Hydrological statistics

honggarae 16/03/2023 425

There is a background

hydrological phenomenon in addition to periodic factors determined by the daily relationship, affected by a large number of random factors due to the influence of the deterministic factors constrained by the physical relationship. . Therefore, the probability statistical method has become an important means of analyzing hydrological phenomena and revealing its statistical laws. SCIENCE AND TECHNOLOGY. SCIENCE AND TECHNOLOGY OF WATER CONSERVANCY AND TECHNOLOGY. Through the engineering hydrological and hydrological analysis and calculation, hydrological statistics have great impact on the rationality of hydrological design data in the project, there is an important socio-economic significance.

Basic content

includes random variables, distribution functions, parameter estimation, assumption test, regression analysis, multivariable analysis, random process basic theory, hydrological time series analysis, and hydrological materials .

Research Ordinance

(1) is mainly to determine the distribution function of hydrological random variables, several statistical relationships of random variables or their joint distribution functions, and thus make inferrances.

(2) Understand the common line type commonly used in the water frequency curve, master the nature and calculation method of the P-Group III distribution curve and the experimental frequency curve;

(3) Understand the frequency curve Estimation method of parameters, to master a mission method, three-point method estimate parameters;

(4) Master the specific steps and methods of the hydrological frequency calculation of the method, especially the influence of the parameter on the frequency curve;

(5) Understand the basic concepts and methods of correlation analysis, especially the two variables straight line correlation, curve-related methods and specific steps.

Research path

Determines the distribution function of random variables, usually includes two aspects.

1 hypothesis test: that is, the method of selecting the distribution function is selected by the method of hypothesis. First select a hypothesis, then calculate the value of the relevant statistic for the selected assumption according to the sample data. This value is compared to the critical value of the corresponding table, thereby deciding to accept or reject the selected assumption. Statistics of commonly used inspection distribution functions: Kirmo Siro-Silov Statistics, Coho Statistics, Clem Von Miis Statistics, Watson Statistics and Andon To make statistics, etc. Assumption test, there may be two errors, and the aqueous literature is called the model uncertainty. The first mistake is that it is true, decided to refuse; the second error is that it is not true and decided to accept. The statistic adopted should be minimized in the probability of the second error in the probability of a given first error.

2 Parameter estimation: Select a certain parameter estimate, calculate the parameter value contained in the distribution function according to the sample data, referred to as the estimate of the parameter. Because it is generally not equal to the true value of the parameter, there is an error, called a sampling error, or is called the parameter uncertainty. The selected parameter estimation method should make the sampling error smaller and the calculation is simple. Commonly used parameter estimation methods have a torque method, a general likelihood, probability weighted torque method, a method for normalization. In the actual work of hydrological statistics, China uses a diagram suitable line method. On this basis, in the early 1970s, Chinese hydlicants put forward an objective and normal method for the Pieron-II type curve (see hydrological random variable), with other methods as good performance. This approach has been written into China's parameter estimation method in 1987. In the 1980s, American water literatists had new development in this field. The work of parameter estimation is often referred to as frequency analysis in hydroxation.

Model uncertainty and parameter uncertainty are related to the methods used, and on the other hand, on the other hand, it is related to the number of materials used. The more the general data is, the smaller the uncertainty; that the less the amount of information is, the greater the uncertainty. Since the number of hydrological materials is often limited, rarely more than a hundred years, in statistics belong to small samples. Therefore, it is necessary to strengthen the study of small sample hypothesis and parameter estimation theory. The hydrological statistics are currently mainly statistical, and it is difficult to consider the physical relationship of hydrological phenomena, and can develop hydrological statistics to a new stage by introducing the relevant content of the random differential equation.