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We present the results of our QCD analysis for polarized
quark distribution and structure function $xg_1 (x,Q^2)$. We use
very recently experimental data to parameterize our model. New
parameterizations are derived for the quark and gluon distributions
for the kinematic range $x\;\epsilon\;[10^{-8},1]$, $Q^2\;\epsilon\;[1,10^6]$ GeV$^2$. The
analysis is based on the Jacobi polynomials expansion of the
polarized structure functions. Our calculations for two approach,
Bernstein polynomials and Jacobi polynomials are presented.
The values of $\Lambda_{QCD}$ and $\alpha_s(M_z)$ are determined.
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