Maximum Likelihood Estimation of the Parameters of the Beta Distribution from Smallest Order Statistics

Numerical methods, useful with high-speed computers, are described for obtaining the maximum likelihood estimat.es of the two (shape) parameters of a beta distribution using the smallest M order statistics, 0 < u 1 ≤ ... ≤ ≤ ... ≤ u M , in a random sample of size K(≥M). The maximum likelihood est...

Full description

Saved in:
Bibliographic Details
Published in:Technometrics 1967-11, Vol.9 (4), p.607-620
Main Authors: Gnanadesikan, R., Pinkham, R. S., Hughes, Laura P.
Format: Article
Language:English
Subjects:
Approximation
Maximum likelihood estimation
Maximum likelihood estimators
Probabilities
Quantiles
Random sampling
Sample size
Sampling distributions
Statistical estimation
Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Numerical methods, useful with high-speed computers, are described for obtaining the maximum likelihood estimat.es of the two (shape) parameters of a beta distribution using the smallest M order statistics, 0 < u 1 ≤ ... ≤ ≤ ... ≤ u M , in a random sample of size K(≥M). The maximum likelihood estimates are functions only of the ratio, n = M/K, the Mth ordered observation, u M , and the two statistics, G 1 = [II M i=1 u i ] 1/M , and G 1 = [II M i=1 (1 - u i )] 1/M . For the case of the complete sample (i.e., R = 1), however, the estimates are functions only of G 1 and G 2 , and hence, for this case, explicit tables of the estimates are provided. When R < 1, the methods described depend crucially for their usefulness on the availability of a high-speed computer. Some esamples are given of the use of the procedures described for fitting beta distributions to sets of data. In one example, the fit is studied by using beta probability plots.
ISSN:0040-1706
1537-2723
DOI:10.1080/00401706.1967.10490509