Example of six DBEM input parameters with their corresponding uncertainties used in reverse modeling plotted in histograms (y-axis is density) as probability-density functions (PDFs) for the first event (January 8, 1997) from the analyzed CME list. The given uncertainties (99.7% confidence intervals or 3σ) are given above each plot (lower uncertainty < input value < upper uncertainty). The solid red line indicates the calculated normal distribution. Since the CME time, the angular half-width, and longitude of CME source position are set without the uncertainties, they are shown in the histograms as just a vertical line. In the reverse-modeling scheme, we allow all γ values with equal probability (no weight is applied); thus, the γ has continuous uniform distribution.