Positron emission tomography (PET) is a unique method to investigate physiology in the living body. Kinetic models with kinetic rate constants describe the dynamic radioactive tracer uptake in living tissue. If the variation of the kinetic parameter values within a specific tissue region could be determined accurately, it would give valuable quantitative information about the tissue heterogeneity. In this study we developed a unique method to estimate the variation from the regional kinetic parameter histograms. To determine the kinetic parameter values, we chose non-penalized maximum likelihood (ML) estimation due to the specific statistical error properties of the ML estimates. The parameter values were estimated directly from the time series of PET projections. The choice of the estimation method enabled us to utilize the ML theory in error correction. We developed a Monte Carlo approach to determine the regional error distributions. The true variation of the kinetic parameters could then be revealed by correcting the regional ML estimate histograms with the estimated error distributions. The method was tested with simulated data. In simulations both the average and the deviation of the kinetic parameters were determined from the error-corrected histograms with good numerical accuracy for the selected region of interest.