Integral of a product between a function and a Cumulative Normal Distribution

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Javier
Javier 2013-3-26
Hi.
I need to compute an integral of a function that consist in the product between a Cumulative distribution of a Normal, and another term.
I tried using the command int, but in that case I was not able to execute the normcdf command.
Matlab said: CNaux2=normcdf(aux5) Error using NaN Trailing string input must be 'single' or 'double'.
Instead, i tried using the quad command. In that case, the normcdf could be defined as a function handle, but then i coul not excute the quad command. In this case matlab said
Error using * Inner matrix dimensions must agree.
And i don´t understand why, because i don´t have any matrix here, i have only a product of functions of one variable.
Could you please help me?
Thanks! Javier
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Javier
Javier 2013-3-27
What i have to do is to compute a definite integral for the function:
N(a(t))*b(t)*C(d(t)) dt
Where N(a(t)) is a normal probability function valued at the value a, which is in fact a function that depends on t. C(d(t)) is a cumulative normal probability function valued d, which is also a function that depends on t. And b(t) is another function of t.
I have tried to define first the functions a(t) b(t) and c(t) as function handles. Then i used the commandsnormcdf and normpdf to compute the normal cumulative and probability function on this function (i think this way i obtain also a function handle that depends on t, but i am not sure if this is ok. For example, CNaux1 = @(t)normcdf((K*(T-t))/sigma/sqrt(T-t)) )
Later, i define another function handle integrand= N(a(t)).*b(t).*C(d(t)) and i use the quad (integrand, 0, T) (T previously defined)
I thinh i probably made more than one mistake, i am quite a bit lost...
Thank you very much!
Tom Lane
Tom Lane 2013-3-27
This works:
K = 1; T = 1; sigma = 2; f = @(t)normcdf((K*(T-t))/sigma./sqrt(T-t));
quad(f,0,1)
If you tried something else that does not work, you should say what you tried.

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采纳的回答

Tom Lane
Tom Lane 2013-3-27
You didn't really explain what you tried. Here's an example that works:
quad(@(x) x.*normcdf(x),-1,1)
If I use matrix multiplication "*" instead of elementwise multiplication ".*" I get the same error you report. So if your integrand is something like this, maybe you need to switch to elementwise multiplication.
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Javier
Javier 2013-3-27
Thanks, i did not know that. However, i still can´t solve the integral (now the error message is Undefined function 'times' for input arguments of type 'function_handle)
What i have to do is to compute a definite integral for the function:
N(a(t))*b(t)*C(d(t)) dt
Where N(a(t)) is a normal probability function valued at the value a, which is in fact a function that depends on t. C(d(t)) is a cumulative normal probability function valued d, which is also a function that depends on t. And b(t) is another function of t.
I have tried to define first the functions a(t) b(t) and c(t) as function handles. Then i used the commandsnormcdf and normpdf to compute the normal cumulative and probability function on this function (i think this way i obtain also a function handle that depends on t, but i am not sure if this is ok. For example, CNaux1 = @(t)normcdf((K*(T-t))/sigma/sqrt(T-t)) )
Later, i define another function handle integrand= N(a(t)).*b(t).*C(d(t)) and i use the quad (integrand, 0, T) (T previously defined)
I thinh i probably made more than one mistake, i am quite a bit lost...
Thank you very much!

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更多回答（1 个）

Youssef Khmou
Youssef Khmou 2013-3-27
编辑：Youssef Khmou 2013-3-27
hi,
I am no sure about the error you get, but try this version :
m=0;
s=1;
x=0:0.1:10;
C=normcdf(x,m,s);
PHI=2*exp(j*2*pi*x); % Consider it as wave function
N=abs(PHI).^2; % consider it as the probability of existence .
b=exp(-(x-2).^2);; % the thrid function as you consider
II=C.*b.*N;
figure, plot(x,II);
F=trapz(x,II);
So the integral is evaluated using the function "trapz" along the X axis ,
I hope this helps

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