  A simple analytical argument is proposed for a possible explanation of the
characteristics of the lateral shower age ($s$) of proton
($p$)/nuclei-initiated showers. The analytical argument states that lateral
density distribution (LDD) of electrons of a $p$-initiated shower is due to
superposition of several electromagnetic (EM) sub-showers developed at a very
early stage in the atmosphere from the decay of neutral pions ($\pi^{0}$s).
Thanks to the superposition property of the electron LDD in a $p$ shower, a
plausible analytical parametrization has been worked out by giving well
represented analytic function for the electron LDDs of $p$- and
$\pi^{0}$-initiated showers. Based on cosmic ray extensive air shower
simulations, we have validated how the various characteristics of $s$ can be
understood in the context of the present analytical argument. The $s$ parameter
of a $p$ shower and its correlations with the shower ages of electron- and
$\pi^{0}$-initiated showers supports the idea that the result of superposition
of several EM sub-showers initiated by $\pi^{0}$s with varied energies at a
very early stage might produce the LDD of electrons of a $p$ shower. It is also
noticed with the simulated data that the stated feature still persists
concerning the notion of the local shower age parameter.
