dear group, 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? A first (but slow) approach is using some form of GAMINV implementation and then looping over a number of values. As the number of dependent chances increases, so again does the number of nested loops --> not very efficient. Someone suggested by using some form of Laplace transform but I don't quite know how this would go about. any help is greatly appreciated. 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/ . =================================================================
