We study the effects of correlations on cumulants and their ratios of net-proton multiplicity distributions which have been measured for central (0%–5%) Au + Au collisions at the Relativistic Heavy Ion Collider  (RHIC). This effect has been studied by assuming individual proton and antiproton distributions as a Poisson or negative binomial distribution (NBD). In spite of significantly correlated production due to baryon number, electric charge conservation, and kinematical correlations of protons and antiprotons, the measured cumulants of the net-proton distribution follow the independent-production model. In the present work we demonstrate how the introduction of the correlations will affect the cumulants and their ratios for the difference distributions. We have also demonstrated this study using the proton and antiproton distributions obtained from the HIJING event generator.