  Various well-known statistical measures like \emph{L\'opez-Ruiz, Mancini,
Calbet} (LMC) and \emph{Fisher-Shannon} complexity have been explored for
confined isotropic harmonic oscillator (CHO) in composite position ($r$) and
momentum ($p$) spaces. To get a deeper insight about CHO, a more generalized
form of these quantities with R\'enyi entropy ($R$) is invoked here. The
importance of scaling parameter in the exponential part is also investigated.
$R$ is estimated considering order of entropic moments $\alpha, \beta$ as
$(\frac{2}{3},3)$ in $r$ and $p$ spaces respectively. Explicit results of these
measures with respect to variation of confinement radius $r_c$ is provided
systematically for first eight energy states, namely,
$1s,~1p,~1d,~2s,~1f,~2p,~1g$ and $2d$. Detailed analysis of these complexity
measures provides many hitherto unreported interesting features.
