Re: About normcdf() function integration method

[Rik]

On 10/16/2017 09:00 AM, address@hidden wrote:

Subject:

About normcdf() function integration method

From:

José Luis García Pallero <address@hidden>

Date:

10/16/2017 06:23 AM

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Octave Maintainers <address@hidden>, Octave Maintainers List <address@hidden>

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Hello:

I'm teaching this semester some maths and I'll explain numerical
integration methods. In one exercise the students must write a script
in order to compute areas below the normal distribution curve and then
use the normcdf() function to check the results and the theoretical
error level for the Simpson and the trapezoidal methods.

My question is, which method for numerical integration uses Octave in
normcdf()? If uses the trapezoidal or Simpson method, what is the
level of discretization?

Thanks

The function normcdf() is implemented in an m-file which means you can just look at the source to see what Octave is doing.  Inside normcdf.m there is this line

cdf = stdnormal_cdf ((x - mu) / sigma);

So Octave is centering and scaling the distribution, and then using the CDF for the standard normal function with mu = 0, sigma = 1.

stdnormal_cdf is also implemented as an m-file.  Inside that one finds

  cdf = erfc (x / (-sqrt(2))) / 2;

Octave relies on the C++ standard library for the complimentary error function erfc.

For students, definitely have them try trapz() or one of the 1-D integrators (quad, quadv, quadgk, etc.).

--Rik