General properties of probability density $A\cdot\exp(-(x-c)^2/(a(x-c)+2b^2))$

General properties (parametric scaling, mean value, variance, width, asymmetry) of probability density $A\cdot\exp(-(x-c)^2/(a(x-c)+2b^2))$ are investigated as a general cause of the normal and exponential ones. It is able to describe wider class of processes than just ones. Methods determination, visual interpretation and calculation its parameters are presented. One can operate with the distribution as well as with normal distribution. Formulae and example are adduced.