This paper presents results from photometric and statistical-parallax analysis of a sample of 850 field RR Lyrae (RRL) variables. The photometric and spectroscopic data for sample RRLs are obtained from (1) our new spectroscopic observations (for 448 RRLs) carried out with the Southern African Large Telescope (SALT); (2) our photometric observations using the 1.0-m telescope of the South African Astronomical Observatory (SAAO), and (3) literature. These are combined with accurate proper motion data from the second release of textit{Gaia} mission (DR2). This study primarily determines the velocity distribution of solar neighborhood RRLs, and it also calibrates the zero points of the RRLs visual V-band luminosity-metallicity (LZ or $M_V-$[text{Fe/H}]) relation and their period-luminosity-metallicity (PLZ) relations in the textit{WISE} $W_1-$ and textit{2MASS} $Ks-$band. The calibrated PLZ and LZ relations are used to estimate the Galactic Center distance and the distance modulus of the Large Magellanic Cloud (LMC), which are found to be 7.99$pm$0.49,kpc and 18.46$pm$0.09 ,mag, respectively. All our results are in excellent agreement with available literature based on statistical parallax analysis, but are considerably more accurate and precise. Moreover, the zero-points of our calibrated PLZ and LZ relations are quite consistent with current results found by other techniques and yield the LMC distance modulus that is within 0.04,mag of the current most precise estimate.
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