帕累託分佈

P(x)

=

(ab^a)/(x^(a+1))

D(x)

=

1-(b/x)^a

n

mu_1^

=

(ab)/(a-1)

mu_2^

=

(ab^2)/(a-2)

mu_3^

=

(ab^3)/(a-3)

mu_4^

=

(ab^4)/(a-4).

n

mu_n

=

ab^nGamma(a-n)_2F^~_1(a-n,-n;1+a-n;a/(a-1))

=

(1-a)^(a-n)(-a)^(n-a)ab^nB(a/(a-1);a-n,n+1),

Gamma(z)

_2F^~_1(a,b;c;z)

B(z;a,b)

mu_2

=

(ab^2)/((a-1)^2(a-2))

mu_3

=

(2a(a+1)b^3)/((a-1)^3(a-2)(a-3))

mu_4

=

(3a(3a^3+a+2)b^4)/((a-1)^4(a-2)(a-3)(a-4)).

mu

=

(ab)/(a-1)

sigma^2

=

(ab^2)/((a-1)^2(a-2))

gamma_1

=

sqrt((a-2)/a)(2(a+1))/(a-3)

gamma_2

=

(6(a^3+a^2-6a-2))/(a(a-3)(a-4)).