Here is part of mydata:

The raw data is very large, so I uploaded part of 20 rows.

x <- [7.6,2.2,1.1,4.7,8.6,7.5,7.5,29.9,5.0,3.0,2.4,1.5,14.9,3.9,3.7,3.2,5.0,1.7,2.9,2.3]

Here is the function description

1. ol:y=A*x^-(u)
2. index:y=B*exp^(-βx)

uNow, I want to get power law and exponential distribution using MLE (maximum likelihood method) .β

#set likelihood function of power law
pl <- function(u){-n*log(u-1)-n*(u-1)*log(min(x))+u*sum(log(x))}

#set likelihood function of exponential distribution
ex <- function(β){-n*log(β)+β*sum(x)}

Are these functions correct?

Use mle2() to get parameters:

#get the parameter u of power law
s1 <- mle2(pl,start = list(u=2),data = list(x))
summary(s1)
#get the parameter lamda of exponential distribution
s2 <- mle2(ex,start = list(β=2),data = list(x))
summary(s2)

Now here are two questions:

1. How to determine which one is the best fit for the model

   Using confint() to get 95% confidence, how to get Rsquared and AIC (Akaike weigths) for both models?

2. How can I plot the fit on top of the original data after getting which one is the best fit for the data?

I am using R.3.2.2 in Windows 7.