solarwindpy.tools.normal_parameters

normal_parameters(m, s)[source]

Convert log-normal parameters to normal distribution parameters.

Parameters:

m (pandas.Series or numpy.ndarray) – Mean of the log-normal distribution.
s (pandas.Series or numpy.ndarray) – Standard deviation of the log-normal distribution.

Returns:

Data frame with columns mu and sigma.

Return type:

pandas.DataFrame

Notes

The conversion uses

\[\mu = \exp[m + s^2/2]\]

\[\sigma = \sqrt{\exp[s^2 + 2m]\,(\exp[s^2] - 1)}\]

These expressions apply to both natural logarithms and base-10 logarithms.

Examples

>>> import numpy as np
>>> m, s = 1.0, 0.5  # log-normal parameters
>>> mu, sigma = normal_parameters(m, s)
>>> mu > 1.0  # Normal mean should be > 1
True