discrete probability distribution functions

In the present study, the variable of the time interval between the peak flood and the peak of drought in thirteen basins of Karkheh basin was investigated. Since the time interval variable from the flood peak and the peak of previous drought has a discrete nature, eight well-known discrete probability distribution functions were tested for frequency analysis. In general, the results of the research showed that in most of the studied small and fourth-degree basins, with the increase in the intensity of annual droughts, the corresponding peak flood discharges will decrease up to SPI= -1, and after that, as the droughts continue to intensify (SPI <-1), the discharges will decrease. The flood peak will increase with an exponential and quadratic pattern. While in large basins and the third level, with the intensification of drought, the peak discharges of floods will also decrease. The results of the frequency analysis determined that the probability distribution functions of DPO and NBI have the most appropriate fits to the time interval variable between the peak of flood and the peak of drought. Based on the frequency analysis, it was found that the time interval between the peak of flood and the peak of drought is approximately 6 to 8 months. The defined variable reflects the interaction and impact of two extreme events of flood and drought in a basin.