Title: Basic Statistics Climatological Class Limits

Probability distributions are widely used in climate prediction. The most basic application is definition of class limits for defining forecast categories. NWS/NCEP Climate Prediction Center uses equally probable terciles (below, near and above normal) from the 1971-2000 series as climatological class limits. Figure 1 shows example for this.

Illustration of CLimatology: top picture shows fitted normal distribution to temperature data with shaded areas for below, near or above normal. Bottom picture show histogram of the data used to fit the normal distibution.
Figure 1. Equally probable terciles (top) for daily temperature data (bottom) at Olympia Airport, Washington

Tercile limits divide the data into three equal pools (relative frequency of data to fall in each class is equal to 1/3). The area under the curve of the PDF is equal to 0.33 (equal chance) for each the three bins. This Figure 1 example shows a slightly shifted lower bin (the below normal class) as the mode deviates from the distribution mean.