Sometimes the exponential family is parameterized by using a scale parameter. Sometimes a rate parameter.
If E ~ Exp(1), then
- The random variable sigma*E is exponential with scale parameter sigma.
- The random variable E/lambda is exponential with rate parameter lambda.
The lower bound of an exponential r.v. is 0, so adding 1 would translate the threshold to 1.
I think you do not need the 8. If you want a truncated exponential distribution, you would use an IF-THEN statement to accept/reject the random values in [1,8], such as
x = 1 + rand("expo")/lambda;
if x <= 8;
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