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If sampling from the density is the only goal, then you are absolutely right. Can directly estimate empirical CDF as you pointed below. But histograms can still
by vvanirudh 2y ago
If sampling from the density is the only goal, then you are absolutely right. Can directly estimate empirical CDF as you pointed below. But histograms can still be useful to approximate the PDF itself? (taking the derivative of the empirical CDF to estimate PDF is wild as you said)
- andrewla 2y agoYes, if you need an approximate pdf. I've found that when I'm working non-parametrically (or in robust statistics) I like to stay in cdf space or use quantile functions more than trying to use those nasty derivatives.