Weibull analyses given to the initial mass function (IMF) deduced by Miller and Scalo (1979) have shown that the mass dependence of IMF is an exp$[-{alpha}m]$- form in low mass range while in the high mass range it assumes an exp$[-{alpha}sqrt{m}]/sqrt{m}$-form with the break-up being at about the solar mass. Various astrophysical reasonings are given for identifying the exp$[-{alpha}m]$ and exp$[-{alpha}sqrt{m}]/sqrt{m}$ with halo and disk star characteristics, respectively. The physical conditions during the halo formation were such that low mass stars were preferentially formed and those in the disk high mass stars favoured. The two component nature of IMF is in general accord with the dichotomies in various stellar properties.