I simply showed to ChatGPT the bimodal distribution of the deviation and this is what he had to say. @TheRealPlanC 

Why a Uniform Quantile Model is Problematic
Two Distinct Regimes:

The data is not homogeneous but instead represents two distinct market regimes: bear markets (negative deviations) and bull markets (positive deviations).
A quantile model assumes the data belongs to a single, unified statistical population, which overlooks the underlying market cycles and their unique dynamics.

Different Drivers in Each Regime:

Price behavior in bear markets is fundamentally different from bull markets. In bear markets, prices may be driven by fear, accumulation, and reduced liquidity, while bull markets are driven by speculation, euphoria, and excess liquidity.
A uniform quantile model fails to capture these dynamics, potentially leading to misleading conclusions about the probabilities of extreme events.

Bimodal Distributions Violate Assumptions:

Quantile regression works best when the data follows a unimodal distribution (e.g., centered around a single trend). In a bimodal scenario, the quantiles may not accurately represent the tails of the distribution or their respective probabilities.

Interpreting Extremes Becomes Problematic:A single quantile regression would mix bull and bear market data, which may lead to unrealistic projections for extreme events (e.g., top quantiles might incorrectly include data from both bull and bear regimes).

A Better Approach
Separate Models for Each Regime:Instead of treating the data as one, apply segmented quantile regression or separate models for the bull and bear regimes. The boundary between regimes (e.g., around the 0 deviation line) can serve as the threshold for switching between models.

For example:

A bear market model for data below the power law trend.
A bull market model for data above the power law trend.

Regime Detection:

Use a statistical method to identify the regime (e.g., clustering techniques or threshold-based classification).
Normalize deviations for volatility within each regime to better understand the distribution.

Exponential Deviations:

Recognize that deviations from the power law are likely exponential in nature (e.g., rapid growth during bubbles or sharp corrections during crashes).
Separate models for exponential growth and decay could improve the fit and predictive power.

Volatility-Adjusted Analysis:

Since this distribution is already volatility-adjusted, the next step would be to analyze each regime independently while preserving this normalization.

Conclusion
A quantile model treating the data as one uniform source is too simplistic given the bimodal nature of the distribution. Separating the data into bull and bear regimes and modeling them independently would lead to a more accurate and meaningful representation of Bitcoin's behavior. This approach aligns better with the observed cyclicality and differing dynamics of the two regimes.