A generalized two-parameter biexponential distribution (BIED) is suggested to map surface heterogeneity which in turn can be visualized as a linear combination of three popular site energy distributions, viz., the negative exponential, positive exponential, and constant. Taking advantage of the linearity property of ther Mellin transform operator, closed form expressions for isotherms and their pressure derivatives are derived. Depending on the values of alpha and beta parameters, the relative weights given to each of the component distributions are different, and a wide spectrum of isotherm and isosteric heat behavior is possible. When alpha and beta parameters are equal, the BIED is symmetrical and the isosteric heat vs surface coverage shows a linear fall resembling the constant distribution. A method based on the product of the surface coverage and pressure derivative is used to discriminate between the BIED and constant distributions. The symmetrical BIED also can approximate the Gaussian distribution and when alpha and beta are unequal, even the skewed Gaussian distribution. This is true only as far as isotherms are concerned, but their isosteric enthalpy of adsorption vs surface coverage show markedly different behavior. A limited applicability of the BIED to the experimental system/Ar/Rutile and the data of Drain and Morrison is shown. It appears that the data can be adequately fitted by the Skewed-Gauss distribution, as has been originally done by Sokolowski et al. or by the BIED. The local isotherm employed is the Langmuir model.