Expounds the theories of applying probability integral method to analysis coal mining and surface subsidence and applying cubic spline interpolation method to draw the subsidence graphs.

In this paper,I gove several calculated methods of the probability integral.

Based on the prediction model of probability integration method, the paper studied the utility method of mining subsidence dynamic prediction, gave a formula for computing subsidence velocity factor.

Non-dimensionalized with average wave height,the accumulative probability of wave height in wave groups with long runs is remarkably larger than in wave groups with short.

Nolte derived the accumulative probability of multi-wave heights in a wave group on the basis of the linear theory of ocean waves and the Rayleigh distribution of wave height.

It presents the generalized calculating methods and the formularized generic results of integrals ~_0x~ne~(-αx)dx and ~_0x~ne~(-(αx)~m)dx and probability integrals ~_0x~ne~(-αx~2)dx and some frequently used integrals in (Boltzmann) statisticsBose statistics and Fermi statistics.