非中心卡方分佈

lambda

P_r(x)

=

(e^(-(x+lambda)/2)x^(r/2-1))/(2^(r/2))sum_(k=0)^(infty)((lambdax)^k)/(2^(2k)k!Gamma(k+1/2r))

=

(e^(-(x+lambda)/2)x^((r-1)/2)sqrt(lambda))/(2(lambdax)^(r/4))I_(r/2-1)(sqrt(lambdax))

=

2^(-r/2)e^(-(lambda+x)/2)x^(r/2-1)_0F^~_1(;1/2r;1/4lambdax),

I_n(x)

_0F^~_1

mu

=

lambda+r

sigma^2

=

2(2lambda+r)

gamma_1

=

(2sqrt(2)(3lambda+r))/((2lambda+r)^(3/2))

gamma_2

=

(12(4lambda+r))/((2lambda+r)^2).

mu_1^

=

r+lambda

mu_2^

=

r^2+2r(lambda+1)+lambda(lambda+4)

mu_3^

=

r^3+3r^2(lambda+2)+lambda(lambda^2+12lambda+24)+r(3lambda^2+18lambda+8).

mu_2

=

2(r+2lambda)

mu_3

=

8(r+3lambda)

mu_4

=

12[r^2+4r(lambda+1)+4lambda(lambda+4)].