| 摘要(英) |
The collection of stable distributions is a particular class of distributions studied in probability and statistics. Let $X,X_1,ldots,X_k$ denote a sequence of i.i.d. random variables with a common distribution $R$. If for all positive integer $k$, $X$ and $frac{X_1+cdots+X_k}{k^alpha}$ have the same distribution for
some constant $alpha$, then $R$ is a stable distribution with exponent $frac{1}{alpha}$. It is difficult to estimate exponent $alpha$ since $alpha$ does not appear in probability density function. The purpose of this paper is to study some estimators of $alpha$ and their applications. We find that under unimodal assumption $alpha$ is a functional of probability density function
or distribution function. Consequently, $alpha$ can be estimated by kernel density estimators or empirical distributions. |
| 參考文獻 |
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