Learned indexes are assisting or gradually replacing traditional index structures due to their low memory usage and high query performance. However, the online retraining caused by data updates makes it unable to adapt to the scenario of frequent data updates. To avoid index reconstruction due to frequent data updates without significantly increasing memory consumption, this study proposes an adaptive update-distribution-aware learned index named DRAMA. It uses an LSM-Tree-like delayed learning method to actively learn the characteristics of the data update distribution, approximate fitting techniques to quickly establish the update-distribution model, a model merging strategy to replace the frequent retraining, and a hybrid compression technique to reduce the memory usage of model parameters in the index. The index is constructed and validated on both real and synthetic datasets. The results show that, compared to traditional indexes and state-of-the-art learned indexes, the proposed index can effectively reduce query delay in a data update environment without additional memory consumption.