# Estimating the mean from knowing the first n largest values

There is a sample of n values that are the first n largest values of a population. Is there a way of getting any statistic such as mean or dispersion from such piece of information provided that the population is normally distributed with its size either known or unknown?

• You can estimate the parameters of a normal from order statistics. Note that for the population to be normal, it must be infinite (and therefore really only notional). You could treat what you're calling the population as a random sample from the infinite population, and then you'd treat your largest $n$ values as the largest order statistics from that large sample. You would then estimate the $\mu$ and $\sigma$ of the underlying 'infinite' normal population. – Glen_b -Reinstate Monica May 20 '14 at 23:43
• Thanks, now, from "and then you'd treat.." on. How to? – Germaniawerks May 21 '14 at 10:14
• You observe the n largest samples, but do you know how many samples q were drawn in the first place? Do you have a reasonable prior on the value of q? – Giancarlo May 21 '14 at 15:34
• I have n largest values from a sample of N values and I need to estimate the sample mean and deviation - or whatever statistic I can get. Sample size N may be either known or unknown. – Germaniawerks May 21 '14 at 15:44
• what's stopping you from taking an MLE approach? – Dale C Dec 19 '19 at 5:56