Hi Tapas,

In order to find the confidence interval (CI) against various return periods you have to first select the distributions for your case in which the data fits the best (e.g., log normal, log Pearson III, etc.) then you have to find the standard normal deviate corresponding to each return period. Further calculate the CI by using the formula given in this reference below:

https://directives.sc.egov.usda.gov/OpenNonWebContent.aspx?content=17781.wba

Also please remember that for log normal and log Pearson you have to use different skewness while going for CI.

Thanks

Ankur

Ankur Srivastava Thank you so much for your valuable information.

Tapasranjan Das,

The subject you asked, in general, is Uncertainty Quantification (UQ), you want to know the uncertainty in a fitting of a PDF (or CDF) to the data (then you can find the confidence interval). Very good sources with example worked are:

1- Flood Flow Frequency Bulletin of USGS (known as USGS 177B)

https://water.usgs.gov/osw/bulletin17b/dl_flow.pdf

2- Experimentation, Validation, and Uncertainty Analysis for Engineers

by Hugh W. Coleman and, W. Glenn Steele

3- An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements 2nd Edition

by John R. Taylor (Author)

4- ASME V&V 20:

Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer

V&V 20 - 2009

Here you have step by step solved examples of the finding CI for a fitting.

Hope it helps,

Kaveh

Kaveh Zamani Thank you so much for your valuable information. But I could only download the 1st source i.e Flood Flow Frequency Bulletin of USGS (known as USGS 177B) https://water.usgs.gov/osw/bulletin17b/dl_flow.pdf. After I went through that I found that only Log Pearson 3 is used for calculating confidence interval. But for my study I need to find confidence interval of fitted data for minimum 3 probability distribution. The distribution will be among

i) Log Pearson 3

ii) Gamma

iii) Weibull

iv) Pearson 5

v) Log Normal

vi) Log Normal (3P)

vii) Normal

viii) Gumbel Max

ix) Gumbel Min

So isn't there any general method to find the confidence interval of fitted data of any distribution??

And also I could not download the other three sources. So if it is possible could you please sent those sources through email... My email id is [email protected].

Thanks and regards.

Tapasranjan Das

The other three books are cop-righted material, maybe you can borrow them from a library.

The general procedure on the confidence interval of a fitting is the same. If you want exactly those distributions see this book (it is a classic):

Applied Linear Regression Models

Michael H. Kutner, ‎Chris J. Nachtsheim, ‎John Neter

A generalized methodology for constructing confidence intervals based on Monte Carlo simulation can be found in the report:

https://www.researchgate.net/publication/267840803

with application in the paper

https://www.researchgate.net/publication/240687313

and in the software package:

http://hydrognomon.org/

A more theoretical development of the concept can be found in the paper:

https://www.researchgate.net/publication/257338134

You can work it out using the z value, n, sd, mean and margin of error