Even though the number of internet users has increased tremendously and various services have appeared, the current IP network cannot support the quality of service sufficiently because of its inherently best effort service type. Two types of QoS(Quality of Service) enabled architectures, integrated services and differentiated services networks, are proposed in the IP networks. Integrated service network can provide strict QoS. On the other hand, it has a scalability problem. Differentiated service network can solve this scalability problem but the ability to provide the strict QoS is not sufficient because of its lack of standardized connection admission control function. Thus, an efficient connection admission control function is required to provide the strict QoS in the DiffServ network. For connection admission control, the network QoS parameters, such as delay, delay variation, loss can be taken into account. The QoS parameter monitoring mechanism should be accurate and its overhead should be lightly loaded. A monitoring mechanism for estimating the end-to-end delay distribution is proposed using an extended 3 parameters Weibull distribution and the performance of the proposed algorithm is evaluated.