  We propose a model based on extreme value statistics (EVS) and combine it
with different models for single asperity contact, including adhesive and
elasto-plastic contacts, to derive a relation between the applied load and the
friction force on a rough interface. We find that when the summit distribution
is Gumbel, and the contact model is Hertzian we have the closest conformity
with Amontons law. The range over which Gumbel distribution mimics Amontons law
is wider than the Greenwood-Williamson Model. However exact conformity with
Amonton's law does not seem for any of the well-known EVS distributions. On the
other hand plastic deformations in contact area reduce the relative change of
pressure slightly with Gumbel distribution. Elastic-plastic contact mixes with
Gumbel distribution for summits. it shows the best conformity with Amonton`s
law. Other extreme value statistics are also studied, and results presented. We
combine Gumbel distribution with GW-Mc Cool model which is an improved case of
GW model, it takes into account a bandwidth for wavelengths of {\alpha}.
Comparison of this model with original GW-Mc Cool model and other simplified
versions of BGT reveals that Gumbel distribution has a better conformity with
Amonton`s law for all values of {\alpha}. When adhesive contact model is used,
the main observation is that for zero or even negative applied load, there is
some friction. Asperities with height even less than the separation of two
surfaces are in contact. For a small value of adhesion parameter, a better
conformity with Amontons law is observed. Relative pressure increases for
stronger adhesion which means that adhesion controlled friction dominated by
load controlled friction. We also observe that adhesion increases on a surface
with a lower value of roughness.
