KCHITWO Computes the cumulant generating function formula for noncentral Chi2-process. CALL: [K]=kchitwo(s,t,gam,bet,S12,S22); Note that s,t must be constants (vectors are not allowed):
Saddlepoint approximation of the crossing intensity for the noncentral Chi^2 process |
01 function [K]=kchitwo(s,t,gam,bet,S12,S22); 02 % KCHITWO Computes the cumulant generating function formula for noncentral Chi2-process. 03 % 04 % CALL: [K]=kchitwo(s,t,gam,bet,S12,S22); 05 % 06 % Note that s,t must be constants (vectors are not allowed): 07 % 08 09 10 % Reference: "Five lectures on reliability applications of Rice's formula for 11 % level crossings" Rychlik (2003). 12 % 13 % tested on matlab 6.1 14 % by IR 12.11.03, changed name and added some checks and comments. 15 % rev. IR 24.11.03, changed name and added some checks and comments. 16 17 n=length(gam); 18 V=S22-S12'*S12; 19 Gam=diag(gam); 20 I=eye(n); 21 A=I-2*s*Gam-2*t*(Gam*S12'+S12*Gam)-4*t*t*Gam*V*Gam; 22 T=(s*I+t*S12+2*t*t*Gam*V)*bet'; 23 K=-log(det(A))/2+t*t*bet*V*bet'/2+T'*inv(A)*T/2; 24 25 26
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