  Several well-known statistical measures similar to \emph{LMC} and
\emph{Fisher-Shannon} complexity have been computed for confined hydrogen atom
in both position ($r$) and momentum ($p$) spaces. Further, a more generalized
form of these quantities with R\'enyi entropy ($R$) is explored here. The role
of scaling parameter in the exponential part is also pursued. $R$ is evaluated
taking order of entropic moments $\alpha, \beta$ as $(\frac{2}{3},3)$ in $r$
and $p$ spaces. Detailed systematic results of these measures with respect to
variation of confinement radius $r_c$ is presented for low-lying states such
as, $1s$-$3d,~4f$ and $5g$. For \emph{nodal} states, such as $2s,~3s$ and $3p$,
as $r_c$ progresses there appears a maximum followed by a minimum in $r$ space,
having certain values of the scaling parameter. However, the corresponding
$p$-space results lack such distinct patterns. This study reveals many other
interesting features.
