Estimating the Total Volume of Queries to a Search Engine

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. 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.