Name

nisp_sumsa — Returns the sensitivity indices of the Sum function

Calling Sequence

   exact = nisp_sumsa ( a , mu , sigma )
   
   

Parameters

a:

a 5-by-1 matrix of doubles

mu:

a 4-by-1 matrix of doubles, the means.

sigma:

a 4-by-1 matrix of doubles, the standard deviations.

exact:

a struct with the following fields: expectation, var, S1, S2, S3, S4.

Description

This function returns the sensitivity indices of the Sum function. The second order sensitivity indices Sij, for i,j=1,4 and i different from j are all zeros. The third order indices Sijk are all zero. The fourth order indice S1234 is zero. The total order sensitivity indices are equal to the first order indices: STi=Si.

This function is defined by

where X1, X2, X3, X4 are normal random variables with means mu1,mu2,mu3,mu4 and standard variations sigma1,sigma2,sigma3,sigma4.

Examples

mu=[0 0 0 0]';
sigma=[1 2 3 4]';
a = [1 1 1 1 0]'
exact = nisp_sumsa ( x , a , mu , sigma )

mu=[1 2 3 4]';
sigma=[5 6 7 8]';
a = [1 2 3 4 5]';
exact = nisp_sumsa ( x , a , mu , sigma )

   

Authors

Copyright (C) 2008-2011 - INRIA - Michael Baudin

Bibliography

"Sensitivity analysis in practice", Saltelli, Tarantolla, Compolongo, Ratto, Wiley, 2004

"An importance quantification technique in uncertainty analysis for computer models", Ishigami, Homma, 1990, Proceedings of the ISUMA'90. First international symposium on uncertainty modelling and Analysis, University of Maryland, USA, pp. 398-403.