Accession Number:

ADA061524

Title:

Approximations to Densities in Geometric Probability

Descriptive Note:

Technical rept.

Corporate Author:

STANFORD UNIV CA DEPT OF STATISTICS

Report Date:

1978-10-27

Pagination or Media Count:

23.0

Abstract:

Many random variables arising in problems of geometric probability have intractable densities, and it is very difficult to find probabilities or percentage points based on these densities. A simple approximation, a generalization of the chi-square distribution, is suggested. To approximate such densities the approximation uses the first three moments. These may be theoretically derived, or may be obtained from Monte Carlo sampling. The approximation is illustrated on random variables the area, the perimeter, and the number of sides associated with random polygons arising from two processes in the plane. Where it can be checked theoretically, the approximation gives good results. It is compared also with Pearson curve fits to the densities.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE