  We explore the initial conditions for cosmological N-body simulations
suitable for calculating the skewness and kurtosis of the density field. In
general, the initial conditions based on the perturbation theory (PT) provide
incorrect second-order and higher-order growth. These errors implied by the use
of the perturbation theory to set up the initial conditions in N-body
simulations are called transients. Unless these transients are completely
suppressed compared with the dominant growing mode, we can not reproduce the
correct evolution of cumulants with orders higher than two, even though there
is no problem with the numerical scheme. We investigate the impact of
transients on the observable statistical quantities by performing $N$-body
simulations with initial conditions based on Lagrangian perturbation theory
(LPT). We show that the effects of transients on the kurtosis from the initial
conditions, based on second-order Lagrangian perturbation theory (2LPT) have
almost disappeared by $z\sim5$, as long as the initial conditions are set at $z
> 30$. This means that for practical purposes, the initial conditions based on
2LPT are accurate enough for numerical calculations of skewness and kurtosis.
