In this thesis, we introduce some theoretical statistical studies of some distribution functions to calculate distances for some stellar groups in our galaxy. Along the Gaussian method suggested by Sharaf et. al. (2003), we continued with some modifications resulted in Gaussian A, B, C. The Malmquist bias was taken into account. We added the percentage error to determine the dispersion for spectral type and subtypes. The philosophy of the Gaussian A, B, C is due to changes in the limits of integrands due to what we named mg and mL (defined later). These changes are related to the sun, the sample and the telescopes used. In turn it changed the shape of the integrands, and gave, as we believe, more accurate results compared to others. The Exponential distribution function was then used and treated following the same procedure as the Gaussian. We found that the method as such does not contain the transcendental parameter. Taylor expansion was then used with the first two terms as approximation. The fourth and sixth terms were derived but, they diverge.

Dr. Helal Ismaeil Abdel Rahman Ali National Research Institute in Astronomy and Geophysics, Helwan, Cairo, Egypt.Ph.D. in Astrostatistics, Al Azhar Univ.M.Sc. in Statistics, ISSR, Cairo univ.Higher Diploma in Statistics from ISSR, Cairo univ.B.Sc. in Astronomy,Faculty of Science, Cairo Univ.current work: Shaqra Univ. Saudi Arabia.