The asymptotic and numerical inversion of the marcum Q-function

DOI: 
10.1111/sapm.12050
Publication date: 
01/01/2014
Main author: 
Gil A.
IAA authors: 
Gil A.;Segura J.;Temme N.M.
Authors: 
Gil A., Segura J., Temme N.M.
Journal: 
Studies in Applied Mathematics
Publication type: 
Article
Volume: 
133
Pages: 
257-278
Number: 
Abstract: 
The generalized Marcum functions appear in problems of technical and scientific areas such as, for example, radar detection and communications. In mathematical statistics and probability theory these functions are called the noncentral gamma or the noncentral chi-squared cumulative distribution functions. In this paper, we describe a new asymptotic method for inverting the generalized Marcum Q-function and for the complementary Marcum P-function. Also, we show how monotonicity and convexity properties of these functions can be used to find initial values for reliable Newton or secant methods to invert the function. We present details of numerical computations that show the reliability of the asymptotic approximations. © 2014 by the Massachusetts Institute of Technology.
Database: 
SCOPUS
Keywords: