  In this paper, we introduce a new way to estimate the scaling parameter of a
self-similar process by considering the maximum probability density function
(pdf) of tis increments. We prove this for $H$-self-similar processes in
general and experimentally investigate it for turbulent velocity and
temperature increments. We consider turbulent velocity database from an
experimental homogeneous and nearly isotropic turbulent channel flow, and
temperature data set obtained near the sidewall of a Rayleigh-B\'{e}nard
convection cell, where the turbulent flow is driven by buoyancy. For the former
database, it is found that the maximum value of increment pdf $p_{\max}(\tau)$
is in a good agreement with lognormal distribution. We also obtain a scaling
exponent $\alpha\simeq 0.37$, which is consistent with the scaling exponent for
the first-order structure function reported in other studies. For the latter
one, we obtain a scaling exponent $\alpha_{\theta}\simeq0.33$. This index value
is consistent with the Kolmogorov-Obukhov-Corrsin scaling for passive scalar
turbulence, but different from the scaling exponent of the first-order
structure function that is found to be $\zeta_{\theta}(1)\simeq 0.19$, which is
in favor of Bolgiano-Obukhov scaling. A possible explanation for these results
is also given.
