pyrtid.utils.random_field.get_log_normalized_std_from_normal_params#

pyrtid.utils.random_field.get_log_normalized_std_from_normal_params(mean: float, std: float) → float[source]#

Get the mean of the log-normalized normal distribution.

Let $Z$ be normally distributed. Denote $mu_{Z}$ and $sigma_{Z}$ as the mean and standard deviation of $Z$. The standard deviation $sigma$ of $e_{Z}$ is given by:

\[\sigma = e^{\mu + \tfrac{1}{2}\sigma^2}\sqrt{e^{\sigma^2} - 1}\]

See: https://en.wikipedia.org/wiki/Log-normal_distribution#Arithmetic_moments

Parameters

  • mean (float) – The mean of the normal distribution.

  • std (float) – The standard deviation of the normal distribution.

Returns

The standard deviation of the log-normalized distribution.

Return type

float