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Reduced Variate 'Y' in Gumbel's Method Formula

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Reduced Variate 'Y' is a transformed variable that allows for the Gumbel distribution to be used to model extreme values. Check FAQs

y = (\frac{1.285 \cdot (x T - x m)}{σ}) + 0.577

y - Reduced Variate 'Y'?x_T - Variate 'X' with a Recurrence Interval?x_m - Mean of the Variate X?σ - Standard Deviation of the Z Variate Sample?

Reduced Variate 'Y' in Gumbel's Method Example

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Here is how the Reduced Variate 'Y' in Gumbel's Method equation looks like with Values.

Here is how the Reduced Variate 'Y' in Gumbel's Method equation looks like with Units.

Here is how the Reduced Variate 'Y' in Gumbel's Method equation looks like.

9.6769 = (\frac{1.285 \cdot (9.43 - 0.578)}{1.25}) + 0.577

9.6769 = (\frac{1.285 \cdot (9.43 - 0.578)}{1.25}) + 0.577

9.6769 = (\frac{1.285 \cdot (9.43 - 0.578)}{1.25}) + 0.577

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Reduced Variate 'Y' in Gumbel's Method Solution

Follow our step by step solution on how to calculate Reduced Variate 'Y' in Gumbel's Method?

FIRST Step Consider the formula

y = (\frac{1.285 \cdot (x T - x m)}{σ}) + 0.577

Next Step Substitute values of Variables

∴

y = (\frac{1.285 \cdot (9.43 - 0.578)}{1.25}) + 0.577

Next Step Prepare to Evaluate

∴

y = (\frac{1.285 \cdot (9.43 - 0.578)}{1.25}) + 0.577

Next Step Evaluate

∴

y = 9.676856

LAST Step Rounding Answer

∴

y = 9.6769

Reduced Variate 'Y' in Gumbel's Method Formula Elements

Variables

Reduced Variate 'Y'

Reduced Variate 'Y' is a transformed variable that allows for the Gumbel distribution to be used to model extreme values.

Symbol: y

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Reduced Variate 'Y'

Variate 'X' with a Recurrence Interval

Variate 'X' with a Recurrence Interval of a random hydrologic series with a return period.

Symbol: x_T

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Variate 'X' with a Recurrence Interval

Mean of the Variate X

Mean of the Variate X of a random hydrologic series with a return period.

Symbol: x_m

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Mean of the Variate X

Standard Deviation of the Z Variate Sample

Standard Deviation of the Z Variate Sample follows a certain probability distribution of a hydrologic model.

Symbol: σ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Standard Deviation of the Z Variate Sample

Other formulas in Gumbel's Method for Prediction of Flood's Peak category

Go Reduced Variate concerning Return Period

y T = - (\ln (\ln (\frac{T r}{T r - 1})))

Go Reduced Variate 'Y' for given Return Period

y T = - (0.834 + 2.303 \cdot \log 10 (\log 10 (\frac{T r}{T r - 1})))

Go Frequency Factor as applicable to Infinite Sample Size

K z = \frac{y T - 0.577}{1.2825}

Go Reduced Variate for Return Period when Frequency Factor is Considered

y tf = (K z \cdot 1.2825) + 0.577

How to Evaluate Reduced Variate 'Y' in Gumbel's Method?

Reduced Variate 'Y' in Gumbel's Method evaluator uses Reduced Variate 'Y' = ((1.285*(Variate 'X' with a Recurrence Interval-Mean of the Variate X))/Standard Deviation of the Z Variate Sample)+0.577 to evaluate the Reduced Variate 'Y', The Reduced Variate 'Y' in Gumbel's Method formula is defined as the dimensionless variable in Gumbel's Method, one of the most widely used probability distribution functions for extreme values in hydrologic and meteorological studies for prediction of flood peaks. Reduced Variate 'Y' is denoted by y symbol.

How to evaluate Reduced Variate 'Y' in Gumbel's Method using this online evaluator? To use this online evaluator for Reduced Variate 'Y' in Gumbel's Method, enter Variate 'X' with a Recurrence Interval (x_T), Mean of the Variate X (x_m) & Standard Deviation of the Z Variate Sample (σ) and hit the calculate button.

FAQs on Reduced Variate 'Y' in Gumbel's Method

What is the formula to find Reduced Variate 'Y' in Gumbel's Method?

The formula of Reduced Variate 'Y' in Gumbel's Method is expressed as Reduced Variate 'Y' = ((1.285*(Variate 'X' with a Recurrence Interval-Mean of the Variate X))/Standard Deviation of the Z Variate Sample)+0.577. Here is an example- 9.6748 = ((1.285*(9.43-0.578))/1.25)+0.577.

How to calculate Reduced Variate 'Y' in Gumbel's Method?

With Variate 'X' with a Recurrence Interval (x_T), Mean of the Variate X (x_m) & Standard Deviation of the Z Variate Sample (σ) we can find Reduced Variate 'Y' in Gumbel's Method using the formula - Reduced Variate 'Y' = ((1.285*(Variate 'X' with a Recurrence Interval-Mean of the Variate X))/Standard Deviation of the Z Variate Sample)+0.577.

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Reduced Variate 'Y' in Gumbel's Method Formula

Reduced Variate 'Y' in Gumbel's Method Example

Reduced Variate 'Y' in Gumbel's Method Solution

Reduced Variate 'Y' in Gumbel's Method Formula Elements

Other formulas in Gumbel's Method for Prediction of Flood's Peak category

How to Evaluate Reduced Variate 'Y' in Gumbel's Method?

FAQs on Reduced Variate 'Y' in Gumbel's Method

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