...
Variations, probabilities of non-exceedance and return periods can be computed for the following frequency distributions:
1. Normal distribution,
2. Log-normal distribution,
3. Box-Cox transformation to normality,
4. Pearson Type III or Gamma distribution,
5. Raleigh distribution,
6. Exponential distribution,
7. General Pearson distribution,
8. Log-Pearson Type III distribution,
9. Extreme Type I or Gumbel distribution,
10. Extreme Type II or Frechet distribution,
11. Extreme Type III distribution,
12. Goodrich/Weibull distribution,
13. Pareto distribution,
14. Peaks over Threshold (pot)-method for extremes (Pareto distribution),
15. Student-t distribution, and
16. Fisher F-distribution.
The distributions 1 to 14 are described in the previous paragraph. The distributions 15 and 16 are presented in the next paragraph. The data requirements for this option are dealt with in the last section of this paragraph.
05 - Time Series Analysis^image043.gif!
Frequency distributions
Reference is made to the previous paragraph for the description of the distributions 1 to 14. The Student t-distribution and Fisher F-distribution are presented below.
...
The probability of non-exceedance is given by:
05 - Time Series Analysis^image045.gif!
with:
n = degrees of freedom (>2)
mean = 0.
st. dev. = Ö(n/(n-2)
...
The F-distribution is a ratio of two Chi-square distributed variables with respectively m and n degrees of freedom, where the Chi-square in its turn is a sum of squared standardised normally distributed variables; the number of elements in the sum is the degree of freedom.
The probability of non-exceedance is given by:
05 - Time Series Analysis^image047.gif!
with:
m, n = degrees of freedom
mean = m/(n+1)
st. dev. = n Ö((m+2)/(m(n-2)(n-4))
...