How to fit distribution models for a frequency analysis?

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To fit distribution models for frequency analysis of rainfall data, the focus is on using log-Pearson Type III and Gumbel Distributions. The goal is to determine the best-fitting model for annual maximum rainfall data, which involves obtaining predicted rainfall depths. The Chi-square goodness of fit test will be utilized to measure the fit of these distributions. Clarification is needed on how to derive the predicted rainfall depths necessary for the fitting test. Ultimately, identifying the fittest distribution will aid in accurately modeling the rainfall frequency for the catch basin.
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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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