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所有长尾分布都是重尾分布，但反之不一定，事实是可以构造出非长尾分布的重尾分布。
所有长尾分布都是重尾分布，但反之不一定，事实是可以构造出非长尾分布的重尾分布。
=== Subexponential distributions 长尾分布的定义 ===
=== Subexponential distributions 次指数分布 ===
Subexponentiality is defined in terms of [[Convolution of probability distributions|convolutions of probability distributions]]. For two independent, identically distributed [[random variables]] <math> X_1,X_2</math> with common distribution function <math>F</math> the convolution of <math>F</math> with itself, <math>F^{*2}</math> is convolution square, using [[Lebesgue–Stieltjes integration]], by:
Subexponentiality is defined in terms of [[Convolution of probability distributions|convolutions of probability distributions]]. For two independent, identically distributed [[random variables]] <math> X_1,X_2</math> with common distribution function <math>F</math> the convolution of <math>F</math> with itself, <math>F^{*2}</math> is convolution square, using [[Lebesgue–Stieltjes integration]], by: