a,b and c are empirical constant. If you have x and y you can fit the equation to your data and find constants, b and c. The process of deriving x and y is well explained in "Statistical distribution of daily rainfall and its association with the coefficient of variation of rainfall series" paper.

http://onlinelibrary.wiley.com/doi/10.1002/joc.3370090504/full

To restate the example in that paper,

Assume you have a station with daily rainfall series for any month for m years. Consider month July, which has 31 days so you have 31*m days for m years.

Assume we have N days with measurable rainfall. Then we sort these N days in ascending order {r1,r2,r3,..., rN}. Consider R as the sum of rainfalls then x and y can be calculated as follow,

Xi = sum(ri / R)

yi = i / N

i = {1,2,3,...,N}

Thank you very much Matin Rahnamay Naeini Sir, I have calculated evrything as you said but in that paper finally they had mentioned some values for a, b, and c. Therefore I got doubt how to calculate constants.

Thanks alot...!!!

You can find some directions to create formulas and calculating the a and b coefficients of a trend line (equation) in the following link:

The attached is related to simple equations and you should look for a solution by combining different functions.

http://spreadsheetpage.com/index.php/tip/chart_trendline_formulas/

Hi Vinay,

If you have known the values of 'x' and 'y' (i guess you have those values), you can easily find the constants 'b' and 'c' using the solver in Microsoft excel. It is very easy and I am sure that you can find many example videos in youtube. However, for explanations for that particular equation, I think the explanation given by Matin above is enough. Good luck.

You can use a linear transformation as it follows:

x transformed = Xo = log10{[ln(y)-ln(x)]^2}

y transformed = Yo = log10(100-y)

b transformed = Bo = became 2*log10(b)

c transformed = Co = became 2*c

Fit by least square method the straight line: Xo=Bo+Co*Yo and find Bo And Co, then 

b = power(10, Bo/2) - pay attention: this is an absolute value

c = Co/2