Orthogonal parameters for two parameter distributions

Orthogonal parameters for a distribution, f(x,8_i), (i=l,2,...,n), are defined such that E (- ∂² log f/∂β_i∂β_j=0 for all i, j, (i≠j). It has been pointed out that the problem of estimating the parameters of a distribution by maximum likelihood procedures, when the likelihood equations require iterative schemes for their solution, may be simplified by the use of orthogonal parameters. Distribution: having maximum likelihood equations where iteration is required include a number of two-parameter contagious distributions, like the Neyman type A and the Poisson-Binomial. The general method for finding orthogonal parameters is examined, and is seen to be inappropriate for the contagious distributions. An alternate method is developed by which orthogonal parameters are obtained for the Neyman type A, Poisson-Binomial, Binomial-Poisson, Geometric-Poisson, Logarithmic-Binomial, Logarithmic-Poisson and Normal-Poisson distributions, as well as for three Gram-Charlier type distributions. Some characteristics of the class of distributions to which the alternate method is applicable are discussed. The limitations of the general and the alternate methods are examined, and an example given where neither is of any use. It is also pointed out that, in many cases where orthogonal parameters are determined, simple transformations by which one can write the distribution in terms of the orthogonal parameters may not exist. It is concluded that the methods for determining the parameters are somewhat limited in scope; and that although the characteristics of the orthogonal parameters may be useful, the disadvantages associated with them may restrict their application.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Statistics

Department dc:contributor.department

Statistics

Grantor dc:publisher

Virginia Polytechnic Institute

Year dc:date.issued

1964

Author dc:creator

• Philpot, John W.

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/10919/54831

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/54831