The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.stat.math

Topic: A "plausible range" for a random variable
Replies: 9   Last Post: Jun 11, 2013 7:42 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 77
Registered: 7/21/06
A "plausible range" for a random variable
Posted: Jun 7, 2013 12:30 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


I run a Monte Carlo simulation of a black box code,i.e., I assign probability distributions to the code inputs and I obtain a Monte Carlo sample of the output variable Y. Y doesn't have to be Gaussian, because the input distribution aren't necessarily Gaussian, and even if they were, the output depends nonlinearly on inputs.

My bosses asked me to give them a "plausible range" for the variable Y. Trying to rephrase this question in a statistical framework, I thought about finding a lower bound L and an upper bound U for Y, such that p(L<=Y<=U) equal to, say, 95%. In practice, that's percentiles estimation. For example, if I were to set L=-inf, then U would be precisely the 95-th percentile of the distribution of Y, so the problem would become to estimate the 95-th percentile of Y.
1. Is there a preferred way to select L and U? I don't think so, since I don't know which is the distribution of Y. So I was thinking to just select two percentiles "symmetrical about the median", such that p(L<=Y<=U) = alpha. For example, if alpha = .95, I just choose L as the 2.5-percentile and U as the 97.5th percentile.
2. How do I estimate L and U? I know I could just load my samples in R and use bootstrap. However, I'd prefer to have also an analytical formula, for a variety of reasons. I have fairly large samples (usually N ~= 2000), so I guess that there should be some expression for the confidence intervals of percentiles, based on CLT. Can you post them?


Best Regards


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2017. All Rights Reserved.