# 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 (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 a value close to zero. Here is an example, of Gaussian-distributed noise (

`NS_norm_L1000_a0_b10_4`

) which obtains a score of -0.36.

Time series with a symmetric distribution but with density far from the origin, like this Chirikov map (

`MP_chirikov_L1000_IC_0.2_6_x`

) obtain high (positive or negative) values:

Time series with positively skewed distributions, like this example of beta-distributed noise (

`NS_beta_L10000_a1_b3_2.dat`

), obtain negative values as shown below:

(and similarly negatively skewed distributions obtain positive values)

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