ETL 1110-2-537
31 Oct 97
*
F ( Yp )i
(1-F ( Yp))i
**
i
c
p
F ( Yp ) ' m / ( n % 1 ) ' 0.833
(1)
(2)
(3)
(4)
(5)
0.8333
0.1672
3
5!/(3!2!)=10.0
0.159
where
0.8334
0.1671
4
5!/(4!1!)=5.0
0.396
m = event rank
0.410
5
0
5
5!/(5!0!)=1.0
0.833
0.167
0.96
n = number of years of record
*
Binomial coefficient.
**
Product of columns 2,3,4.
Given that the 0.833 nonexceedance probability event
Consequently, there is a 0.96 probability, or 96 percent
or 0.167 exceedance probability event occurs, the
chance, that the stage corresponding to the 0.167-
the third-ranked observation, Yj = Y3 can be computed
event Y3.
using Equation 1:
DISTRIBUTION DUE
TO APPLICATION OF
VARIABLE
INCOMPLETE BETA
FUNCTION
Xn
PREDICTION
LIMITS
X
1
1.0
0.95
O.5
0.05
0.0
EXCEEDANCE PROBABILITY
Figure 1. Uncertainty with order statistics
3