Re: Distribution of a Percetile

Re: Distribution of a Percetile
Posted: Sep 21, 2005 7:37 PM
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> I have some traffic speed data which consists of the
> speeds of individual
> vehicles as they pass a point on the road. These
> daily speed measurements
> (the sample size, n, is large but variable each day)
> can be charted and
> approximated with a skewed distribution.
>
> Some data was collected before and some after a
> change. I would like to
> obtain the distribution of the 85th%ile of these
> speed distributions and
> test whether they are the same.
>
> Can someone point me to a web resource which will
> allow me to conduct this
> test? Thanks.
>

*****
Here's one possible approach. A log-normal distribution might be a reasonable distribution to assume. In that case, the 85th percentiles for each of the two distributions are

exp(mu+z(0.85)*sigma),

where mu and sigma are the population mean and standard deviation of the logs.

So we're testing whether mu+z(0.85)*sigma is equal for the two populations.

The parameters mu and sigma are estimated by taking the log of the data and calculating the sample mean and standard deviation for the two samples.

For each sample, let N be the sample size involved in estimating mu and let m be the degrees of freedom for estimating sigma. For large sample sizes,

y(0.85) = xbar + z(0.85)*s is approximately normal with variance estimated by

Var(y(0.85)) ~ s^2[1/N + {z(0.85)^2}*(1-1/a(m)^2)],

where a(m) = sqrt(m/2)*Gamma(m/2)/Gamma((m+1)/2)

What you end up with is a comparison of two normal quantities.

Jack



My response
Why? Why LOGNORMAL is a suitable distribution. To be reasonable is sufficient? Why not any other?
It is simply asked how to compare two fractiles (ante and post the point border point: that left 85% of data behind. It is a plain Bernoulli case WHATEVER the distributions are. Is this difficult to understand?
____________________licas
.

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