Display omitted •A new versatile probability distribution function called “hyper-EMG” is presented.•Modeling of asymmetric MR-TOF mass spectra using the hyper-EMG is demonstrated.•Peak shape is precisely modeled over 5 orders of magnitude in abundance.•Hyper-EMG outperforms the common peak shape models in case of overlapping peaks.•Improved mass and abundance values are obtained for overlapping peaks in MR-TOF-MS. A new probability distribution function (PDF) called hyper-Exponentially Modified Gaussian (hyper-EMG) is introduced for the analysis of high-resolution spectra from multiple-reflection time-of-flight mass spectrometers. The hyper-EMG consists of a central Gaussian distribution modified by multiple exponential tails with different strengths at one or both sides. The basic statistical properties of the new PDF are given and the analysis of mass spectra containing separated and overlapping peaks is presented. The main requirement is to accurately determine the positions and areas of the individual mass peaks. From the distances of positions the mass values can be determined, from the areas the population of different ground and isomeric states can be obtained. The hyper-EMG has been applied to high-resolution time and mass spectra characterized by mass resolving powers of 140,000 and 520,000 obtained with Cs+133 and K+39 ions, respectively. From the measured mass distribution of K+39 ions, an overlapping distribution of two peaks with an area ratio of 1:10 and a mass difference of 2.6ppm (parts-per-million) is generated and analyzed. The results reveal significant advantages of the new PDF for the evaluation of overlapping distributions for accurate mass and area determinations compared with commonly used PDFs which are more than one order of magnitude less accurate. It is obvious that the hyper-EMG can be favorably applied also to other fields.