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Title: Discrete Pearson distributions

These distributions are generated by a first order recursive scheme which equates the ratio of successive probabilities to the ratio of two corresponding quadratics. The use of a linearized form of this model will produce equations in the unknowns matched by an appropriate set of moments (assumed to exist). Given the moments we may find valid solutions. These are two cases; (1) distributions defined on the non-negative integers (finite or infinite) and (2) distributions defined on negative integers as well. For (1), given the first four moments, it is possible to set this up as equations of finite or infinite degree in the probability of a zero occurrence, the sth component being a product of s ratios of linear forms in this probability in general. For (2) the equation for the zero probability is purely linear but may involve slowly converging series; here a particular case is the discrete normal. Regions of validity are being studied. 11 refs.
Authors:
 [1] ;  [2] ;  [3]
  1. Oak Ridge National Lab., TN (United States)
  2. Georgia Univ., Athens, GA (United States)
  3. Kastenbaum (M.A.), Basye, VA (United States)
Publication Date:
OSTI Identifier:
10103630
Report Number(s):
ORNL/TM--11899
ON: DE92004700
DOE Contract Number:
AC05-84OR21400
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: Nov 1991
Research Org:
Oak Ridge National Lab., TN (United States)
Sponsoring Org:
USDOE, Washington, DC (United States)
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; DISTRIBUTION; STATISTICAL MODELS; PROBABILITY 990200; MATHEMATICS AND COMPUTERS