windpowerlib.tools.gauss_distribution

windpowerlib.tools.gauss_distribution(function_variable, standard_deviation, mean=0)[source]

Gauss distribution.

The Gauss distribution is used in the function smooth_power_curve() for power curve smoothing.

Parameters:
  • function_variable (float) – Variable of the gaussian distribution.
  • standard_deviation (float) – Standard deviation of the Gauss distribution.
  • mean (float) – Defines the offset of the Gauss distribution. Default: 0.
Returns:

Wind speed at hub height. Data type depends on the type of wind_speed.
Return type:

pandas.Series or numpy.array

Notes

The following equation is used [1]:

f(x)=\frac{1}{\sigma \sqrt{2 \pi}} \exp \left[-\frac{(x-\mu)^2}{2 \sigma^2}\right]

with:
\sigma: standard deviation, \mu: mean

References

[1]Berendsen, H.: “A Student’s Guide to Data and Error Analysis”. New York, Cambridge University Press, 2011, p. 37