# popmon.stats package

## popmon.stats.numpy module

popmon.stats.numpy.covariance_multinomial_probability_distribution(entries)

Calculate covariance matrix of a single multinomial probability distribution

Parameters

entries – entries of input histogram

Returns

numpy 2D array with covariance matrix of multinomial probability distribution

Median Absolute Deviation along given axis of an array

Parameters
• a – array_like Input array.

• c (float) – optional. The normalization constant. Defined as scipy.stats.norm.ppf(3/4.), which is approximately .6745.

• axis (int) – optional. The default is 0. Can also be None.

• center – callable or float. If a callable is provided, such as the default np.median then it is expected to be called center(a). The axis argument will be applied via np.apply_over_axes. Otherwise, provide a float.

Returns

Return type

float

popmon.stats.numpy.mean(a, weights=None, axis=None, dtype=None, keepdims=False, ddof=0)

Compute the weighted mean along the specified axis.

Parameters
• a – Array containing numbers whose mean is desired. If a is not an array, a conversion is attempted.

• weights – Array containing weights for the elements of a. If weights is not an array, a conversion is attempted.

• axis – Axis or axes along which the means are computed. The default is to compute the mean of the flattened array. Type is None or int or tuple of ints, optional.

• dtype – data type to use in computing the mean.

• keepdims (bool) – If this is set to True, the axes which are reduced are left in the result as dimensions with size one.

• ddof (int) – delta degrees of freedom

Returns

np.ndarray

popmon.stats.numpy.median(a, weights=None, axis=None, keepdims=False)

Compute the weighted median along the specified axis.

Parameters
• a – Array containing numbers whose median is desired. If a is not an array, a conversion is attempted.

• weights – Array containing weights for the elements of a. If weights is not an array, a conversion is attempted.

• axis – Axis or axes along which the means are computed. The default is to compute the mean of the flattened array. Type is None or int or tuple of ints, optional.

• keepdims (bool) – If this is set to True, the axes which are reduced are left in the result as dimensions with size one.

Returns

number or array

popmon.stats.numpy.probability_distribution_mean_covariance(entries_list)

Mean normalized histogram and covariance of list of input histograms

Parameters

entries_list – numpy 2D array shape (n_histos, n_bins,) with bin counts of histograms

Returns

mean normalized histogram, covariance probability matrix

popmon.stats.numpy.quantile(a, q, weights=None, axis=None, keepdims=False)

Compute the weighted quantiles along the specified axis

If q is a single quantile and axis=None, then the result is a scalar. If multiple quantiles are given, first axis of the result corresponds to the quantiles. The other axes are the axes that remain after the reduction of a.

Parameters
• a – Array containing numbers whose median is desired. If a is not an array, a conversion is attempted

• q – Quantile or sequence of quantiles to compute, which must be between 0 and 1 inclusive

• weights – Array containing weights for the elements of a. If weights is not an array, a conversion is attempted.

• axis – Axis or axes along which the quantiles are computed. The default is to compute the quantile(s) along a flattened. Type is int, tuple of int, None, optional. version of the array

• keepdims (bool) – If this is set to True, the axes which are reduced are left in the result as dimensions with size one.

Returns

scalar or ndarray

popmon.stats.numpy.std(a, weights=None, axis=None, dtype=None, ddof=0, keepdims=False)

Compute the weighted standard deviation along the specified axis.

Parameters
• a – Array containing numbers whose standard deviation is desired. If a is not an array, a conversion is attempted.

• weights – Array containing weights for the elements of a. If weights is not an array, a conversion is attempted.

• axis – Axis or axes along which the means are computed. The default is to compute the mean of the flattened array. Type is None or int or tuple of ints, optional.

• dtype – data type to use in computing the mean.

• ddof (int) – Delta Degrees of Freedom. The divisor used in calculations is `W - ddof`, where `W` is the sum of weights (or number of elements if weights is None). By default ddof is zero

• keepdims (bool) – If this is set to True, the axes which are reduced are left in the result as dimensions with size one.

Returns

np.ndarray