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Merge pull request #27 from Serapieum-of-alex/more-distributions
More distributions
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Original file line number | Diff line number | Diff line change |
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@@ -0,0 +1,56 @@ | ||
############# | ||
Distributions | ||
############# | ||
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******************************************** | ||
Generalized extreme value distribution (GEV) | ||
******************************************** | ||
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- The generalised extreme value (or generalized extreme value) distribution characterises the behaviour of ‘block | ||
maxima’ | ||
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probability density function (pdf) | ||
================================== | ||
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.. math:: | ||
f(x) = \frac{1}{\sigma}\ast{Q(x)}^{\xi+1}\ast e^{-Q(x)} | ||
.. math:: | ||
Q(x) = | ||
\begin{cases} | ||
{(1+\xi(\frac{x-\mu}{\delta}))}^\frac{-1}{\xi} & \quad \text{if } \xi \text{ \neq 0}\\ | ||
e^{-(\frac{x-\mu}{\delta})} & \quad \text{if } \xi \text{ = 0} | ||
\end{cases} | ||
- where | ||
- :math: `\sigma` is the scale parameter | ||
- :math: `\mu` is the location parameter | ||
- :math: `\delta` is the scale parameter | ||
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Cumulative distribution function (cdf) | ||
====================================== | ||
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.. math:: | ||
F(x)=e^{-Q(x)} | ||
******************* | ||
Gumbel Distribution | ||
******************* | ||
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- The Gumbel distribution is a special case of the `Generalized extreme value distribution (GEV)`_ when the shape | ||
parameter :math: `\sigma` equals zero. | ||
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probability density function (pdf) | ||
================================== | ||
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.. math:: | ||
f(x) = \frac{1}{\sigma} \ast { {e}^{-(\frac{x-\mu}{\delta}) - {e}^{- (\frac{x-\mu}{\delta})} }} | ||
Cumulative distribution function (cdf) | ||
====================================== | ||
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.. math:: | ||
F(x) = {e}^{- {e}^{- (\frac{x-\mu}{\delta})} } |
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Original file line number | Diff line number | Diff line change |
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channels: | ||
- conda-forge | ||
dependencies: | ||
- python >=3.9.0 | ||
- pip >=21.3.1 | ||
- matplotlib >=3.4.2,<3.6.0 | ||
# - pandas >=1.3.2,<1.4.3 | ||
# - pip: | ||
# - geoplot >=0.5.1 | ||
# - loguru >=0.5.3 | ||
- python >=3.9,<3.11 | ||
- pip >=22.3.1 | ||
- pandas | ||
- numpy==1.20.* | ||
- numpydoc==1.1.0 | ||
- typing-extensions==3.10.* | ||
- pip: | ||
- pydata-sphinx-theme | ||
- nbsphinx | ||
- easydev |
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