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As somebody who has not much to do with statistics, what are the bad consequences of misidentifying a distribution? After skimming the paper it seems that there
by danbruc 10y ago
As somebody who has not much to do with statistics, what are the bad consequences of misidentifying a distribution? After skimming the paper it seems that there are several distributions that are similar in the sense that it is hard to tell which one a given dataset actually follows. So naively it seems that it should not really matter which one one picks if they are similar enough that it is hard to tell them apart to begin with. Is picking the wrong distribution bad because it leads to wrong conclusions when trying to explain the mechanism causing the distribution? Because extrapolations may yield significantly different results? Or is it more specifically about log–log charts and that small deviations on a logarithmic scale can correspond to significant differences on a linear scale so that a seemingly good fit is not actually a good fit?
- curuinor 10y agoMean of lognormal distribution: e ^ (parameter + (other parameter ^ 2) / 2) Mean of pareto (power law) distribution, where parameter < 1: infinity
- danbruc 10y agoYou mean - pun not really intended - that making choices based on the mean of the supposed distribution, say for risk assessment purposes, may lead to wildly wrong conclusions? Or more generally, that characteristics of different distributions can be very different even if they fit a given dataset similarly well?
- curuinor 10y agoBoth, actually. And of mechanistic statements. For example, if you have this sort of multiplicative central limit theorem with no lower bound, where you imagine independent variables being multiplied together - the attractor of that dynamical process, the result of that universal phenomenon, is lognormal. Add a lower bound, bam, power law (champernowne 1953 "A Model of Income Distribution"). So you're really making different claims about reality.