How to fit distribution models for a frequency analysis?

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SUMMARY

The discussion focuses on fitting distribution models, specifically the log-Pearson Type III and Gumbel Distributions, to annual maximum rainfall data for frequency analysis of a catch basin. The user aims to determine the best-fitting model by measuring fit using the Chi-square goodness of fit test. The challenge lies in obtaining the "predicted" rainfall depths necessary for this statistical test. Establishing the correct distribution is crucial for accurately modeling rainfall frequency.

PREREQUISITES
  • Understanding of log-Pearson Type III and Gumbel Distributions
  • Familiarity with Chi-square goodness of fit testing
  • Proficiency in data analysis using Excel or similar tools
  • Knowledge of frequency analysis in hydrology
NEXT STEPS
  • Research methods for calculating predicted rainfall depths using log-Pearson Type III and Gumbel Distributions
  • Learn how to perform Chi-square goodness of fit tests in Excel
  • Explore advanced statistical software options for distribution fitting, such as R or Python
  • Study case studies on rainfall frequency analysis for practical insights
USEFUL FOR

This discussion is beneficial for hydrologists, data analysts, and environmental engineers involved in rainfall frequency analysis and modeling. It provides insights into statistical methods for fitting distribution models to hydrological data.

median27
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I have a rainfall (mm) vs. year plot of a catch basin (see Excel file below) and I would like to get it's frequency curve. But before that, I need to fit certain distribution models (i.e. log-Pearson Type III and Gumbel Distributions) to my plot to be able to know the fittest model that I can use for my frequency analysis. How will I do that?

(I'll measure the fit using Chi-square goodness of fit.)
 

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It's not clear what you mean by 'frequency curve'. Your data appear to be cumulative rainfall amounts sampled on an annual basis.
 
The plotted data are the "observed" data for the annual maximum rainfall - daily basis. I need to get the "predicted" rainfall depths using the said distributions above and perform the fitting test. The fittest distribution will be the appropriate distribution to model the rainfall frequency of the catch basin. My only problem is, I don't know how to get the "predicted" rainfall depth which is needed in performing the chi-square goodness of fit test.
 

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