[R] Fitting Theoretical Distributions to Daily Rainfall Data

[Mohammad Ehsanul Karim]

Dear List Members, 

I need a bit help about fitting some theoretical
distributions (such as geometric, exponential,
lognormal or weibull distribution) to the following
*dry spell*, *wet spell*, *cycles (Wet-Dry or
Dry-Wet)* from my meteorological (daily rainfall) data
http://www.angelfire.com/ab5/get5/R.rainfall.txt only
for rainy seasen (july - september) of 14 years only:

dryspell<-c(1,1,4,1,1,4,2,2,3,4,1,2,1,1,1,3,1,3,
2,3,1,2,3,3,2,2,6,2,1,1,3,1,2,1,4,4,1,1,2,1,1,2,
2,4,1,1,1,3,4,1,7,1,3,2,5,1,3,1,1,3,4,8,4,3,1,1,
1,2,3,1,1,2,1,1,2,2,2,3,3,13,13,7,1,1,1,1,7,3,2,
1,3,1,1,2,5,1,2,1,3,1,1,2,3,2,3,2,1,5,1,2,2,2,1,
9,2,2,1,1,4,5,1,1,3,1,3,3,2,1,1,1,17,1,4,5,1,1,
1,1,2,1,2,1,1,7,3,8,2,1,1,2,4,5,1,1,1,2,3,1,1,2,
1,1,3,2,3,1,1,1,3,6,4,1,2,1,2,2,4,2,4,2,1,2,1,3,
1,2,2,1,1,1,1,4,2,1,12,3,1,1,5,1,1,5,1,2,1,1,1,1,
5,3,1,1,3,1,1,6,10,1,1,1,2,1,3,2,2,5,1,1,2,2,1,2,
3,1,3,6,2,1,1,4,6,1,1,1,3,2,2,1,1,1,5,1,1,1,1,3,
1,2,1,7,1,3,1,3,4,1,1,3,4,3,1,4,4,1,3,1,5,3,1,2,
2,1,1,1,2,1,1,6,1,1,1,3,1,3,4,1,1,3,4,1,1,8,1)

wetspell<-c(1,5,6,4,1,5,3,4,5,2,3,1,5,4,1,4,1,2,3
,1,5,4,5,2,1,1,1,6,2,19,5,4,6,5,2,7,1,3,1,1,2,1,
3,8,2,3,1,2,5,1,3,8,9,1,1,7,1,2,3,7,9,4,4,1,2,3,
1,1,1,1,1,2,6,7,1,4,1,6,1,5,5,3,2,3,1,1,1,1,6,1,
3,2,1,3,5,6,3,2,6,1,1,3,1,7,3,5,1,2,2,3,1,12,1,8,
3,1,2,1,1,2,1,2,4,2,3,1,1,3,1,4,1,6,5,2,11,6,2,1,
1,9,2,7,1,7,4,1,6,4,8,2,1,1,1,9,3,3,7,2,1,3,3,8,2,
1,7,1,2,2,1,1,1,1,1,5,1,1,3,1,1,1,9,1,7,1,4,3,1,5,
7,1,5,1,5,6,8,5,3,4,1,2,7,9,3,1,4,2,1,1,2,3,1,1,8,
5,2,1,1,1,4,1,1,1,8,4,9,6,3,1,6,5,3,5,2,2,1,5,9,8,
1,6,4,1,2,8,6,1,3,1,2,2,2,3,1,1,5,2,3,11,1,1,1,5,
3,5,1,2,1,9,3,1,1,1,4,10,6,1,1,1,1,1,3,4,1,2,1,5,
2,1,3,2,9,2,1,1,4,2,1,2,9,3,1,1,1,2,6,6,3)

cycleWetDry<-c(2,9,7,5,5,7,5,7,9,3,5,2,6,5,4,5,4,4,
6,2,7,7,12,5,3,3,7,8,3,20,8,5,8,6,6,11,2,4,3,2,3,3,
5,9,6,4,2,3,8,5,4,15,10,4,3,12,2,5,4,8,12,8,9,5,5,
4,2,2,3,4,2,3,8,8,2,6,3,8,4,8,18,16,9,4,2,2,2,8,9,
3,4,5,2,4,7,11,4,4,7,4,2,4,3,10,5,8,3,3,16,4,3,14,
3,9,12,3,4,2,2,6,6,3,5,5,4,4,4,5,2,5,2,17,6,6,16,
7,3,2,2,11,3,9,2,8,11,4,14,6,16,3,3,5,6,10,4,4,9,
5,2,4,5,9,3,4,9,4,3,3,2,4,7,5,2,10,2,3,5,5,3,5,11,
2,9,2,7,4,3,7,8,2,6,2,9,8,9,9,14,6,5,2,7,8,10,8,2,
6,3,2,2,3,8,4,2,9,8,3,2,7,3,5,2,2,3,9,7,11,8,8,2,
7,7,5,6,4,5,2,8,12,10,2,7,8,7,3,9,7,4,5,3,3,3,3,8,
2,2,6,3,6,18,2,3,2,12,4,8,2,5,5,10,4,4,5,4,5,14,
10,2,4,2,6,4,4,6,3,4,2,6,3,3,4,3,15,3,2,2,7,3,4,
6,10,4,4,5,2,3,14,7,4)

cycleDryWet<-c(2,6,10,5,2,9,5,6,8,6,4,3,6,5,2,7,2,
5,5,4,6,6,8,4,4,3,3,12,4,20,6,7,7,7,3,11,5,4,2,3,3,
2,5,10,3,7,2,3,6,4,7,9,16,2,4,9,6,3,6,8,10,7,8,9,6,
6,2,2,2,3,4,3,7,9,2,5,3,8,3,8,8,16,15,11,2,2,2,2,13,
4,5,3,4,4,6,8,8,3,8,2,4,4,2,9,6,7,4,4,3,8,2,14,3,10,
4,10,4,3,2,3,5,7,5,3,6,2,4,6,3,5,2,7,22,3,15,11,3,2,
2,10,4,8,3,8,5,8,9,12,10,3,2,3,5,14,4,4,8,4,4,4,4,
10,3,2,10,3,5,3,2,2,4,7,5,6,3,2,5,3,5,3,13,3,8,3,
5,6,2,7,9,2,6,2,6,10,10,6,3,15,7,2,3,12,10,4,6,5,
4,2,2,3,4,6,4,9,6,5,2,2,7,14,2,2,2,10,5,12,8,5,6,
7,6,5,7,3,4,4,6,12,14,3,7,5,5,8,9,7,2,6,3,4,3,3,4,
6,2,6,3,4,14,15,2,3,6,10,6,4,3,4,13,4,2,4,5,7,11,
10,5,2,4,2,6,6,5,3,4,3,6,3,2,5,3,10,8,2,2,5,5,2,
5,13,4,2,4,5,3,7,14,4)


Using table() to each dryspell, wetspell, cycleWetDry,
cycleDryWet we find the empirical distribution
functions all of which seem to be positively skewed
with long tail. Therefore, i'd like to fit geometric,
exponential, lognormal or weibull distribution for
each dryspell, wetspell, cycleWetDry, cycleDryWet.
Better fit may be defined by higher p-values of
goodness-of-fit tests.

Is there any way i can do fit data to those
theoretical distributions in R? Is there any existing
program/function/package to solve such problem? 

Any suggestion, direction, references, help, replies
will be highly appreciated. 

Thank you for your time. 


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Mohammad Ehsanul Karim 

Web: http://snipurl.com/ehsan 
ISRT, University of Dhaka, BD 

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