In the project of irrigation and addition structure of hydraulic, it is important to assess the specific probability of extreme rainfall. The novelty of this study is the use of KS, Chi-square, root mean square error (RMSE), and peak weight root means square error (PWRMSE) to evaluate the fit theoretical and Empirical distributions. Thirty-seven years of meteorological data from 1980 to 2017, the frequency analysis of the annual maximum rainfall in 10 regions of Pakistan was conducted. Used eight formulas to predict the annual return period of the maximum hourly precipitation every year. Five different probability distribution functions (PDF) are used to predict the probability distribution of the annual maximum hourly rainfall. Use the chi-square test and Kolmogorov- Smirnov to assess the goodness of fit. It shows that the log-logistics distribution is the overall best-fitting PDF of the annual maximum hourly rainfall in most areas of Pakistan. Besides, the peak weight relative mean square error and root mean square error goodness of fit test indicators both indicate that most suitable distribution of the probability function of all stations analysis is similar. The value of root means square error (RMSE) is almost always smaller than peak weight root means square error (PWRMSE). This is due to the higher weighting of value above the average value in the PWRMSE goodness of fit index, while for the RMSE goodness of fit index individual value has an equal weight.

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