Research Projects

The main advantage of a finite mixture model is that it can capture heterogeneity contained in the given data set. There are various situations, where the data are actually heterogeneous. For example, suppose a machine has several components, which have been manufactured by using different raw materials. Then, the survival times of the components become heterogeneous. There is another possibility that heterogeneity may occur due to assembled components of a machine may be acquired from different producers. Thus, in order to model the life cycle of a machine more accurately, it is always preferable to use a mixture model instead of a single probability model. Stochastic comparisons of two finite mixture models are useful tools to obtain a better system with respect to its performance. Thus, we study stochastic comparison results between two finite mixture models for some general family of distributions in this proposal. Here, we have mainly considered five problems. In the first problem, we will consider mixture models with components having exponentiated location scale models. In the second problem, we study models with multiple-outlier components. The third problem is associated with the general components with a general survival function having two model parameters. The dependence among the mixture models is included in the fourth problem. In the final problem, we consider alpha-mixture models and explore some ordering results. The successful implementation of this project will fullfill the gap in the literature and will open a new direction in this field of research. Further, the outputs of this project will help us to answer the following question "which of two systems perform better in suitable stochastic sense?"