Re: Least Squares solution for fitting beta distribution to empirical distrbution

beliavsky_at_aol.com
Date: 02/23/05 

Date: 23 Feb 2005 03:44:01 -0800

clemenr@wmin.ac.uk wrote:
> Hi.
>
> I would like to look at the following case. I have a set of data that
I
> can use as a probability distribution using kernel density
estimation.
> I would like to find the best possible (I'm thinking at the moment,
> least squares) beta distribution to approximate this empirical
> distribution.

In general, when fitting a distribution to data, it is better to fit to
the raw data rather than to a kernel density estimate. Why not use
maximum likelihood? At
http://mathworld.wolfram.com/BetaDistribution.html there are
expressions for the moments of the beta distribution. You could
calculate the moments of the data and solve a set of nonlinear
equations to get initial estimates of the beta parameters, and then you
could use a nonlinear optimization algrorithm to find the MLE.

Relevant Pages

  • Re: Help with BUGS model
    ... With the model where the Lambdas are drawn from only one gamma prior I ... sure why your MLE estimation procedure had problems. ... the expected value of the cell under the assumption of independence of ... The posterior distribution of lambda given N has a closed form. ...
    (sci.stat.math)
  • Least Squares solution for fitting beta distribution to empirical distrbution
    ... can use as a probability distribution using kernel density estimation. ... I'm wondering if there is an analytic solution to this. ...
    (sci.stat.math)
  • Re: significant test of the 2 approaches
    ... Let's say your estimation methods A and B were ways to estimate the mean of the distribution from which you are drawing data. ... You now have empirical estimates of the sampling distribution of your methods under the assumption of Nfor sample size n. ... Now consider using different sample sizes or parameter values or distributions. ...
    (comp.soft-sys.matlab)
  • Bayesian estimation of structured correlation/covariance
    ... there are many delay elements that have are normally ... positive-definite correlation matrix symbolically and the ... I would like to apply bayesian parameter estimation for the unknown ... distribution with a chi-square distribution - in which I can formulate ...
    (sci.stat.math)
  • Re: percentiles estimation
    ... The estimation depends on the data. ... If the data set is quite nice, say has a shape of known distribution, ... using parametric method to estimate the distribution and calculating ... Subj: percentiles estimation ...
    (sci.stat.math)