Is there a way to compare power-laws between two series and take something from the data? For example the slopes of public market returns are different than th

Is there a way to compare power-laws between two series and take something from the data? For example the slopes of public market returns are different than that of illiquid markets. Is a power law w more slope more random? I was really looking for a t-test or chi-squared type take away. My smarter, math under grad interns pointed out that we were at the edge of interpretive capabilities - but this was ~2000s.