A stochastic model for the publishing and citation process is discussed in Detecting h-index manipulation through self-citation analysis, from the fraud-detection point of view of the OP. The functional form of the h-index curve following from this model is a sum of incomplete Beta functions, with parameters being the productivity of the researcher and the career length.
One telltale signal is the "humpback", resulting from self-citation of a paper close the the h-index.
Here is Mathematica code for the function:
e[theta_,alpha_,nu_,t_,n_]:=theta*t-(theta*alpha/(nu-1))*
Sum[Beta[t/(alpha+t),r+1,nu-1]/Beta[r+1,nu-1],{r,0,n-1}]
For example, e[2,1,5,10,13]=13.6 the expected number of papers receiving at least n=13 citations by time t=10, for a researcher with a publication rate of theta=2, and a mean citation rate of nu/alpha=5/1.