## Report Quantile Std Devs

Key

**in Model[Simulation] refers to a boolean that controls whether the estimated standard deviations of the requested quantiles in a non-randomized simulation should be also calculated and reported.**

*Report Quantile Std Devs*This entry is ignored in a randomized simulation, where such estimated standard deviations are always calculated, since the additional computational effort is low.

It is needed though in a standard, non-randomized simulation because then the standard deviation formula involves the density probability function, the construction of which materially slows down the simulation process.

It is a mathematical fact that the estimated p-th quantile is asymptotically normal around the true p-th quantile

**with variance equal to**

*α***where**

*p(1-p)/[Nf(α)²]***is the probability density function of the related random variable and**

*f(x)***is the sample size.The standard deviation of the estimated p-th quantile equals the square root of that variance.**

*N*