# Distribution shape

*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:

1. *z*-score the input time series.
2. Compute a histogram using a given number of (linearly spaced) bins (5 bins for`mode_5`) and 10 bins for `mode_10`).
3. 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.

![](/files/-MfHIaVC-lfYcVohKRgZ)

* 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:

![](/files/-MfHIvrFBbR1Daue2y61)

* 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:

![](/files/-MfHJYFu3Lz2_XHuok3R)

* (and similarly negatively skewed distributions obtain positive values)


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