Joint Probability Density Function of Selected Order Statistics and the Sum of the Remainder as Applied to Arbitrary Independent Random Variables
Abstract
A set of N independent random variables (Xn! with arbitrary probability density functions ?pn(x)! are ordered into a new set of dependent random variables, each with a different probability density function. From this latter set, the M-1 largest random variables are selected. Then, the sum of the remaining N + 1 - M random variables is computed, giving a total of M dependent random variables. Several statistics are computed for these M random variables, including their joint probability density function, a quantity called the "combined probability and joint probability density function" of particular selections, and their distribution. Most of the results can be expressed as a single Bromwich contour integral in the moment-generating domain. This integral is most easily numerically evaluated by locating (approximately) the real saddlepoint of the integrand and passing the contour through that point. Very high accuracy in the joint probability density function evaluations is available by using numerical integration on this latter contour, instead of a saddlepoint approximation.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 06, 2003
- Accession Number
- ADA419339
Entities
People
- Albert H. Nuttall
Organizations
- Naval Undersea Warfare Center