Equation for Z Series for any Recurrence Interval Calculator

✖Mean of Z Variates for 'x' variate of a random hydrologic cycle.ⓘ Mean of Z Variates [z_m]			+10% -10%
✖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).ⓘ Frequency Factor [K_z]			+10% -10%
✖Standard Deviation of the Z Variate Sample follows a certain probability distribution of a hydrologic model.ⓘ Standard Deviation of the Z Variate Sample [σ]			+10% -10%

✖Z Series for any Recurrence Interval in Log-Pearson Type III Distribution.ⓘ Equation for Z Series for any Recurrence Interval [Z_t]

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Formula

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Equation for Z Series for any Recurrence Interval

Formula

`"Z"_{"t"} = "z"_{"m"}+"K"_{"z"}*"σ"`

Example

`"9.52"="0.77"+"7"*"1.25"`

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Equation for Z Series for any Recurrence Interval Solution

STEP 0: Pre-Calculation Summary

Formula Used

Z Series for any Recurrence Interval = Mean of Z Variates+Frequency Factor*Standard Deviation of the Z Variate Sample
Z_t = z_m+K_z*σ
This formula uses 4 Variables

Variables Used

Z Series for any Recurrence Interval - Z Series for any Recurrence Interval in Log-Pearson Type III Distribution.
Mean of Z Variates - Mean of Z Variates for 'x' variate of a random hydrologic cycle.
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

Mean of Z Variates: 0.77 --> 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

Z_t = z_m+K_z*σ --> 0.77+7*1.25

Evaluating ... ...

Z_t = 9.52

STEP 3: Convert Result to Output's Unit

9.52 --> No Conversion Required

FINAL ANSWER

9.52 <-- Z Series for any Recurrence Interval

(Calculation completed in 00.004 seconds)

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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)

Equation for Z Series for any Recurrence Interval Formula

Z Series for any Recurrence Interval = Mean of Z Variates+Frequency Factor*Standard Deviation of the Z Variate Sample
Z_t = z_m+K_z*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 Equation for Z Series for any Recurrence Interval?

Equation for Z Series for any Recurrence Interval calculator uses Z Series for any Recurrence Interval = Mean of Z Variates+Frequency Factor*Standard Deviation of the Z Variate Sample to calculate the Z Series for any Recurrence Interval, Equation for Z Series for any Recurrence Interval formula is defined as the series of Z variates of a random hydrologic series for any recurrence interval or return period T. Z Series for any Recurrence Interval is denoted by Z_t symbol.

How to calculate Equation for Z Series for any Recurrence Interval using this online calculator? To use this online calculator for Equation for Z Series for any Recurrence Interval, enter Mean of Z Variates (z_m), Frequency Factor (K_z) & Standard Deviation of the Z Variate Sample (σ) and hit the calculate button. Here is how the Equation for Z Series for any Recurrence Interval calculation can be explained with given input values -> 9.52 = 0.77+7*1.25.

FAQ

What is Equation for Z Series for any Recurrence Interval?

Equation for Z Series for any Recurrence Interval formula is defined as the series of Z variates of a random hydrologic series for any recurrence interval or return period T and is represented as Z_t = z_m+K_z*σ or Z Series for any Recurrence Interval = Mean of Z Variates+Frequency Factor*Standard Deviation of the Z Variate Sample. Mean of Z Variates for 'x' variate of a random hydrologic cycle, 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 Equation for Z Series for any Recurrence Interval?

Equation for Z Series for any Recurrence Interval formula is defined as the series of Z variates of a random hydrologic series for any recurrence interval or return period T is calculated using Z Series for any Recurrence Interval = Mean of Z Variates+Frequency Factor*Standard Deviation of the Z Variate Sample. To calculate Equation for Z Series for any Recurrence Interval, you need Mean of Z Variates (z_m), Frequency Factor (K_z) & Standard Deviation of the Z Variate Sample (σ). With our tool, you need to enter the respective value for Mean of Z Variates, 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.

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