estimate the cdf 95% with a confidence interval of a 95%

Dear all,

I do networking simulations and I have the following problem. Imagine
that I set up a certain scenario, for instance N stations in my
wireless network, and I want to obtain an estimation of which is the
delay that my stations are suffering when they sent a packet to a
certain node that acts as a gateway.

What I do is that every station writes in a file the delay that it took
for it to send every packet. Then at the end of a simulation I have N
files, each file containing the delays of all the packets that every
station has sent. If I run the simulation M times, with M different
random seeds, then I have N*M files each one containing the delays that
one station suffered for each one of its packets.

Now assume that the delay that one station can suffer when sending a
packet in my network is a random process, what I want to do is to
compute an estimate of the 95% cdf of such the delay, i.e the delay d_0
such that a packet sent by the station will suffer a delay lower than
d_0 with probability 0.95.

What I do to compute this delay is to put all the samples from all the
N*M files together, as a samples of the same random process or
realizations of the random variable delay, and then I compute an
empirical cdf out of all these samples, and from that emprirical cdf I
compute the 95% cdf. To compute the cdf I use the 'ecdf' function in
matlab. This in my understanding is the best estimation of the 95% cdf
that I can obtain given all my samples.

Now my problem is that I want to give this 95% cdf delay with a certain
level of confidence. The point is that using the method described above
I can not give any confidence because I need samples to compute an
interval, and according to what I described previously I only have one
sample. The other alternative is to compute an estimation of the 95%
cdf for each one of the simulation runs, having thus M samples of the
95% cdf, and then I can compute the average of my M samples, having the
"expected" 95% cdf, and compute the confidence interval around the
expected 95% cdf using a gaussian aproximation, or the T-student
method.

Which is according to you the best procedure to follow? Would there be
another way to give the estimation of the 95% cdf with a certian level
of confidence ?

Best Regards

Dani

.

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