The motivation of this article is to estimate multifractality classification and model selection parameters: the first-order scaling exponent \(c_1\) and the second-order scaling exponent (or intermittency coefficient) \(c_2\) . These exponents are derived from wavelet leaders, which are fundamental tools in applied multifractal analysis. While most estimation methods, particularly Bayesian approaches, assume log-normality, we challenge this hypothesis by statistically testing the normality of log-leaders. Upon rejecting this assumption, we propose a novel and more flexible model based on log-concave distributions. We validate this model on well-known stochastic processes, including fractional Brownian motion, the multifractal random walk, and the canonical Mandelbrot cascade, as well as on real-world marathon runner data. Under the log-normality hypothesis, we revisit the estimation procedure for \(c_1\) , providing confidence intervals, and for \(c_2\) , applying it to fractional Brownian motions with various Hurst indices and to the multifractal random walk. Finally, we establish several theoretical results on the distribution of log-leaders in random wavelet series, which align with our numerical findings.
