There is a sample of n values that are the first n largest values of a population. Is there a way of getting any statistics such as mean or dispersion from such pieces of information, provided the population is normally distributed with its size either known or unknown?
You could consider the data as being drawn from a truncated normal distribution, where the truncation point lies at the (unobserved) (n+1)-th point. You can model this in a Bayesian framework, marginalizing over the uncertainty about what the truncation point is. You probably have to provide the model with a rather informative prior for the truncation point to be able to get a sensible estimate of the mean and variation in the source population.
Good idea, may be with potential application.
It is someway analogues to the ranked set sampling. For estimation of any statistics, you must also account the position value (rank).
Thanks.
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