Amount calculation of frequency:
The relative frequency m/n of random events appearing m times in n tests. In general physical science, frequency refers to the number of vibrations per second, which can be random or deterministic. Under certain conditions, observing or testing the studied object is called a test every time the condition group is realized. The result is called an event. In experiments, events that may or may not occur are called random events.
The probability p(A) of random event A is a measure of the probability of this event. Its value is between 0 and 1. Under certain conditions, if event A is impossible, then p (a) = 0; If event A must occur, then p(A)= 1. With the increase of test times n, the probability of frequency approaching probability is greater, that is, δ in the formula is an arbitrary decimal value.
Hydrological phenomenon is a complex natural phenomenon, and its occurrence probability cannot be known, which can only be inferred by counting the occurrence frequency in the measured hydrological data. Due to the limitation of data, there will always be some errors.
The random variable X, which describes hydrological stochastic phenomena, generally belongs to continuous type. Therefore, the probability that x is equal to any number x is p{X=x}. Cumulative percentage curve FX (x) ~ x is used to describe the statistical characteristics of hydrological variables in hydrological calculation. If the probability of annual flood peak discharge at Yichang Station of the Yangtze River is greater than or equal to 80000m3/s, p{X≥80000}=FX(80000).
In hydrological calculation, the frequency density function FX(x) of hydrological variables is generally estimated by statistical analysis based on measured data, and then the cumulative percentage function fX(x) of hydrological variables can be obtained by integrating fX(x) (see figure). In hydrological calculation, cumulative percentage curve FX(x) is customarily called frequency curve, and FX (x) ~ x curve is called frequency density distribution curve.