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Reduced Mean is a function of sample size N in Gumbel's Extreme Value distribution. It represents a transformed variable used in extreme value analysis to model rare events and calculate return periods for hydrological and meteorological events.
The calculator uses the formula:
Where:
Explanation: The formula calculates the reduced mean by subtracting the product of frequency factor and reduced standard deviation from the reduced variate for the return period.
Details: Accurate calculation of reduced mean is crucial for extreme value analysis in hydrology and meteorology. It helps in determining return periods of rare events such as floods, droughts, and extreme weather conditions, which is essential for infrastructure planning and risk assessment.
Tips: Enter the reduced variate for return period (yT), frequency factor (Kz), and reduced standard deviation (Sn). All values must be valid numerical values to get accurate results.
Q1: What is Gumbel's Extreme Value Distribution?
A: Gumbel's distribution is used to model the distribution of the maximum (or minimum) of a number of samples of various distributions. It's particularly useful in extreme value theory.
Q2: How is Frequency Factor determined?
A: Frequency factor varies between 5 to 30 according to rainfall duration and is a function of recurrence interval (T) and the coefficient of skew (Cs).
Q3: What is the significance of Reduced Standard Deviation?
A: Reduced standard deviation is a function of sample size N and measures how much variation from the mean exists in Gumbel's Distribution Table.
Q4: When should this calculation be used?
A: This calculation is primarily used in hydrological studies for flood frequency analysis and in meteorological studies for extreme weather event prediction.
Q5: Are there limitations to this approach?
A: The accuracy depends on the quality of input data and the assumption that the data follows Gumbel's distribution. It may not be suitable for all types of extreme value analysis.