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2017 Dec 21
0
Fitting Beta Distribution
I answer my own question: I had overlooked the fact that the normalization
factor is also a function of the parameters I want to optimise, hence I
should write
dbeta2 <- function(x, shape){
res <- x^(shape-1)*(1-x)^(shape-1)/beta(shape, shape)
return(res)
}
after which the results are consistent.
---------- Forwarded message ----------
From: Lorenzo Isella <lorenzo.isella at yopmail.com>
Date: 21 December 2017 at 11:29
Subject: Fitting...
2017 Dec 21
1
Fitting Beta Distribution
...shape2
are identical) to my data.
The trouble is that I experience some problems also when dealing with the
plain vanilla symmetric beta distribution.
Please consider the code at the end of the email.
In the code, dbeta1 is the density of the beta distribution for
shape1=shape2=shape.
In the code, dbeta2 is the same quantity written explicitly, without the
normalization factor (which should not matter at all if we talk about
maximizing a quantity).
I then generate some random numbers according to Beta(0.2, 0.2) and I try
to estimate the shape parameter using
1) fitdistr from MASS
2) mle from stat...