🚀 go-pugleaf

I'd appreciate any thoughts you might have on this stumper in
marketing statistics:

Information Resources, Inc. (IRI) publishes statistics describing
the purchasing of tens of thousands of different products sold in
supermarkets. Among the statistics are "% of households buying."
This measure cannot be simply aggregated across time. For
example, if you know that 30% of all households buy cat food in
one 13 week quarter, you would not assume that over the course of
a 52 week year, the % of households buying cat food is 4 time 30%
or 120%. Typically, you would have to pay IRI to retabulate
purchasing for each household over the desired time period.
However, we want to find a another way.

What we need is a rough way to quickly estimate % of households
buying various products during typical 2 week periods, assuming
we already know from IRI the exact statistics for 52 and 13 weeks
periods.

The other statistic of relevance that we already have for the 52
and 13 week periods is "# of purchase occasions among buyers." If
you multiply % of households buying times number of purchase
occasions among those buyers, you get the average number of
purchase occasions among all shoppers. For example, if 30% of the
shoppers bought cat food, and on average those cat food buyers
bought it 3.33 times per quarter, then the overall average
shopper (including both cat lovers and cat haters) bought cat
food 1.0 times per quarter. For this statistic, in contrast to
the other two, it _is_ reasonable to extrapolate the average
annual number of cat food purchases among all shoppers: 1.0 times
4 = 4 (assuming no seasonal fluctuations or long term growth or
decline).

All right, here are some examples to help you think:

                               52 Weeks 13 Weeks  2 Weeks
Cold Cereal - All Brands       -------- --------  -------
  % of Households Buying           94.7%    77.0%       ?
  Purchase Occasions/Buyer         11.7      3.6        ?
                                  -----     ----     ----
  Pur Occ/All Shoppers            11.08     2.77     0.43

Kellogg's Corn Flakes
  % of Households Buying           36.7%    17.6%       ?
  Purchase Occasions/Buyer          2.9      1.5        ?
                                   ----     ----     ----
  Pur Occ/All Shoppers             1.06     0.26     0.04

Dry Dog Food - All Brands
  % of Households Buying           31.3%    21.3%       ?
  Purchase Occasions/Buyer          6.8      2.5        ?
                                   ----     ----     ----
  Pur Occ/All Shoppers             2.13     0.53     0.08


It has been suggested that a negative binomial distribution is
the key to the problem, but I'm not qualified to comment on that.

Once again, we greatly appreciate your help with any suggestions
you might have. Please E-mail or post if you think the question
is of general interest.


-- 
Steve Sailer
VideOcart, Inc.      ssailer@hq.videocart.com