  We study the problem of estimating the total number of searches (volume) of
queries in a specific domain, which were submitted to a search engine in a
given time period. Our statistical model assumes that the distribution of
searches follows a Zipf's law, and that the observed sample volumes are biased
accordingly to three possible scenarios. These assumptions are consistent with
empirical data, with keyword research practices, and with approximate
algorithms used to take counts of query frequencies. A few estimators of the
parameters of the distribution are devised and experimented, based on the
nature of the empirical/simulated data. For continuous data, we recommend using
nonlinear least square regression (NLS) on the top-volume queries, where the
bound on the volume is obtained from the well-known Clauset, Shalizi and Newman
(CSN) estimation of power-law parameters. For binned data, we propose using a
Chi-square minimization approach restricted to the top-volume queries, where
the bound is obtained by the binned version of the CSN method. Estimations are
then derived for the total number of queries and for the total volume of the
population, including statistical error bounds. We apply the methods on the
domain of recipes and cooking queries searched in Italian in 2017. The observed
volumes of sample queries are collected from Google Trends (continuous data)
and SearchVolume (binned data). The estimated total number of queries and total
volume are computed for the two cases, and the results are compared and
discussed.
