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with:
Z = (ln(X - X0 )-Y{~}0 ) / β,
X0 ,Y0 = location parameters,
β = scale parameter.
β γ = shape parameter.
The location parameter X0, (X0 < X) is provided by the user, while the parameters Y0, band gare estimated by:
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with:
X0 = location parameter, (X0 < X) !!
β = scale parameter,
γ = shape parameter. (k < 0)
The location parameter may be given (2-parameter distribution) or estimated (3-parameter distribution). The parameters can be estimated by the modified maximum likelihood method.
Extreme Type III Distribution:
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The pot-method uses the Pareto distribution. An additional parameter lis λ is introduced, which is the average number of exceedances per year. A return period of T years corresponds in the POT method to one occurrence of the extreme in a series of T λT exceedances above a fixed threshold X0 (the location parameter X0 is equal to the selected lower threshold). Hence the related probability of non-exceedance in a series of all exceedances above a threshold is 1 - 1/(lTλT).
Selection of Data
Data used for the distribution functions will be read from the hymosdatabase. All distribution functions, except the Pareto with POT method, require the numberof selected data to be equal to the number years for a correct interpretation of probability of non-exceedance versus return period. Only for the Pareto with POT method a correction is applied for the return period. For all other methods a manual correction have to be made when the number of selected data is not equal to the number of years.
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