In various data-centric applications, a huge amount of data is collected and stored in the form of event time histories. An event time history is a collection of events that have occurred in an event based system over a period of time. The granularity of a history can be any time unit, like second, minute, or day. A distance in the history is defined as the number of time ticks between two occurrences of the event. In our work, we propose an approximation method that efficiently and accurately estimates the count of a single event history at any coarser time granularity by examining the distance distribution of the base history. We then show how this count estimation method can be embedded in any association rule mining algorithm in order to generate associations at coarser time granularities. The proposed methods are implemented and tested on different real data sets and the results are presented to show the effectiveness of the methods.