The rapid growth of elderly population makes the health of the elderly one of the major social concerns. The elderly is often facing with several physical and mental healthcare related problems, among those, instance of fall and injuries ranked at the top. If people fall unexpectedly and without timely assistance, it is easy to cause irreparable harm. Therefore, how to automatically detect fall and alert for care/attention using advanced assisted technologies is a hot area of research. In this paper, we examine six machine learning-based methods and propose and carefully configure two novel deep learning-based architectures for fall detection. We compare the relative performance of these methods using an open source dataset, MobiAct, which was collected with four simulated fall types and nine daily living activities using smartphones. Our experimental results show that the proposed long short-term memory (LSTM) deep learning model is quite effective for the fall detection classification; its accuracy reaches 98.83%, the specificity is 99.38%, the sensitivity is 90.57% and the F1 score is 90.33%. These results are better than existing machine learning methods in all types of fall and most of daily activities.