I'm taking a course in computer simulation. I have a few questions on exponential distribution. I've tried to google on the subject but could not find a satisfactory answers to my questions. Here are my questions:
1. What is the different between negative and positive exponential distribution? Quite often I've read passages in the papers: "the job arrival rate is negative exponential distribution with mean 50 seconds".
Why is it refer to negative? what would happen if we have positive exponential distribution instead?
Also, as far as I know there is only one parameter in exponential distribution which is the lamda: x.exponential( lambda). If I want to simulate this exponential distribution with mean X seconds e.g. 50 seconds, what value should i plug for lambda?
I have tried to plug lambda as 50 in the simulation but the mean value of the total generated numbers do not tally to 50.
You explanations would be very much appreciated.
Thank you.
regards,
Amril
ANSWER: amril -
the terms "exponential distribution" and "negative exponential distribution" mean the same thing. some books use the first expression and other books, the second one.
the expression you write for the (negative) exponential distribution is incorrect.
if you rewrite it, i may be able to help you further.
i'll just mention that, depending on how the density function is written, the mean of the distribution is either lambda or 1/lambda. you should check your text to see which convention they are using.
ronny
---------- FOLLOW-UP ----------
QUESTION: Thank you Ronny for you reply,
Now at least I know that the negative and positive exponential distribution is the actually same thing
With regards to your explanation, it'd be appreciated if you could explain how I should check whether the distribution is either lambda or 1/lambda? How can I verify this? So, if the mean is 1/lambda, I presume i need to plug the value 1.0/50.0 seconds [exponential(1.0/50.00)] instead? Is this the correct approach?
As for the incorrect expression which I wrote before, here the experimental parameters from the paper which I was referring to:
Number of computers: 100
Number of requesters: 10,20,...,90,100
Job arrival rate: Negative exponential distribution with mean=50 seconds
Deadline of waiting jos: 20 seconds
Experiment period: 2.5 hours
My aim is to simulate the above parameters using c++ program but I don't really understand what is meant by exponential distribution with mean 50 seconds.
Would really appreciate your explanations.
Thank you.
regards,
Amril
Answer amril -
the standard exponential distribution has the pdf f(x) = exp{-x} for x > 0.
this distribution has mean = 1. all other exponential distributions are
just rescalings of this one. so if X has a standard exponental distribution
and Y has an exponential distribution with mean = 2, then Y has the same
distribution as 2X. so you can simulate Y by simulating X and multiplying
the X-values obtained by 2. for the record, the pdf of Y is g(y) = (1/2)exp{-y/2}
for y > 0, ahtho, as explained above, you really do not need to use this pdf to
simulate Y.
judging from the additional information you sent, it looks like you might be
simulating some sort of queuing system. i hope it is clear from the above how
you can generate exponential variables with mean 50 in doing this.
