> > Take the following probability: P(X1 > a & X1+X2 < b) > > > > Where X1 and X2 are sums of exponential variables (all with the same > > rate parameter). So the resulting sums are gamma distributed, right? > > > > A first possible way to solve this is by conditioning on one of these > > variables and doing a lot of the math by hand. However, as the number > > of variables rises, so does the complexity of the calculations. > > > > Is there a way of determining this type of probability numerically? > > [...] > > Since X1 and X2 are positive, the conditions X1 > a and X1+X2 < b > correspond to the interior of a triangle whose vertices are (a,0), > (b,0), and (a,b-a). So why not integrate F2(b-x)*f1(x)dx from a to b, > where f1 is the pdf of X1 and F2 is the cdf of X2. Both f1 and F2 > should be simple function calls, no matter how many variables go into > X1 and X2. What "math by hand" are you talking about?
So what about: P(X1>a & X1+X2<b & X2+X3>c) The example in X1,X2 is a very simple one... The "math by hand" I'm referring to is conditioning on several variables leading to some lengthy calculations (splitting up integrals, ...). thanks, Miyuko. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
