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.
.
.
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