Q Function

The Q Function implemented as integegraion of density function.

Description

This function computes the Q function by integrating the Normal distribution.

It takes one paramter and calculates the right tail probablity.
Ex. x=q(0)
x would have the value of .5

For an arbitrary Gaussian distribution with mean, mu, and variance, sigma^2, then the function is passed this form.
((y-mu)/sigma)

Ex. Say you have a distribution of G(3,4). mu = 3, and sigma = 2. You want to calculate the right tail probability that it will be greater than 3.5. The function call would look like
answer=q((3.5-3)/2);

This is not the most efficient way of calculating this. I wrote this because I didn't have the proper toolbox. If you have the toolbox its just QFunc.

• MATLAB release: MATLAB 6.5 (R13)
• Other requirements: As far as I know there are no known requirements other than having Matlab installed. I have only tested this on R13 though.

[carlos lopez]

Probably it would be nice to have a definition of the Q function. Some other submissions suffer from the same problem: the authors are so inmersed in their own field that it is difficult to an outsider to take advantage of the submissions.

[Tim Felty]

Sorry about that. It calculates the tail end probability of a Gaussain distribution. It calculates the area from a point x on the distribution to infinity, giving the probability.

[TJ Lim]

The Q function is related to the complementary error function, which is available in Matlab as erfc, so qx = erfc(x/sqrt(2))/2 yields Q(x) without explicit integration.

[Abhimanyu Sharma]

 

[k dg]

good !

[M P]

Thanks Timothy and TJ

[Jerry Chiang]

why not simply use built-in ERF function?

function answer = q(x)
answer = 1/2*(1-erf(x/sqrt(2)));

[Stephen]

This function was needed for a Satellite COmmunictation class. I had to have Q(x), not erf(x). I tested it today on Matlab R2009a and it works. Thanks Mr. Felty!