Compare the goodness of fit probability distributions trend with increasing sample size Case Study: 119 annuals rainfall of Mashhad

Introduction: Annual precipitation is a major meteorological variable. The occurrence of this variable follows a particular law. This rule of law is precisely defined that All rain events occur during the climatic period. But This is impossible. Usually a small sample of this variable is available. Matching several competing laws to data fit and the best with statistical tests of choice, which is an approximate successor to real law. Increasing the sample size increases the accuracy of the test and closer to the actual law. This is more prominent in arid and semi-arid regions such as Iran. The acceptable statistical period for arid and semi-arid regions (such as Mashhad) is at least 70 years old. If this length is more than 100 years old then statistical analysis of the data can be assured relative. Also, if the return period is a phenomenon more than one-fifth of the length of the data, then the estimation of this phenomenon is not accurate. Statistical analysis of precipitation is one of the important requirements of meteorology, climatology, hydrology, drought forecasting and so on. The Sample size is important in results of the statistical analysis of rainfall. The duration of rainfall stations in Iran are often short and the maximum durations of a few stations are 61 years. This study analyzes the frequency of data after collecting and repairing the long-term data of Mashhad. Comparison of the effect of sample size variation on the results of statistical analysis is necessary in order to evaluate the trust of existing data.