Three
Key Statistical Concepts
1.
Cumulative probability (F_{i}) is probability that
precipitation takes a value less than or equal to a given amount. To calculate the cumulative probability function (e.g., annual rainfall equal to or less than a
certain amount):

rank annual rainfall from lowest to highest

rank is m, where 1 is the rank given to the lowest
precipitation

n is number of data points (number of years in this
case)
F_{i}
= m/(n+1) * 100%
F_{i}
= cumulative probability, i.e. the probability that that amount of rainfall or
less will occur in a given year. It is key to note
that for cumulative probability the lowest precipitation quantity receives a
rank of 1. This is a useful
statistic for drought prediction, where we are interested in probability of a
certain amount of precipitation or less occurring.
2.
Exceedence probability (p) is the probability that rainfall of that much or higher
will occur in a given year. Although
simple in concept, no end of confusion is created by the fact that the same
equation is used as for the cumulative probability frequency. The big difference is that m in this case
is rank where the highest value receives a rank of 1 (m = 1).
p = m/(n+1)
This
is a useful statistic for flood prediction, where we are interested in the probability of a
certain amount of precipitation or more that might cause flooding.
3. The Recurrence Interval or Return
Period (T) is the average interval in years between events equaling
or exceeding a certain magnitude. The
return period is calculated from:
T = 1/p = (n+1)/m
Where m is again ranked so that the highest precipitation value gets a rank of 1. The return period is a favorite tool of the press and planning agencies, because at first glance, people can readily grasp the concept of an event that occurs every x years on average. The problem is that people assume this means an event of this size occur once every 20 years, when in fact it may occur 5 years in a row, then not occur for another 95 years (which gives an average of once every 20 years).
4. A working example with 10 years of
precipitation data from Kenya. Therefore
n = 10 and n +
1 = 11.
Year 
Precip (mm) 
Cumulative Probability Rank (1 is lowest to 10 is highest) 
Cumulative
Probability (%) 
Exceedence Probability Rank (1 is highest to 10 is lowest) 
Exceedence Probability 
Recurrence Interval (years) 
1931 
1306 
4 
4/11*100 = 36.4% 
7 
7/11*100 = 63.6% 
11/7 = 1.57 
1932 
1345 
5 
5/11*100 = 45.5% 
6 
6/11 *100 = 54.5% 
11/6 = 1.83 
1933 
1032 
1 
1/11*100 = 9.1% 
10 
10/11*100= 90.9% 
11/10 = 1.1 
1934 
1580 
9 
81.8% 
2 
18.2% 
5.5 
1935 
1293 
3 
27.3% 
8 
72.7% 
1.37 
1936 
1497 
8 
72.7% 
3 
27.3% 
3.67 
1937 
1469 
7 
63.6% 
4 
36.4% 
2.75 
1938 
1392 
6 
54.5% 
5 
45.5% 
2.2 
1939 
1037 
2 
18.2% 
9 
81.8% 
1.22 
1940 
1633 
10 
90.9% 
1 
9.1% 
11 