Is there an analytic/arithmetic method for calculating the standard deviation of a normal distribution given a quantile value of that distribution?

by ctesta01   Last Updated October 09, 2019 21:19 PM

This is an R function I use occasionally:

#' Determine y in the equation `qnorm(mean=m,sd=y,p=p)==x`
get_sd_from_quantile_score <- function(m, p, x) {
  get_quantile_score <- function(y) { 
  f <- function(y) { (get_quantile_score(y) - x)^2 }
  opt <- optim(par = 1, fn = f, method = 'CG')

Is there an analytic or arithmetic method/formula that could solve this? Would it be faster to compute?

Answers 1

I believe simply (x-m)/qnorm(p) will do it. qnorm(p) gives you how many standard deviations away from the mean the value is, and then you scale it by the given difference.

October 09, 2019 20:36 PM

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