# 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.

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
`DN_HistogramMode_5`

and 10 bins for`DN_HistogramMode_10`

). - 3.Return the location of the bin with the most counts.

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)

Last modified 1mo ago