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## Main Question or Discussion Point

Suppose that a given population is endowed with a pair of characteristics T and K. Let's think of these characteristics as random variables

I observe the realisations of T for a sample consisting of those individuals with K<

In terms of the distributions and parameters above, what is

To be more precise, I am trying to establish what information is contained in

*(T,K)∼BiNormal((μT,μS),(σT,σS),ρ)*I observe the realisations of T for a sample consisting of those individuals with K<

*a,*where the selection threshold*a*is unknown. Let*t*denote the minimum observed realisation of T in this sample.In terms of the distributions and parameters above, what is

*t*an estimator of?To be more precise, I am trying to establish what information is contained in

*t*that is not already contained in the truncated sample mean and variance. My intuition is that there must be some information: if selection was taking place on T itself, then it would seem intuitive to think of*t*as an estimator of a; but that's not the case here...