Lifetime distributions play an important role in applied sciences. Keeping this consideration in this paper introduced a general function for mixture distribution, say as Raja General Function and discussed its some properties. Further using RGF introduced new Tariq distribution and conferred statistical properties including mean, variance, m.g.f, rth raw moments, reliability measures, order statistics, and graphical representation of functions also observed better goodness of fit than other lifetime data distribution functions using real-life data applications.