Matlab Numerical Integration - Syntax/Style Query

pete j

Hi,

Pretext: I have no formal background in matlab or maths in general, so apologies if any of the following doesn't make sense. I am also new to this forum, so apologies if this post is incorrect in any way. [n.b. I also posted this thread on mathhelpforum.com]

Context: Ok, so I wanted to find the response value for various parameter values, using the following equation:

[If you can't see the image, it is an integration with infinite bounds over an equation consisting of a Gaussian probability density function multiplied by the the square of a Gaussian cumulative density function plus one minus the square of another Gaussian cumulative density function]

I wasn't sure whether it was possible to do this using the matlab symbolic toolkit (syms), so I thought I'd take a crack at it using numerical integration, using the quad command. After much effort and confusion, I ended up with the following code.

Code:

mu=0;
sigma=1;
s=0;
alpha=0.4;
 
mu=sprintf('%f', mu);
sigma=sprintf('%f', sigma);
s=sprintf('%f', s);
alpha=sprintf('%f', alpha);
 
 
f=strcat('normpdf(x+',s,',',mu,',sqrt(2)*',sigma,').*(normcdf(x,',mu,',sqrt(2)*',alpha,'*',sigma,').^2 + (1 - normcdf(x,',mu,',sqrt(2)*',alpha,'*',sigma,')).^2)');

quad(f,-1000,1000)

This code *DOES* appear to work (i.e. yields the expected answers). But it strikes me as being more than a little crude. My questions therefore are as follows:

From a mathematical point of view, was using numerical integration with suitably wide bounds the right way to go about this problem?
From a programming point of view, is there a more elegant way to execute the above numerical integration? (i.e. a better approach than wrapping everything up as one big string which is then passed to the quad function)

Many thanks for your time,
Best,
pete

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