[R] Beta distribution- help needed

[(Ted Harding)]

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.


On 26-Jul-11 13:12:36, Daniel Malter wrote:
> 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
>> 
> 
> --
> View this message in context:
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> 95639.html
> Sent from the R help mailing list archive at Nabble.com.
> 
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E-Mail: (Ted Harding) <ted.harding at wlandres.net>
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Date: 26-Jul-11                                       Time: 15:42:33
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