  Suppose $X_{t}$ is a one-dimensional and real-valued L\'evy process started
from $X_0=0$, which ({\bf 1}) its nonnegative jumps measure $\nu$ satisfying
$\int_{\Bbb R}\min\{1,x^2\}\nu(dx)<\infty$ and ({\bf 2}) its stopping time
$\tau(q)$ is \emph{either} a geometric \emph{or} an exponential distribution
with parameter $q$ independent of $X_t$ and $\tau(0)=\infty.$ This article
employs the Wiener-Hopf Factorization (WHF) to find, an $L^{p^*}({\Bbb R})$
(where $1/{p^*}+1/p=1$ and $1<p\leq2$), approximation for the extrema's
distributions of $X_{t}.$ Approximating the finite (infinite)-time ruin
probability as a direct application of our findings has been given. Estimation
bounds, for such approximation method, along with two approximation procedures
and several examples are explored.
