Log moments about a point from log partial moments

The log of \(G_k(t) = \int_0^t (t - u)^k f(u) du\) for k = 1, 2, 3 from the partial moments \(m_k(t) = \int_0^t u^k f(u) du\), with \(G_1 = t m_0 - m_1\), \(G_2 = t G_1 - (t m_1 - m_2)\) and \(G_3 = t G_2 - (t (t m_1 - m_2) - (t m_2 - m_3))\), each a difference of positive integrals.

Usage

.moments_from_partial(log_t, log_m0, log_m1, log_m2, log_m3)

Arguments

log_t

Log of the points.

log_m0, log_m1, log_m2, log_m3

Log partial moments at each point.

Value

As for .pcens_tilt_moments().