令α表穩定型(stable)隨機變數之指標(exponent). 通常α是未知的, 必須用樣本來估計, 本文之目的在討論α之點估計. 從現有文獻知, 經驗特徵函數(empirical characteristic function )可用來估計α, 經驗分布(empirical distribution)也可用來估計α. 本文將藉由機率密度函數之均勻核估計式來估計α. 由於機率密度函數之均勻核估計式非常複雜, 我們只討論小樣本情形 In this paper, we discuss the estimation of exponent of a stable distribution. The exponent has been estimated by empirical characteristic function and empirical distribution. We consider the uniform kernel estimator of the likelihood function base which the kernel estimator of the exponent is described. Since the kernel estimator of the likelihood function is extremely complicated, we will discuss only small sample cases.
