stat_values

hep_spt.stat_values(arr, axis=None, weights=None)

Calculate mean and variance and standard deviations of the sample and the mean from the given array. Weights are allowed. The definition of the aforementioned quantities are:

• Mean:

\[\bar{x} = \sum_{i=0}^{n - 1}{\frac{x_i}{n}}\]

• Weighted mean:

\[\bar{x}^w = \frac{\sum_{i=0}^{n - 1}{\omega_i x_i}}{\sum_{i=0}^{n - 1}{\omega_i}}\]

• Variance of the sample:

\[\sigma_s = \sum_{i=0}^{n - 1}{\frac{(x_i - \bar{x})^2}{n - 1}}\]

• Weighted variance of the sample:

\[\sigma^w_s = \frac{N'}{(N' - 1)}\frac{\sum_{i=0}^{n - 1}{\omega_i(x_i - \bar{x}^w)^2}}{\sum_{i=0}^{n - 1}{\omega_i}}\]

where \(\omega_i\) refers to the weights associated with the value \(x_i\), and in the last equation N’ refers to the number of non-zero weights. The variance and standard deviations of the mean are then given by:

• Standard deviation of the mean:

\[s_\bar{x} = \sqrt{\frac{\sigma_s}{n}}\]

• Weighted standard deviation of the mean:

\[s^w_\bar{x} = \sqrt{\frac{\sigma^w_s}{N'}}\]

Parameters

• arr (numpy.ndarray) – input array of data.

• axis (None or int or tuple(int)) – axis or axes along which to calculate the values for “arr”.

• weights (None or numpy.ndarray) – array of weights associated to the values in “arr”.

Returns

Mean, variance, standard deviation, variance of the mean and standard deviation of the mean.

Return type

numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray