<< nisp_sum Test Functions

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nisp_sumsa

Returns the sensitivity indices of the Sum function

Calling Sequence

exact = nisp_sumsa ( a , mu , sigma )

Parameters

a:

a (nx+1)-by-1 or 1-by-(nx+1) matrix of doubles, where nx is the number of parameters

mu:

a nx-by-1 or 1-by-nx matrix of doubles, the means.

sigma:

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

exact:

a struct with the following fields: expectation, var, S, ST.

Description

This function returns the first and total order sensitivity indices of the Sum function.

This function is defined by

where X(i) is a random variables with mean mu(i) and standard variation sigma(i), for i=1,2,...,nx.

The expected value of Y is:

The variance of Y is:

The first order indices are

for i=1,2,...,nx.

Other higher order sensitivity indices are zero, since there is no interaction between the variables.

The total sensitivity indices are equal to the first order indices:

for i=1,2,...,nx.

Examples

mu=[0 0 0 0]';
sigma=[1 2 3 4]';
a = [1 1 1 1 0]'
exact = nisp_sumsa ( a , mu , sigma )
disp(exact.S)
disp(exact.ST)
// expectation: 0
// var: 30
// S: [0.0333333 0.1333333 0.3 0.5333333]'
// ST: [0.0333333 0.1333333 0.3 0.5333333]'

mu=[1 2 3 4]';
sigma=[5 6 7 8]';
a = [1 2 3 4 5]';
exact = nisp_sumsa ( a , mu , sigma )
disp(exact.S)
disp(exact.ST)
// expectation: 35
// var: 1634
// S: [0.0152999 0.0881273 0.2698898 0.6266830]'
// ST: [0.0152999 0.0881273 0.2698898 0.6266830]'

Authors

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.


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