Does the acceptance-rejection method or inverse transform sampling converge to the mean quicker say for beta distribution, assuming acceptance-rejection has suitable envelope function? is there a way to gauge the rate of convergence with increasing sample size? thanks.

  • $\begingroup$ It seems to me that acc-rej sampling is used mainly when the quantile finction (inverse CDF) is not available in a convenient form. As the name implies, acc-rej sampling is inefficient to the extent that rejections happen, whereas the inverse CDF method uses every standard uniform value generated. // Mainly, the inverse CDF method relies on CDFs and hence quantile functions that are available in closed form. But some excellent rational approximations to quantile fcns are in general use. One is Wichura's rat'l aprx to the std normal quantile function (used to simulate normal samples in R). $\endgroup$ – BruceET Jun 20 '19 at 6:17
  • $\begingroup$ @BruceET thanks for your response. given a suitable envelope function, i think that acc-rej MIGHT converge quicker. i reckon the inverse CDF generates prob from 0 to 1 with equal probability so in a small size sample, it is liable to produce deviates far from the mean. on the other hand, given a suitable envelope function, the acc-rej might produce deviates closer to the mean by construction. does this seem reasonable? thanks again for your time and interest. $\endgroup$ – charliealpha Jun 29 '19 at 6:17

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