# Distribution shape

The DN_HistogramMode features measure properties of the shape of the distribution of time-series values.

*catch22 *contains two features involving the `DN_HistogramMode`

function in *hctsa:*

`mode_5`

(the*hctsa*feature`DN_HistogramMode_5`

)`mode_10`

(the*hctsa*feature`DN_HistogramMode_10`

)

**Note**: The C implementation of these features (in *catch22) *does not map perfectly onto the *hctsa* implementation, due to slight differences in how the histogram bins are constructed. But the trends are similar.

## What it does

These functions involve computing the mode of the z-scored time-series through the following steps:

z-score the input time series.

Compute a histogram using a given number of (linearly spaced) bins, e.g., 5 bins for

`mode_5`

and 10 bins for`mode_10.`

Return the location of the bin with the most counts.

## What these features measure

Being distributional properties, these features are completely insensitive to the time-ordering of values in the time series. Instead, they capture how the most probable time-series values are positioned relative to the mean.

Time series with a **symmetric** distribution, with a central peak, will have a mode near the center, and value close to zero. Here is an example of Gaussian-distributed noise:

### Feature output: `-0.36`

`-0.36`

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