We analyze the angle-of-arrival variance of an expanded and collimated laser beam after it has traveled through indoor convective turbulence. A continuous position detector is set at the focus of a lens collecting the light coming from this collimated laser beam. The effect of the different turbulent scales, above the inner scale, is studied changing the diameter of a circular pupil before the lens. The experimental setup follows the design introduced by Masciadri and Vernin (Appl. Opt., Vol. 36, No 6, pp. 1320-1327, February 2004). Tilt data measurements are studied within the fractional Brownian motion model for the turbulent wave-front phase. In a previous paper the turbulent wave-front phase was modeled by using this stochastic process (J. Opt. Soc. Am. A, Vol. 21,No 10, pp. 1962-1969, October 2004). The Hurst exponents associated to the different degree of turbulence are obtained from the new D2H-2 dependence.