-----BEGIN PGP SIGNED MESSAGE-----
yesterday I posted a message,
thank you Duncan,
asymptotic is F(x)=c*x^(-a)+o(x^(-a)) where a belongs to (1,2].
So we conclude that mathematical expectation of X exists, where
variance of X doesn't exist.
Regards, (Наилучшие пожелания)
Ilia Chipitsine (Илья Шипицин)
- ---------- Forwarded message ----------
Date: Wed, 22 Dec 1999 21:28:17 +0500 (ES)
From: Ilia Chipitsine <[log in to unmask]>
To: [log in to unmask]
Subject: QUERY: how can I estimate "a" ?
Dear AllStat-ers,
I have a question (well, I have number of questions, but it will take
me some time to write them in English :-)
Let (X1, X2, ..., Xn) be a sample of iid (independent identically
distributed) nonnegative random variables.
Let F(x) be cdf (cumulative distribution function) of those random
variables.
It is known that F(x)=c*x^a+o(x^a) when x tends to infinity.
It is also known that value of "a" belongs to (1,2].
1. How can I estimate "a" ?
2. How robust is that estimate ?
Regards, (Наилучшие пожелания)
Ilia Chipitsine (Илья Шипицин)
-----BEGIN PGP SIGNATURE-----
Version: 2.6.3ia
Charset: noconv
iQB1AwUBOGGSxuRxlWKN2EXhAQHPEgMAsuVfgbpZlJb6bL2NydHKKCT8BFIqIPtF
4DeMSLpXcGyGFCCqinaKi5SrewK1REY362vjfnDVIw5yfP7Mdl2CpD3Nu8EfvV3R
pZm+7VXYAhjtebSmQOAdJ8squ7XCZJcH
=5fnz
-----END PGP SIGNATURE-----
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|