# Probability of hitting tails [closed]

I have 5 variables for 1000 observations. Given the data, I need to

1. Calculate probability of hitting top 5 pct in each of the distributions separately. For example, for the value of 123.45 I need to calculate how probable is that this vale is from the top 5pct.

2. Calculate probability that a particular observation (given with 5 values for each variables) will be in the tails of each of the distributions... In the same time

3. Calculate probability that a particular observation will hit at least one 5pct tail.

• Do you have any information about the joint distribution of the five variables or are you trying to estimate it? If you specify a distribution, this problem reduces to simple calculations of areas under the joint density. Jun 28, 2011 at 17:06
• I don't have any info on joint distribution... Jun 28, 2011 at 17:14
• @Ryan I imagine 1000 observations would tell you something about the data distribution :-).
– whuber
Jun 28, 2011 at 21:23
• It's not market data. It's not any particular (know) statistical distribution. It looks like normal distribution with very fat right tail (all 5 variables)... Jun 28, 2011 at 21:24

so how you can tell is you should plot the quantiles of your data against the theoretical quantiles of the weibull distribution, t distribution, ect. If the quantiles lie on a 45 degree line, then the data is from that distribution.

if you have R you can use the fitdistr function that is part of the MASS library. this will tell you the parameter values of your distribution so you can then use the density function of your distribution to get the probabilities.

If you dont have R i would download it cause this would be computationally taxing otherwise.

• can you please be a little bit more precise? How do you suggest I get joint probability of all 5 vars being in top 5% and then probability of at least one hitting top 5%? Jun 28, 2011 at 21:49
• @Ryan How exactly does the t distribution apply here?
– whuber
Jun 28, 2011 at 21:52
• I have data for each variable. So my dataset has 5 columns and aprox. 1000 rows Jun 28, 2011 at 22:25
• btw. I think my distributions are closest to Weibull(1,1) Jun 28, 2011 at 22:25
• Yeah.. But, let's say that I have to work out solution for the case where I don't know distribution... Jun 29, 2011 at 7:23