In this investigation we parametrize the numerical results of Laframboise with the function f(chi) = a(b + chi)(c), where a, b, and c are fit parameters and chi is the normalized probe potential. The fits show a clear relation between these fitting parameters and the probe characteristic. With these parameters we construct a self-consistent algorithm to fit measured cylindrical probe characteristics of a Maxwellian plasma without any assumption for the relation of the characteristic Langmuir probe dimension to the Debye length. The measured probe characteristics of an anodic Cu-vapor vacuum are are analyzed by means of this nonlinear fitting algorithm. From the determined plasma parameters we obtain clear indications for hot ions. The mean deviation of the calculated theoretical probe characteristic from the measured characteristic is <2%.