  Prior statistical knowledge of the atmospheric turbulence is essential for
designing, optimizing and evaluating tomographic adaptive optics systems. We
present the statistics of the vertical profiles of $C_N^2$ and the outer scale
at Maunakea estimated using a Slope Detection And Ranging (SLODAR) method from
on-sky telemetry taken by RAVEN, which is a MOAO demonstrator in the Subaru
telescope. In our SLODAR method, the profiles are estimated by a fit of the
theoretical auto- and cross-correlation of measurements from multiple
Shack-Haltmann wavefront sensors to the observed correlations via the
non-linear Levenberg-Marquardt Algorithm (LMA), and the analytic derivatives of
the spatial phase structure function with respect to its parameters for the LMA
are also developed. The estimated profile has the median total seeing of
0.460$^{\prime\prime}$ and large $C_N^2$ fraction of the ground layer of 54.3%.
The $C_N^2$ profile has a good agreement with the result from literatures,
except for the ground layer. The median value of the outer scale is 25.5m and
the outer scale is larger at higher altitudes, and these trends of the outer
scale are consistent with findings in literatures.
