help for ^beta4^

Fitting beta distribution by moments and maximum likelihood -----------------------------------------------------------

^beta4^ varname [^if^ exp] [^in^ range] [, ^s(^#^)^ ^t^ol^(^#^) sec^ ]

Description -----------

^beta4^ works on a single variable. All non-missing values must be between 0 and 1. A two-parameter beta distribution is fitted by the method of moments (a closed-form calculation) and by the method of maximum likelihood (ML) (an iterative calculation, which may occasionally be rather slow). The parameters are shape parameters, here called alpha and beta.

The algorithm used for ML estimation was proposed by P.W. Mielke (1975). Mielke uses a parameterisation in terms of a location parameter

p = alpha / (alpha + beta)

and a scale parameter

gamma = alpha + beta

and moments and ML estimates of these are recorded in macros S_6-S_9.

Note: this is the original version of ^beta^, written for Stata 4. Users of Stata 8 up should switch to ^betafit^.

Options -------

^s(^#^)^ controls the number of terms used within ^beta4^ in a series approximation. The default is 25. This is a technical option and should not normally be changed. See Mielke (1975) for enlightenment.

^tol(^#^)^ controls the tolerance used within ^beta4^ to control iteration. The default is 0.0000001. This is a technical option and should not normally be changed. See Mielke (1975) for enlightenment.

^sec^ produces estimates of the standard errors of alpha and beta and the correlation between alpha and beta.

Example -------

. ^beta4 hail^

Saved values ------------

S_1 number of values used S_2 ML estimate of alpha S_3 ML estimate of beta S_4 moments estimate of alpha S_5 moments estimate of beta S_6 ML estimate of p S_7 ML estimate of gamma S_8 moments estimate of p S_9 moments estimate of gamma S_10 standard error of alpha (^sec^ option) S_11 standard error of beta (^sec^ option) S_12 correlation between alpha and beta (^sec^ option)

Reference ---------

Mielke, P.W. 1975. Convenient beta distribution likelihood techniques for describing and comparing meteorological data. Journal of Applied Meteorology 14, 985-90.

Author ------ Nicholas J. Cox, University of Durham, U.K. n.j.cox@@durham.ac.uk

Also see --------

On-line: help for @pbeta4@ (if installed), @qbeta4@ (if installed)