Estimation of Population Size Using Sample Maximum

Most of statistical inference is developed around the sample mean. Very little attention is paid to other sample quantities like the sample maximum. However, there are many situations where the interest is in the maximum rather than in the average. In sports, for example, the winner is not decided by the average, but by the best performance. Investment decisions are not governed by the average returns, but the maximum possible returns. This paper attempts to identify statistical inference that can be drawn from the sample maximum.