A Pathway Idea in Model Building

The pathway idea is a way of going from one family of functions to another family of functions and yet another family of functions through a parameter in the model so that a switching mechanism is introduced into the model through a parameter. The advantage of the idea is that the model can cover the ideal or stable situation in a physical situation as well as cover the unstable neighborhoods or move from unstable neighborhoods to the stable situation. The basic idea is illustrated for the real scalar case here and its connections to topics in astrophysics and non-extensive statistical mechanics, namely superstatistics and Tsallis statistics, Mittag-Leffler models, hypergeometric functions and generalized special functions such as the H-function etc are pointed out. The pathway idea is available for the real and complex rectangular matrix variate cases but only the real scalar case is illustrated here.