Statistical estimations for probability distributions having tails of special shape, such as a double-mode distri-bution as well as the so-called heavy-tailed or fat-tailed distribution, are quantitatively discussed through virtual experiments using computer simulations. In this paper, a probability distribution describing the damage degree of concrete liners of tunnels in cold region is examined as an example of the double-mode probability distribution. First, virtual data sets of observations are generated by the use of quasi-random numbers for a Pareto distribution as a typical example of the fat-tailed distribution, whereas the actual data set obtained for the damage degree of concrete liners is used for generating virtual data set for the double-mode distribution. Next, statistical estimations are executed by the use of probability papers to identify the probability distribution showing the “best” fitting among supposed plural candidates for probability distributions. Finally, the accuracy of the estimation is quantified by applying the coefficient of determination. The results show that the accuracy of the estimation in the tail region is scarcely improved even if the number of data is increased.
