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.

Precise maximum temperature probability distribution information is indeed of accurately significance for numerous temperature uses. The purpose of this research to assess the appropriateness of these functions likelihood for evaluating the temperature models at different sites in southern part of Pakistan. The Kumaraswamy distribution function is used initially to approximation the models of maximum temperature. Compare the presentation of the Kumaraswamy distribution with twelve commonly used the probability functions. The consequences obtained show that the more effective functions are not similar across all sites. The maximum temperature features, quality and quantity of the noted temperature observation can be regarded as a factors that affect the presentation of the function. Similarly, the skewness of the noted maximum temperature observations may affect the precision of Kumaraswamy distribution. For the Hyderabad, Lahore and Sialkot sites, the Kumaraswamy distribution obtainable the topmost presentation, however for the Karachi, Multan stations, the generalized extreme value (GEV) distributions provided the best fit, respectively. According to the calculations, the Kumaraswamy distribution usually be regarded as a valid distribution because it runs 3 best fit sites and ranks 2 to 3 among the remaining sites. Though, the tight presentation of the Kumaraswamy and GEV and the flexibility of the Weibull distribution which has been usually verified, more evaluations of the presentation of the Kumaraswamy distribution are needed.