Question by Isabela: What is the interpretation for log pdf in a plot?
I have to make a plot of the log probability density function of an action. I have to compare it’s empirical log density with the normal log density. Why is it different from the normal form of pdf?

Best answer:

Answer by JoeyV
I’d go the other direction and ask why you are not plotting log(log(pdf)). The reason is that you usually want to get a straight line when you do these sorts of plots if the distribution is as you have specified. Hence straight line means normal, curve means violation of normality. This is the basis of the Q-Q plot which is much more standard than your empirical pdf (btw what is an empirical pdf – there’s a really clear meaning of empirical cdf but empirical pdf’s need smoothing parameters which confound your plot). Anyway, I guess the idea is that you plot something that looks like x^2 for both and you can compare them. I guess…

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