Beta distribution- help needed

On a point of information, the beta distribution is indeed
defined for x >= 0 and, respectively, for x <= 1 so long as
the parameters a="shape1" and b="shape2" are respectively
not less than 1:

  dbeta(x,a,b) = (x^(a-1))*((1-x)^(b-1))/Beta(a,b)

When a=1 and b=1 we have the uniform distribution on [0,1]
which certainly allows x=0 or x=1.

If a<1 then the density --> Inf as x --> 0.
If b<1 then the density --> Inf as x --> 1.
In these cases the density does not have a finite value
for x=0 respectively x=1. For a >=1 and b >= 1, the density
is finite at x=0 and at x=1, so either is a legitimate value.

The help info '?dbeta' says:

  The Beta distribution with parameters 'shape1' = a and
  ?shape2' = b has density
    Gamma(a+b)/(Gamma(a)Gamma(b))x^(a-1)(1-x)^(b-1)          
  for a > 0, b > 0 and 0 <= x <= 1 where the boundary values
  at x=0 or x=1 are defined as by continuity (as limits).

So R itself has no problem with x=0 or x=1 when the density
makes sense mathematically. Indeed, it also gives the expected
results when a<1 and/or b<1:

  dbeta(0,0.5,0.5)
  # [1] Inf

I don't know how fitdist() works: maybe it automatically
rejects x=0 and x=1 whatever the values of a and b if < 1.
Possibly, however, in baxy77's example fitdist() was trying
to use values of a or b which are less that 1, and fitdist
threw an error because of the infinity.

Hoping this helps,
Ted.

This is not very confusing. It is the exact same error in
the sense that this time the values of x1 are not only
outside the interval (0-1) but within [0-1] as in your
first example, but this time they are also outside [0-1].
The reason is that you did not divide x1 by sum(x1) this
time. In other words, the problem that the values you
supply to fitdist() are not permissible by the definition
of the distribution "got even worse" if one may say so.
For fitdist() to estimate the parameters of a beta
distribution it needs the values to be in the open interval (0-1).

Read up on http://en.wikipedia.org/wiki/Beta_distribution
where the first sentence says: "In probability theory and
statistics, the beta distribution is a family of continuous
probability distributions defined on the interval (0, 1)..."

HTH,
Daniel


baxy77 wrote:

ok then this is confusing 

if i do it like this:

x1 <- c(100,200,140,98,97,56,42,10,2,2,1,4,3,2,12,3,1,1,1,1,0,0);
k <-fitdist(x1, "beta")
plot(k)

 it says 


Error in mledist(data, distname, start, fix.arg, ...) : 
  values must be in [0-1] to fit a beta distribution
Calls: fitdist -> mledist


I mean the real problem is the Cullen-Frey plot says it is a beta
distribution and i want to see its function . how do i do this

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Date: 26-Jul-11                                       Time: 15:42:33
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