Within the framework of demographic changes and the constraint of permanent growth of the elderly number in European population (i.e. France) which the health sector is confronted to, the detection of abnormal behaviors in the supervisory framework has known a particular interest during these last years. Thereby, the main objective of this paper is to propose a new learning method of the behavior in smarthomes while using a Mixture of Gaussian Hidden Semi-Markov Model. Several experiments, based on data benchmarks acquired from a living lab1, are carried out to show the reliability of this new approach.