[R] How to fit the cumulative probability distributive functiion with the gamma distribution?

[Chris Campbell]

val_w_time <- data.frame(time = 1:12,    
    val = c(24,7,4,1,2,1,0,0,0,1,0,0))    
    
fitdistr(val_w_time$val,"gamma")     
# Error in optim(x = c(24, 7, 4, 1, 2, 1, 0, 0, 0, 1, 0, 0), par = list( :      
#   initial value in 'vmmin' is not finite    
    
# this error message doesn't necessarily mean that it    
# won't fit the distribution; just that it can't.   
    
# fitdistr is usually used to fit data to a distribution,     
# rather than data representing the shape of a distribution     
# to that distribution.    
    
  
plot(val_w_time)     
    
g1 <- nls(histd ~ dgamma(time/12, shape = gamma, rate = theta), data = val_w_time,     
    start = list(gamma = 0.5, theta = 4),     
    trace = TRUE)    
# 495.188 :  0.5 4.0    
# 250.5561 :   5.943122 54.029829    
# 241.5951 :  11.20099 98.36401    
# Error in numericDeriv(form[[3L]], names(ind), env) :     
#   Missing value or an infinity produced when evaluating the model    
# In addition: Warning message:    
# In dgamma(time/12, shape = gamma, rate = theta) : NaNs produced    
    
# okay, so we don't get convergence with nls    
    
lines(val_w_time$time,     
    dgamma((1:12)/12, shape = 11.20099, rate = 98.36401), col = "grey", lwd = 2)    
    
# but we're basically fitting to 3 data points    
    
# but we can mess around with the x axis    
    
g2 <- nls(histd ~ dgamma((time/12)^2, shape = gamma, rate = theta), data = val_w_time,     
    start = list(gamma = 0.5, theta = 4),     
    trace = TRUE)    
    
with(val_w_time, lines(time,     
    predict(g2), col = "red", lwd = 2))    
    
# so that the distribution looks more like the data    
    
http://i1277.photobucket.com/albums/y496/CSJCampbell/armel_data_gamma_zpsbb0146ee.png
    
# hopefully this gives you some ideas    
     

Chris Campbell, PhD    
Tel. +44 (0) 1249 705 450 | Mobile. +44 (0) 7929 628349    
mailto:ccampbell at mango-solutions.com | http://www.mango-solutions.com    
Mango Solutions, 2 Methuen Park,  Chippenham, Wiltshire , SN14 OGB UK    

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Kaptue Tchuente, Armel
Sent: 12 June 2013 20:22
To: r-help at r-project.org
Subject: [R] How to fit the cumulative probability distributive functiion with the gamma distribution?

Hello everyone,



I'm trying to fit the PDF of time series datasets with the gamma distribution.

Nonetheless, this isn't possible for several datasets since the gamma distribution can only been used to fit continuous distribution. For instance, gam<-fitdrib(hist<-c(24,7,4,1,2,1,0,0,0,1,0,0),"gamma") will yield an error message.

To solve this issue, I decided to fit the cumulative distributive function i.e. gam<-fitdistr(hist_cum<-c(24,31,35,36,38,39,39,39,40,40,40)).

Now I don't know how to obtain the corresponding CDF of the gamma distribution which will fit the empirical CDF.

I have already tried some instructions like pgamma(seq(4,4*12,4), scale=1/gam$estimate[2],shape=gam$estimate[1]) without success as you can see on this picture https://docs.google.com/file/d/0BwjZP-sfazLMaDM2bHBDYnFOSWs/edit?usp=sharing where the curve in blue was supposed to be the fitted gamma CDF.

I said "was supposed" because I was obliged to use the instruction par(new=T) in order to super-impose the fitted gamma CDF



Cheers



Armel


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