Approximating the Minimum Distribution of Two Normally Distributed Variables Each with the Same Mean and Variance

Several integrals impose excessive computational burden in the solution of the minimum distribution of two normally distributed variables each with the same mean and variance. To overcome the inefficiency, this paper first investigates the probability and maximum value of deviation occurrence between the normal distributions, and then proposes an approximation method of the mean and variance of the distribution. The test results show that the approximations give high accuracy in the range from 10 to 10000, and the more importance is that one can modify the fitting parameters in the method to obtain approximations for other ranges.