Mean Series of Z Variates given Z Series for Recurrence Interval Solution

STEP 0: Pre-Calculation Summary
Formula Used
Mean of Z Variates = Z Series for any Recurrence Interval-Frequency Factor*Standard Deviation of the Z Variate Sample
zm = Zt-Kz*σ
This formula uses 4 Variables
Variables Used
Mean of Z Variates - Mean of Z Variates for 'x' variate of a random hydrologic cycle.
Z Series for any Recurrence Interval - Z Series for any Recurrence Interval in Log-Pearson Type III Distribution.
Frequency Factor - Frequency Factor which varies between 5 to 30 according to rainfall duration is a function of recurrence interval (T) and the coefficient of skew (Cs).
Standard Deviation of the Z Variate Sample - Standard Deviation of the Z Variate Sample follows a certain probability distribution of a hydrologic model.
STEP 1: Convert Input(s) to Base Unit
Z Series for any Recurrence Interval: 9.5 --> No Conversion Required
Frequency Factor: 7 --> No Conversion Required
Standard Deviation of the Z Variate Sample: 1.25 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
zm = Zt-Kz*σ --> 9.5-7*1.25
Evaluating ... ...
zm = 0.75
STEP 3: Convert Result to Output's Unit
0.75 --> No Conversion Required
FINAL ANSWER
0.75 <-- Mean of Z Variates
(Calculation completed in 00.004 seconds)

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Coorg Institute of Technology (CIT), Coorg
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8 Log-Pearson Type III Distribution Calculators

Frequency Factor given Z Series for Recurrence Interval
Go Frequency Factor = (Z Series for any Recurrence Interval-Mean of Z Variates)/Standard Deviation of the Z Variate Sample
Mean Series of Z Variates given Z Series for Recurrence Interval
Go Mean of Z Variates = Z Series for any Recurrence Interval-Frequency Factor*Standard Deviation of the Z Variate Sample
Equation for Z Series for any Recurrence Interval
Go Z Series for any Recurrence Interval = Mean of Z Variates+Frequency Factor*Standard Deviation of the Z Variate Sample
Partial Duration Series
Go Partial Duration Series = 1/((ln(Annual Series))-(ln(Annual Series-1)))
Coefficient of Skew of Variate Z given Adjusted Coefficient of Skew
Go Coefficient of Skew of Variate Z = Adjusted Coefficient of Skew/((1+8.5)/Sample Size)
Adjusted Coefficient of Skew
Go Adjusted Coefficient of Skew = Coefficient of Skew of Variate Z*((1+8.5)/Sample Size)
Sample Size given Adjusted Coefficient of Skew
Go Sample Size = Coefficient of Skew of Variate Z*(1+8.5)/Adjusted Coefficient of Skew
Equation for Base Series of Z Variates
Go Mean of Z Variates = log10(Variate 'z' of a Random Hydrologic Cycle)

Mean Series of Z Variates given Z Series for Recurrence Interval Formula

Mean of Z Variates = Z Series for any Recurrence Interval-Frequency Factor*Standard Deviation of the Z Variate Sample
zm = Zt-Kz*σ

What is Log-Pearson Type III Distribution?

The Log-Pearson Type III distribution is a statistical technique for fitting frequency distribution data to predict the design flood for a river at some site. Once the statistical information is calculated for the river site, a frequency distribution can be constructed.

How to Calculate Mean Series of Z Variates given Z Series for Recurrence Interval?

Mean Series of Z Variates given Z Series for Recurrence Interval calculator uses Mean of Z Variates = Z Series for any Recurrence Interval-Frequency Factor*Standard Deviation of the Z Variate Sample to calculate the Mean of Z Variates, The Mean Series of Z Variates given Z Series for Recurrence Interval formula is defined as the series of Z variates of a random hydrologic series for any recurrence interval or return period T in Log-Pearson Type III Distribution. Mean of Z Variates is denoted by zm symbol.

How to calculate Mean Series of Z Variates given Z Series for Recurrence Interval using this online calculator? To use this online calculator for Mean Series of Z Variates given Z Series for Recurrence Interval, enter Z Series for any Recurrence Interval (Zt), Frequency Factor (Kz) & Standard Deviation of the Z Variate Sample (σ) and hit the calculate button. Here is how the Mean Series of Z Variates given Z Series for Recurrence Interval calculation can be explained with given input values -> 0.75 = 9.5-7*1.25.

FAQ

What is Mean Series of Z Variates given Z Series for Recurrence Interval?
The Mean Series of Z Variates given Z Series for Recurrence Interval formula is defined as the series of Z variates of a random hydrologic series for any recurrence interval or return period T in Log-Pearson Type III Distribution and is represented as zm = Zt-Kz or Mean of Z Variates = Z Series for any Recurrence Interval-Frequency Factor*Standard Deviation of the Z Variate Sample. Z Series for any Recurrence Interval in Log-Pearson Type III Distribution, Frequency Factor which varies between 5 to 30 according to rainfall duration is a function of recurrence interval (T) and the coefficient of skew (Cs) & Standard Deviation of the Z Variate Sample follows a certain probability distribution of a hydrologic model.
How to calculate Mean Series of Z Variates given Z Series for Recurrence Interval?
The Mean Series of Z Variates given Z Series for Recurrence Interval formula is defined as the series of Z variates of a random hydrologic series for any recurrence interval or return period T in Log-Pearson Type III Distribution is calculated using Mean of Z Variates = Z Series for any Recurrence Interval-Frequency Factor*Standard Deviation of the Z Variate Sample. To calculate Mean Series of Z Variates given Z Series for Recurrence Interval, you need Z Series for any Recurrence Interval (Zt), Frequency Factor (Kz) & Standard Deviation of the Z Variate Sample (σ). With our tool, you need to enter the respective value for Z Series for any Recurrence Interval, Frequency Factor & Standard Deviation of the Z Variate Sample 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 Mean of Z Variates?
In this formula, Mean of Z Variates uses Z Series for any Recurrence Interval, Frequency Factor & Standard Deviation of the Z Variate Sample. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Mean of Z Variates = log10(Variate 'z' of a Random Hydrologic Cycle)
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