[R] Fitting Theoretical Distributions to Daily Rainfall Data

From: Mohammad Ehsanul Karim <wildscop_at_yahoo.com>
Date: Wed 08 Jun 2005 - 20:40:22 EST

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.


Mohammad Ehsanul Karim

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


                

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