  We use the presently observed number density of large X-ray clusters and
linear mass power spectra to constrain the shape parameter ($\Gamma$), the
spectral index ($n$), the amplitude of matter density perturbations on the
scale of $8 h^{-1}$Mpc ($\sigma_8$), and the redshift distortion parameter
($\beta$). The non-spherical-collapse model as an improvement to the
Press-Schechter formula is used and yields significantly lower $\sigma_8$ and
$\beta$. An analytical formalism for the formation redshift of halos is also
derived.
