This paper utilizes maximum likelihood methods to simulate a Hirschman-Herfindahl index (HHI) for markets in which complete market share information is unavailable or delayed. Many jurisdictions either may be unable to administratively collect data or experience delays in collection that make data regarding turbulent markets of limited use. With the development of this method, regulatory authorities monitoring health-care competition or health-care firms can now use market surveys--in which reliable recall is often limited to the largest three or four firms--to produce an on-the-spot measure of market concentration.