statistics module¶
Statistics associated with the Ishigami use case.
- gemseo.uncertainty.use_cases.ishigami.statistics.MEAN: Final[float] = 3.5¶
The expectation of the output.
\[\mathbb{E}[Y] = \frac{a}{2}\]
- gemseo.uncertainty.use_cases.ishigami.statistics.SOBOL_1: Final[float] = 0.31390519114781146¶
The first-order Sobol’ index of \(X_1\).
\[S_1 = \frac{(1+b\frac{pi^4}{5})^2}{2\mathbb{V}[Y]}\]
- gemseo.uncertainty.use_cases.ishigami.statistics.SOBOL_12: Final[float] = 0.0¶
The second-order Sobol’ index of \(X_1\) and \(X_2\).
\[S_{1,2} = 0\]
- gemseo.uncertainty.use_cases.ishigami.statistics.SOBOL_123: Final[float] = 0.0¶
The second-order Sobol’ index of \(X_1\), \(X_2\) and \(X_3\).
\[S_{1,2,3} = 0\]
- gemseo.uncertainty.use_cases.ishigami.statistics.SOBOL_13: Final[float] = 0.24368366406214773¶
The second-order Sobol’ index of \(X_1\) and \(X_3\).
\[S_{1,3} = \frac{8b^2\pi^8}{225\mathbb{V}[Y]}\]
- gemseo.uncertainty.use_cases.ishigami.statistics.SOBOL_2: Final[float] = 0.4424111447900409¶
The first-order Sobol’ index of \(X_2\).
\[S_2 = \frac{a^2}{8\mathbb{V}[Y]}\]
- gemseo.uncertainty.use_cases.ishigami.statistics.SOBOL_23: Final[float] = 0.0¶
The second-order Sobol’ index of \(X_2\) and \(X_3\).
\[S_{2,3} = 0\]
- gemseo.uncertainty.use_cases.ishigami.statistics.SOBOL_3: Final[float] = 0.0¶
The first-order Sobol’ index of \(X_3\).
\[S_3 = 0\]
- gemseo.uncertainty.use_cases.ishigami.statistics.TOTAL_SOBOL_1: Final[float] = 0.5575888552099592¶
The total Sobol’ index of \(X_1\).
\[S_1^T = S_1 + S_{1,3}\]
- gemseo.uncertainty.use_cases.ishigami.statistics.TOTAL_SOBOL_2: Final[float] = 0.4424111447900409¶
The total Sobol’ index of \(X_2\).
\[S_2^T = S_2\]