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# 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:
• `DN_HistogramMode_5`
• `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. 1.
z-score the input time series.
2. 2.
Compute a histogram using a given number of (linearly spaced) bins (5 bins for`DN_HistogramMode_5`and 10 bins for `DN_HistogramMode_10`).
3. 3.
Return the location of the bin with the most counts.

### What it measures

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)