` or `sum(ismember(X(:),Categories))`.

`'probability'`

`${v}_{i}=\frac{{c}_{i}}{N}$`

• Relative probability.

• The sum of the bin values is less than or equal to `1`.

`'pdf'`

`${v}_{i}=\frac{{c}_{i}}{N\text{\hspace{0.17em}}\text{\hspace{0.17em}}\cdot \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{w}_{i}}$`

• Probability density function estimate.

• For categorical data, this is the same as `'probability'`.

Note

`'pdf'` does not support datetime or duration data.

`'cdf'`

`${v}_{i}=\sum _{j=1}^{i}\text{\hspace{0.17em}}\frac{{c}_{j}}{N}$`

• Cumulative density function estimate.

• `N(end)` is less than or equal to `1`.

Example: `[N,edges] = histcounts(X,'Normalization','pdf')` bins the data using the probability density function estimate.

## Output Arguments

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Bin counts, returned as a row vector.

Bin edges, returned as a vector. `edges(1)` is the left edge of the first bin, and `edges(end)` is the right edge of the last bin.

Bin indices, returned as an array of the same size as `X`. Each element in `bin` describes which numbered bin contains the corresponding element in `X`.

A value of `0` in `bin` indicates an element which does not belong to any of the bins (for example, a `NaN` value).

Categories included in count, returned as a cell vector of character vectors. `Categories` contains the categories in `C` that correspond to each count in `N`.

## Tips

• The behavior of `histcounts` is similar to that of the `discretize` function. Use `histcounts` to find the number of elements in each bin. On the other hand, use `discretize` to find which bin each element belongs to (without counting).