The analyses on the statistical probability of the response spectra have an important role in determining the earthquake demand. Elastic and inelastic spectra on acceleration of the 369 records with a long characteristic period for SDOF systems were presented in statistical analyses. The empirical probability distributions of the spectral values were derived according to the Kolmogorov-Smirnov (KS) goodness-of-fit test. And the spectra considering the probability guaranty were developed to investigate the characteristic of the response spectra. The formula for statistical average spectra of the ground motion ensemble were recommended, which were valuable for current research and code revisal. The results show:(1)the inelastic responses decrease with the increase of ductility demand μ when μ<4, and they decrease unclearly when μ≥4;(2) the inelastic spectra has a large value of Cov (coefficient of variance),the Cov range from 0.2 to 0.3 when T<1s,and it increases linearly when T≥1s;(3)the probabilistic distribution of the spectra value on acceleration is validated as the lognormal or the Gumbel type I distributions;(4) the probabilistic spectra may be a feasible way to determine earthquake load in the future.