Proven theories and observations in specific regions have demonstrated that average climates often exhibit significant nonlinear relationships with extreme climates. Two different types of climate variables that show symmetric and asymmetric probability distributions correspond to nonlinear changes from average to extreme climates. In this paper, the data from several representative stations and relative climatic variable fields are used to prove that theoretical estimated probabilities for extreme climates are more consistent with actual values. Examples are used to demonstrate cases in which the various probability distributions are observed.