Statistical Tables
General
Variations, probabilities of non-exceedance and return periods can be computed for the following frequency distributions:
Normal distribution,
Log-normal distribution,
Box-Cox transformation to normality,
Pearson Type III or Gamma distribution,
Raleigh distribution,
Exponential distribution,
General Pearson distribution,
Log-Pearson Type III distribution,
Extreme Type I or Gumbel distribution,
Extreme Type II or Frechet distribution,
Extreme Type III distribution,
Goodrich/Weibull distribution,
Pareto distribution,
Peaks over Threshold (pot)-method for extremes (Pareto distribution),
Student-t distribution, and
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.
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.
Student t-distribution:
The probability of non-exceedance is given by:
with:
n = degrees of freedom (>2)
mean = 0.
st. dev. = Ö(n/(n-2)
Fisher F-distribution:
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:
with:
m, n = degrees of freedom
mean = m/(n+1)
st. dev. = n Ö((m+2)/(m(n-2)(n-4))
Data input
The type of data required to use the statistical tables is twofold:
1. distribution parameters, for which reference is made either to the previous paragraph or the previous section and
2. a value for either/or:
- variate,
- probability of non-exceedance,
- return period.
After selecting a distribution function and a value for the variate, probability or return period the results will be presented when pressing Execute.
Note : HYMOS uses the standard windows settings, defined in the regional settings of the control panel, for the definition of the number of decimals to show in input boxes. By default the number of decimals set by Windows is two. The parameters of distribution function often require more decimals to be entered, therefore the user must change the number of decimals from the regional settings.
