Obstructive Sleep Apnea (OSA) is a serious disease caused by the collapse of upper airways during sleep. The present method of measuring the severity of OSA is the Apnea Hypopnea Index (AHI). The AHI is defined as the average number of Obstructive events (Apnea and Hypopnea, OAH-events) during the total sleep period. The number of occurrence of OAH events during each hour of sleep is a random variable with an unknown probability density function. Thus the measure AHI alone is insufficient to describe its true nature. We propose a new measure Dynamic Apnea Hypopnea Index Time Series (DAHI), which captures the temporal density of Apnea event over shorter time intervals, and use its higher moments to obtain a dynamic characterization of OSA.