In examining natural hazards, such as hail, statistical analyzes can play a significant role. Due to the great importance of economic and side losses of hail in the northern part of Zagros with maximum frequency and damage, the necessity of studying its temporal and spatial location is felt very distinctly. Therefore, in order to estimate and estimate the probability of occurrence of this phenomenon, 10 hail data data of 10 synoptic stations of the region were used during the statistical period of 2014- 1992. In choosing the best method for calculating the distribution of precipitation probabilities, different types of probability distributions of discrete random variables were tested by means of both Kolmogorov and Anderson-Darling testsThe results showed that the good Poisson distribution test had a good fit for hail occurrence at a high level of 90.99%. Baneh station with the maximum frequency of hail precipitation has the lowest probability (0.023%) and Pearnshahr station has the most probable days without hail (0.39%). Therefore, the probability of occurrence of hail in Baneh has a higher percentage. In the next round, the negative binomial model satisfies the observations of this type of precipitation well. The calculation of probabilistic distributions by these two methods showed that the probability of occurrence of hail with the frequency of 1 to 6 times and more in the region and the highest probability is related to the frequency of 3 occurrences of 0.20%. At a frequency of 1 to 6 times, the probability of occurrence of this phenomenon is 5 times more than the probability that it will not occur, which indicates the region's high vulnerability to this type of climate risk.

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