半正態分佈

theta

x in [0,infty)

P(x)

=

(2theta)/pie^(-x^2theta^2/pi)

D(x)

=

erf((thetax)/(sqrt(pi))).

n

Gamma(z)

mu_1^

=

1/theta

mu_2^

=

pi/(2theta^2)

mu_3^

=

pi/(theta^3)

mu_4^

=

(3pi^2)/(4theta^4).

mu_2

=

(pi-2)/(2theta^2)

mu_3

=

(4-pi)/(2theta^3)

mu_4

=

(3pi^2-4pi-12)/(4theta^4),

mu

=

1/theta

sigma^2

=

(pi-2)/(2theta^2)

gamma_1

=

(sqrt(2)(4-pi))/((pi-2)^(3/2))

gamma_2

=

(8(pi-3))/((pi-2)^2).