it seems to me this study can be done.

Kindly  give me  a clue

If so then the relativistic model will be matched with the observed value and it can be approximated  more appropriately.

In my own idea, taking only single parameter like red shift may be insufficient to express the entire physical quantities like mass, radius, density etc. But with the assumptions of both luminosity and red shift may be simpler (I'm just guessing without mathematical support)

A model of quasar can be done only if to subtract a large value of redshift due to plasma medium around the active quasar. See Ari Brynjolfsson "Redshift of photons penetrating a hot plasma" http://arxiv.org/pdf/astro-ph/0401420v3

Yes, probably this is possible, however it should be kept in mind that for many years, researchers have been reporting possible physical associations between quasi-stellar objects (QSO) and high redshift and normal galaxies of low redshift, as well as associations between galaxies of very different redshifts (see Arp, H.C.: 1986, Quasars, Redshifts and Controversies, interstellar Media, Berkeley, CA. Arp, H.C. and van Flandem, T.: 1992, Phys. Lett. A 164, 263. Burbidge, G. et al.: 1990, Astrophys. J. Suppl. Ser. 74, 675 and references therein). A good example of these associations is provided by the quasar-galaxy pair 3C 232-NGC 3067, in which the hydrogen forms a long tail apparently extending from the galaxy to the quasar (Carilli, C.L., van Gorkom, J.H. and Stocke, J.T.: 1989, Nature 338, 134.) It is clear that if at least one the reported examples proves to be real, then a non cosmological mechanism producing such a redshift has to be found. This problem has been the subject of long discussions (see Arp 1986,; Narlikar, J.V.: 1989, Space Sci. Rev. 50, 523. Narlikar, J.V.: 1977, Ann. Phys. 107, 325. and references therein). However as stressed by Narlikar, it seems that no one of the so far presented alternatives can account for all the different types of discordant phenomena. Under these circumstances, and being aware that new and more precise observational data is required to elucidate this important problem, it would be advisable to keep the mind open, as for the real interpretation of the quasar redshift origin.

Thanks to  Prof Herrera, Prof Chepick and Prof Farook for their nice suggestions