virocon.distributions module¶
- class virocon.distributions.ExponentiatedWeibullDistribution(alpha=1, beta=1, delta=1, f_alpha=None, f_beta=None, f_delta=None)[source]¶
Bases:
virocon.distributions.DistributionAn exponentiated Weibull distribution.
The parametrization used is the same as described by Haselsteiner et al. (2019) [1]_. The distributions cumulative distribution function is given by:
\(F(x) = \left[ 1- \exp \left(-\left( \frac{x}{\alpha} \right)^{\beta} \right) \right] ^{\delta}\)
- Parameters
alpha (float) – Scale parameter of the exponentiated weibull distribution. Defaults to 1.
beta (float) – First shape parameter of the exponentiated weibull distribution. Defaults to 1.
delta (float) – Second shape parameter of the exponentiated weibull distribution. Defaults to 1.
f_alpha (float) – Fixed alpha parameter of the weibull distribution (e.g. given physical parameter). If this parameter is set, alpha is ignored. Defaults to None.
f_beta (float) – Fixed beta parameter of the weibull distribution (e.g. given physical parameter). If this parameter is set, beta is ignored. Defaults to None.
f_delta (float) – Fixed delta parameter of the weibull distribution (e.g. given physical parameter). If this parameter is set, delta is ignored. Defaults to None.
References
- 1
Haselsteiner, A.F.; Thoben, K.D. (2019) Predicting wave heights for marine design by prioritizing extreme events in a global model, Renewable Energy, Volume 156, August 2020, Pages 1146-1157; https://doi.org/10.1016/j.renene.2020.04.112
- property parameters¶
Parameters of the probability distribution.
Dict of the form: {“<parameter_name>” : <parameter_value>, …}
- class virocon.distributions.LogNormalDistribution(mu=0, sigma=1, f_mu=None, f_sigma=None)[source]¶
Bases:
virocon.distributions.DistributionA Lognormal Distribution.
The distributions probability density function is given by [1]_:
\(f(x) = \frac{1}{x\widetilde{\sigma} \sqrt{2\pi}}\exp \left[ \frac{-(\ln x - \widetilde{\mu})^2}{2\widetilde{\sigma}^2}\right]\)
- Parameters
mu (float) – Mean parameter of the corresponding normal distribution. Defaults to 0.
sigma (float) – Standard deviation of the corresponding normal distribution. Defaults to 1.
f_mu (float) – Fixed parameter mu of the lognormal distribution (e.g. given physical parameter). If this parameter is set, mu is ignored. Defaults to None.
f_sigma (float) – Fixed parameter sigma of the lognormal distribution (e.g. given physical parameter). If this parameter is set, sigma is ignored. Defaults to None
References
- 1
Forbes, C.; Evans, M.; Hastings, N; Peacock, B. (2011) Statistical Distributions, 4th Edition, Published by John Wiley & Sons, Inc., Hoboken, New Jersey., Pages 131-132
- property parameters¶
Parameters of the probability distribution.
Dict of the form: {“<parameter_name>” : <parameter_value>, …}
- class virocon.distributions.NormalDistribution(mu=0, sigma=1, f_mu=None, f_sigma=None)[source]¶
Bases:
virocon.distributions.DistributionA Normal (Gaussian) Distribution.
The distributions probability density function is given by [1]_:
\(f(x) = \frac{1}{{\sigma} \sqrt{2\pi}} \exp \left( - \frac{( x - \mu)^2}{2\sigma^2}\right)\)
- Parameters
mu (float) – Location parameter, the mean. Defaults to 0.
sigma (float) – Scale parameter, the standard deviation. Defaults to 1.
f_mu (float) – Fixed parameter mu of the normal distribution (e.g. given physical parameter). If this parameter is set, mu is ignored. Defaults to None.
f_sigma (float) – Fixed parameter sigma of the normal distribution (e.g. given physical parameter). If this parameter is set, sigma is ignored. Defaults to None
References
- 1
Forbes, C.; Evans, M.; Hastings, N; Peacock, B. (2011) Statistical Distributions, 4th Edition, Published by John Wiley & Sons, Inc., Hoboken, New Jersey., Page 143
- property parameters¶
Parameters of the probability distribution.
Dict of the form: {“<parameter_name>” : <parameter_value>, …}
- class virocon.distributions.WeibullDistribution(alpha=1, beta=1, gamma=0, f_alpha=None, f_beta=None, f_gamma=None)[source]¶
Bases:
virocon.distributions.DistributionA weibull distribution.
The distributions probability density function is given by [1]_ :
\(f(x) = \frac{\beta}{\alpha} \left (\frac{x-\gamma}{\alpha} \right)^{\beta -1} \exp \left[-\left( \frac{x-\gamma}{\alpha} \right)^{\beta} \right]\)
- Parameters
alpha (float) – Scale parameter of the weibull distribution. Defaults to 1.
beta (float) – Shape parameter of the weibull distribution. Defaults to 1.
gamma (float) – Location parameter of the weibull distribution (3-parameter weibull distribution). Defaults to 0.
f_alpha (float) – Fixed scale parameter of the weibull distribution (e.g. given physical parameter). If this parameter is set, lambda is ignored. Defaults to None.
f_beta (float) – Fixed shape parameter of the weibull distribution (e.g. given physical parameter). If this parameter is set, k is ignored. Defaults to None.
f_gamma (float) – Fixed location parameter of the weibull distribution (e.g. given physical parameter). If this parameter is set, theta is ignored. Defaults to None.
References
- 1
Haselsteiner, A.F.; Ohlendorf, J.H.; Wosniok, W.; Thoben, K.D.(2017) Deriving environmental contours from highest density regions. Coastal Engineering 123 (2017) 42–51.
- icdf(prob, alpha=None, beta=None, gamma=None)[source]¶
Inverse cumulative distribution function.
- Parameters
prob (array_like) – Probabilities for which the i_cdf is evaluated. Shape: 1-dimensional
- alphafloat, optional
The scale parameter. Defaults to self.aplha .
- betafloat, optional
The shape parameter. Defaults to self.beta.
- gamma: float, optional
The location parameter . Defaults to self.gamma.
- property parameters¶
Parameters of the probability distribution.
Dict of the form: {“<parameter_name>” : <parameter_value>, …}