  The lateral density data obtained for different secondaries of an extensive
air shower (EAS) from an array of detectors are usually described by some
suitable lateral density functions (LDFs). Analyzing non-vertical simulated
EASs generated with the CORSIKA code, it is found that the lateral and polar
density distributions of electrons and muons are asymmetric in the ground
plane. It means that typical expressions for symmetric lateral density
functions (SLDFs) (\emph{e.g.} the Nishimura-Kamata-Greisen function) are
inadequate to reconstruct the lateral and polar dependencies of such asymmetric
electron or muon densities accurately. In order to provide a more consistent
LDF for non-vertical shower reconstruction in the ground plane, the paper
considers the issue of the modification of the SLDF analytically. The asymmetry
arising from additional attenuation and correction of the positional
coordinates (radial and polar) of cascade particles causes a gap length between
the center of concentric equidensity ellipses and the EAS core. A toy function
is introduced as a basic LDF to describe the asymmetric lateral and polar
density distributions of electrons or muons of EASs, thereby predicting the gap
length parameter. Consequently, the desired LDF describing the asymmetric
density distributions of electrons and muons of EASs has emerged. We compare
results from detailed simulations with the predictions of the analytical
parametrization. The LDF derived in this work is found to be well-suited to
reconstruct EASs in the ground plane directly.
