ABSTRACT
In any statistical investigation, we collect data which, in many cases, can be described by observable random variables X1,X2, . . . ,Xn (all or some of which may as well be multi-dimensional). We then assume a suitable probability distribution, called a probability model or simply a model, for the data X = (X1,X2, . . . ,Xn). The choice of the model is dictated partly by the nature of the experiment which gives rise to the data and partly by our past experience with a similar data. Often, mathematical simplicity plays a significant role in choosing the model. In general, the model takes the form of a specification of the joint probability distribution of the observable random variables X1,X2, . . . ,Xn. According to the model, the joint distribution function FX is supposed to be some unspecified member of a suitable class FX of distributions. For the sake of simplicity, we assume that Xi’s are single dimensional if not mentioned otherwise.
