find the probability in normal distibution

hi everyone. i have two normal distribution curves which met each other at two points A and B. how can i find these two points and then how can i calculate the probability between (-inf,A), (A,B) and (B, inf) for each curve? thank you for your time :)

[the cyclist]

When you say you "have" the curves, can you be more specific? For example, do you have the equations of the curves, or do you have empirical values in vectors?

[maryam]

dear cyclist,i have the equations of the curves.(mu and sigma of normal distribution are known so i can plot these graphs).

[the cyclist]

Someone here may be able to help you, but you should be aware that what you are asking is not really a MATLAB problem, but rather a math problem. You might also want to seek help on a math forum.

Answer 1

[dpb]

Approximate (to nearest point of x vector) is fairly simple to do. Define

f=@(x)normpdf(x,mu1,s1)-normpdf(x,mu2,s2)

as the difference between the two. Then simply evaluate and look for the zero crossings--to illustrate I can approximate your plot pretty closely with

>> mu1=-30;s1=30; mu2=mu1; s2=s1/2;
>> x=-150:150;
>> d=f(x);
>> ix=find(diff(dd))+1
ix =
 101   142
>> f(x(ix))
ans =
 1.0e-03 *
 -0.2857    0.4266
>> figure
>> plot(x,[y1;y2;d].')
>> grid on

You can either refine these with an interpolating function around the located values or use a finer mesh for x, noting you don't need the full range to find the intersecting points.

Or, you can solve directly using fzero or similar root solver.

Once you've got the points, the percentiles should be easy enough just standardize those x-values found to the standard normal variate using the known parameters.

[maryam]

thank you very much :)

Answer 2

[John D'Errico]

What is the problem? Just use fzero on the difference between the two PDFs to find the intersection points. Then use normcdf to find the area you desire.