Cosmological Parameter Estimation using $H(z)$ Measurements for Non-flat
  $\Lambda$ Cold Dark Matter Universe
  Accurate estimations of cosmological density parameters
($\Omega_{0m}h_{0}^{2}$, $\Omega_{0k}h_{0}^{2}$, $\Omega_{0\Lambda}h_{0}^{2}$)
and Hubble constant ($h_{0}$) provide detailed understanding of our universe.
We propose a new procedure to estimate these parameters for non-flat
$\Lambda$CDM universe in the Friedmann-Robertson-Walker (FRW) background. We
utilize the Hubble parameter ($H(z)$) measurements in our analysis. These
$H(z)$ are measured using two techniques (DA and BAO). We generalize the
two-point diagnostic method first proposed by Sahni et al.(2008) to the case of
non-flat spatial curvature of the universe. Using three independent $H(z)$
measurements at a time, we solve for three fundamental cosmological density
parameters ($\Omega_{0m}h_{0}^{2}$, $\Omega_{0k}h_{0}^{2}$,
$\Omega_{0\Lambda}h_{0}^{2}$) and repeat the procedure for all possible
combinations of three measurements of Hubble parameters. We divide the $H(z)$
data into three groups comprising all, $31$ DA only and $24$ BAO only
measurements. We perform our analysis separately on each group. In our method,
we use weighted-mean and median statistics to estimate the values of density
parameters. Using these estimated values of density parameters, we also find
the values of $h_{0}$ for each of these three sets corresponding to each of two
statistics. We conclude that median statistic is more reliable in our analysis,
since the sample specific uncertainties are non-Gaussian in nature. Finally, we
achieve the reliable results $\Omega_{0m}h_{0}^{2}=0.1485^{+0.0041}_{-0.0051}$,
$\Omega_{0k}h_{0}^{2}=-0.0137^{+0.0129}_{-0.0125}$,
$\Omega_{0\Lambda}h_{0}^{2}=0.3126^{+0.0131}_{-0.009}$ and
$h_{0}=0.6689^{+0.0141}_{-0.0121}$ using median statistic in our analysis
corresponding to the set of total $53$ $H(z)$. Our estimated median values of
cosmological parameters agree with Planck Collaboration VI.(2020) results
excellently.
