Confidence Interval of Variate Calculator

✖Variate 'X' with a Recurrence Interval of a random hydrologic series with a return period.ⓘ Variate 'X' with a Recurrence Interval [x_T]			+10% -10%
✖Function of Confidence Probability defined by normal variates.ⓘ Function of Confidence Probability [f_c]			+10% -10%
✖Probable Error is the half-range of an interval about a central point for the distribution and in Gumbel's method it defines the range of effective measurement increments.ⓘ Probable Error [S_e]			+10% -10%

✖Value of 'x1' Bounded to Variate 'Xt' influences the limits about the calculated value between which the true value can be said to lie.ⓘ Confidence Interval of Variate [x₁]

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Confidence Interval of Variate

Formula

`"x"_{"1"} = "x"_{"T"}+"f"_{"c"}*"S"_{"e"}`

Example

`"12.43"="9.43"+"15"*"0.2"`

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Download Gumbel's Method for Prediction of Flood's Peak Formulas PDF

Confidence Interval of Variate Solution

STEP 0: Pre-Calculation Summary

Formula Used

Value of 'x1' Bounded to Variate 'Xt' = Variate 'X' with a Recurrence Interval+Function of Confidence Probability*Probable Error
x₁ = x_T+f_c*S_e
This formula uses 4 Variables

Variables Used

Value of 'x1' Bounded to Variate 'Xt' - Value of 'x1' Bounded to Variate 'Xt' influences the limits about the calculated value between which the true value can be said to lie.
Variate 'X' with a Recurrence Interval - Variate 'X' with a Recurrence Interval of a random hydrologic series with a return period.
Function of Confidence Probability - Function of Confidence Probability defined by normal variates.
Probable Error - Probable Error is the half-range of an interval about a central point for the distribution and in Gumbel's method it defines the range of effective measurement increments.

STEP 1: Convert Input(s) to Base Unit

Variate 'X' with a Recurrence Interval: 9.43 --> No Conversion Required
Function of Confidence Probability: 15 --> No Conversion Required
Probable Error: 0.2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x₁ = x_T+f_c*S_e --> 9.43+15*0.2

Evaluating ... ...

x₁ = 12.43

STEP 3: Convert Result to Output's Unit

12.43 --> No Conversion Required

FINAL ANSWER

12.43 <-- Value of 'x1' Bounded to Variate 'Xt'

(Calculation completed in 00.004 seconds)

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< 8 Confidence Limits Calculators

Probable Error

Go Probable Error = Variable 'b' in Probable Error*(Standard Deviation of the Sample of Size N/sqrt(Sample Size))

Variate 'b' given Probable Error

Go Variable 'b' in Probable Error = Probable Error*sqrt(Sample Size)/Standard Deviation of the Sample of Size N

Equation for Confidence Interval of Variate Bounded by x2

Go Value of 'x2' Bounded to Variate 'Xt' = Variate 'X' with a Recurrence Interval-Function of Confidence Probability*Probable Error

Confidence Interval of Variate Bounded by X2

Go Value of 'x2' Bounded to Variate 'Xt' = Variate 'X' with a Recurrence Interval+Function of Confidence Probability*Probable Error

Equation for Confidence Interval of Variate

Go Value of 'x1' Bounded to Variate 'Xt' = Variate 'X' with a Recurrence Interval-Function of Confidence Probability*Probable Error

Confidence Interval of Variate

Go Value of 'x1' Bounded to Variate 'Xt' = Variate 'X' with a Recurrence Interval+Function of Confidence Probability*Probable Error

Sample Size when Probable Error is Considered

Go Sample Size = ((Variable 'b' in Probable Error*Standard Deviation of the Sample of Size N)/Probable Error)^2

Equation for Variate 'b' using Frequency Factor

Go Variable 'b' in Probable Error = sqrt(1+(1.3*Frequency Factor)+(1.1*Frequency Factor^(2)))

Confidence Interval of Variate Formula

Value of 'x1' Bounded to Variate 'Xt' = Variate 'X' with a Recurrence Interval+Function of Confidence Probability*Probable Error
x₁ = x_T+f_c*S_e

What is Flood Frequency Analysis?

Flood frequency analysis is a technique used by hydrologists to predict flow values corresponding to specific return periods or probabilities along a river. The application of statistical frequency curves to floods was first introduced by Gumbel.

What is Peak Discharge?

In Hydrology, the term Peak Discharge stands for the highest concentration of runoff from the basin area. The concentrated flow of the basin greatly exaggerates and overtops the natural or artificial bank, and this might be called a flood.

How to Calculate Confidence Interval of Variate?

Confidence Interval of Variate calculator uses Value of 'x1' Bounded to Variate 'Xt' = Variate 'X' with a Recurrence Interval+Function of Confidence Probability*Probable Error to calculate the Value of 'x1' Bounded to Variate 'Xt', The Confidence Interval of Variate formula is defined as the limits of the calculated value between which the true value can be said to lie with a specific probability based on sampling errors. Value of 'x1' Bounded to Variate 'Xt' is denoted by x₁ symbol.

How to calculate Confidence Interval of Variate using this online calculator? To use this online calculator for Confidence Interval of Variate, enter Variate 'X' with a Recurrence Interval (x_T), Function of Confidence Probability (f_c) & Probable Error (S_e) and hit the calculate button. Here is how the Confidence Interval of Variate calculation can be explained with given input values -> 12.428 = 9.43+15*0.2.

FAQ

What is Confidence Interval of Variate?

The Confidence Interval of Variate formula is defined as the limits of the calculated value between which the true value can be said to lie with a specific probability based on sampling errors and is represented as x₁ = x_T+f_c*S_e or Value of 'x1' Bounded to Variate 'Xt' = Variate 'X' with a Recurrence Interval+Function of Confidence Probability*Probable Error. Variate 'X' with a Recurrence Interval of a random hydrologic series with a return period, Function of Confidence Probability defined by normal variates & Probable Error is the half-range of an interval about a central point for the distribution and in Gumbel's method it defines the range of effective measurement increments.

How to calculate Confidence Interval of Variate?

The Confidence Interval of Variate formula is defined as the limits of the calculated value between which the true value can be said to lie with a specific probability based on sampling errors is calculated using Value of 'x1' Bounded to Variate 'Xt' = Variate 'X' with a Recurrence Interval+Function of Confidence Probability*Probable Error. To calculate Confidence Interval of Variate, you need Variate 'X' with a Recurrence Interval (x_T), Function of Confidence Probability (f_c) & Probable Error (S_e). With our tool, you need to enter the respective value for Variate 'X' with a Recurrence Interval, Function of Confidence Probability & Probable Error and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Value of 'x1' Bounded to Variate 'Xt'?

In this formula, Value of 'x1' Bounded to Variate 'Xt' uses Variate 'X' with a Recurrence Interval, Function of Confidence Probability & Probable Error. We can use 1 other way(s) to calculate the same, which is/are as follows -

Value of 'x1' Bounded to Variate 'Xt' = Variate 'X' with a Recurrence Interval-Function of Confidence Probability*Probable Error

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