[EMAIL PROTECTED] wrote in message news:<[EMAIL PROTECTED]>... > > 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? . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
