The primary objective of the paper is to review the development of approximations of the null distribution of a scan statistic and to show how these approximations were improved. Let $X_1, cdots, X_N$ be a sequence of independent uniform random variables on an interval (0, t]. A can statistic is defined to be the maximum number of observations in a subinterval of length t $leq$ T, when we continuously (or discretely) move the subinterval from 0 to T. A scan statistic is used to test whether certain events occur in a cluster aganist a null hypothesis of the uniformity. It is difficult to calculate the exact null distribution of a scan statistic. Several authors have suggested approximations of the null distribution of a scan statistic since Naus(1966). We conceive that a scan statistic can be used for detecting a "hot region" is defined to be a region at which the frequencies of mutations are relatively high. A "hot region" may be regarded as a generalized version of a hot spot. We leave it for a further study the concrete formulation of deteciton a "hot region" in a mutational spectrum.uot; in a mutational spectrum.