On a new approach to distributions with variable transmuting parameter: The concept and examples with emerging problems

A new concept in the transmutation of distribution applying variable transmuting function has been conceived. Test examples with power function by quadratic and cubic transmutations have been demonstrated by the applications of the error-function and standard logistic function variable transmuting functions. The efficiency and properties of the new approach by numerical examples addressing the rate constants of the transmuting functions and the shape parameter of the test power function have been demonstrated. An additional example with a quadratic transmutation of the exponential distribution through the error function as a variable transmuting parameter has been developed.