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- 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)
For each distribution one can obtain:
- estimation of parameters,
- summary of observed and theoretical probabilities,
- goodness of fit-tests:
- binomial,
- Kolmogorov-Smirnov,
- Chi-squares,
- computation of extreme values for specific return periods, either related to probability of non-exceedance or exceedance, and
- plot of distribution
The plotting of ordered data on extreme probability paper is done according to a general plotting position function: P = (m - a) / (N + 1 - 2a). Constant 'a' is an input variable and is default set to 0.3. Many different plotting functions are used, some of them can be reproduced by changing the constant 'a'.
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For the normal distribution the Blom plotting function can best be used, for the Gumbel distribution Gringorton gives the best results. A plotting function which can be used for all distribution functions is Chegadayev. More information on plotting positions can be found in many hydrological handbooks (i.e. Applied Hydrology: pages. 394-396).
The frequency distributions are briefly described in then next Section. For a detailed description of the frequency distributions reference is made to other text books. The selection procedure of data is dealt with in Section 10.2.3.
Frequency distributions
Normal distribution function:
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Pareto distribution:
PPA (X) = 1 - ee^-ZZ^; 0 < Z < ¥ ; q = 0 (GP-I)
= 1 - (1 - qZ)1 q; 0 < Z < ¥ ; q < 0 (GP-II)
= 1 - (1 - qZ)1 q; 0 < Z < 1/q; q > 0 (GP-III)
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