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06-11-2013 01:11 PM

In my problem, n bidders place $ bids for unopened lots. They are basing their bids on their judgement of the value of the contents. With bids sorted in order, we have n order statistics, repeated for m lots. I am assuming that a single distribution type generates the bidding, e.g. lognormal or the like. In reality the mean and variance would likely be different for each lot, however to simplify initially I am willing to divide each lot's bids by its high bid. E.g. lot A might have "standardized" order statistics high to low {1, .9, .8, .75, .70. .5,...}. I wish to select a distribution type and its parameters based on these "standardized" sets or order statistics.

PROC UNIVARIATE provides Q-Q plots and methods that readily identify the best distribution and good parameter estimates for each lot. e.g., the Q-Q plot of lot A might be shown to have the best fit to lognormal(.5,1.1).. Of course, if I apply this method to each lot in turn, I get m different results. What I wish is the parameter estimates that are the best fit to data for all lots. Is there a built-in procedure in SAS that does that? or am I on my own to specify a nonlinear regression?

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06-11-2013 09:34 PM

Dividing by the maximum bid might not be the best strategy, as extreme value statistics have high variance, especially with long-tailed distributions. I would rather try the transformation *Y*ij = log(*B*ij/*B*mj) where *B*ij is the bid from bidder *i* on lot *j* and *B*mj is the median bid for lot *j*. Then I would give it a shot at fitting a single distribution to the whole set of *Y'*s.

PG

PG

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06-13-2013 09:17 AM

Thanks, your approach helps a lot.