If I know all the parameters of a distribution (mean, deviation, skewness, kurtosis,…) how do I calculate what quantile a certain data is at?

#1
I have a game with levels. I am tracking the time (in seconds) each of my users took to complete a certain level.

What I want to accomplish is to show the user how their time compares to others (i.e. "Your time is better than 60.5%") by using the existing data that I have.

From the raw data, I've extracted a sample of 1000 that represent each 1000th quantile. Based off of this, I was able to determine the basic properties of the distribution.

Mean 90,47152847
Standard Error 1,951841119
Median 75
Mode 300
Standard Deviation 61,75348928
Sample Variance 3813,493439
Kurtosis 2,127713313
Skewness 1,449926474
Range 296
Minimum 4
Maximum 300
Sum 90562
Count 1001

Is there a way to determine what quartile a certain user time would represent, just by using the above descriptive statistics, and not using the quantiles that I already have?
Reason why I would like to avoid comparing user time to a huge table of 1000 numbers is to save space in the code. So I am hoping for some way to calculate what quantile a user is near/at by using least amout of numbers
 

katxt

Active Member
#2
I would find it quite surprising if you could find a formula for the quantiles (effectively the CDF) using your numbers.
A simple approach would be to plot the CFD and approximate it with a piecewise function of say five line segments. Then store the ends of the segments. When the time comes, look up the appropriate segment and do a linear interpolation.
 

hlsmith

Less is more. Stay pure. Stay poor.
#3
Since you came up and used these parameter, are you assuming a normal distribuion or distribution? If so, wouldn't the mean plus or minus the right value multiple of the SD work for finding the area under the curve. So if John had a time of 91.47, couldn't you say he has time 0.51 std above the mean and convert that to a region for the distribution?