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QUERY: how can I estimate "a" ? (typo is corrected)

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Thu, 23 Dec 1999 08:11:00 +0500 (ES)

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 ```-----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----- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ```

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