Abstract: The asymptotic distribution of the Z distribution is st udied by means of decomposing the Fisher-Z distribution properly and the classi cal analysis method-truncation method. It is proved that the asymptotic distr ibution of the Z distribution is normal distribution when the two parameters m and n of the Z distribution are all positive numbers and m/(m+n)→α(m,n→∞, 0 <α<1). As a special example, it is proved that the asymptotic distribu tion of F distribution is normal distribution.

Key words: Fisher-Z distribution, asymptotic distribution, norma l distribution, F distribution