一类特殊Z分布的渐近分布

Asymptotic Distribution of a Specific Z Distribution

通过对Fisher-Z分布进行适当分解,利用截尾法研究Z分布的近似分布.证明了当Z分布中的两个参数m和n都为正整数,且mmm+n→α(m,n→∞,0<α<1)时的渐近分布为正态分布.作为特例,说明了某类F分布的渐近分布也是正态分布.

The asymptotic distribution of the Z distribution is studied by means of decomposing the Fisher-Z distribution properly and the classical analysis method-truncation method. It is proved that the asymptotic (distribution) of the Z distribution is normal distribution when the two parameters m and n of the Z distribution are all positive numbers and mm+n α(m,n, 0<α<1). As a special example, it is proved that the asymptotic distribution of F distribution is normal distribution.