Its origin can be traced back to the mathematicians Niels daniel bell and Edward W Brown in the19th century. 1895, when Bell and Brown studied the limit distribution of binomial distribution, they found that the limit distribution of binomial distribution was close to a normal distribution when the number of experiments was very large.
But they found that the average value of this normal distribution is not fixed, but varies with the number of experiments and the overall size. This phenomenon makes them realize that binomial distribution can not be simply regarded as a discrete random variable, but a continuous random variable.
Therefore, they put forward a new probability distribution, that is, hypergeometric distribution. This distribution describes the probability distribution of the ratio of the number of individuals of an attribute in the sample to the number of individuals of the attribute in the group when the number of individuals in the group and the number of individuals in the sample are known. This probability distribution is widely used in statistics, biology, medicine and other fields, especially when dealing with experimental data of finite population and infinite samples.
Hypergeometric distribution plays an important role in theory, which is closely related to binomial distribution, Poisson distribution and other probability distributions. At the same time, it also has a wide range of values in practical applications, such as industrial production quality control, financial risk management, medical clinical trials and so on.
Application of geometric distribution;
1. queuing theory: in queuing theory, people usually study random variables such as the number of customers waiting in line and service time, and the service time of service desk is a typical geometric distribution. Using geometric distribution, we can calculate the average waiting time and average queue length of customers, so as to better plan and serve the process.
2. Computer science: In computer science, geometric distribution is also widely used in simulation and modeling. For example, when simulating network traffic, geometric distribution can be used to describe the number of packets received or sent by each node in a unit time. Through this method, network performance can be evaluated and network design can be optimized.
3. Biology: There are also many problems in biology that can be described by geometric distribution. For example, in the study of biological population genetics, geometric distribution can be used to calculate the probability of gene frequency stability under natural selection. In addition, in the study of virus transmission, disease outbreaks and other issues, geometric distribution can also be used to describe the probability of infection and transmission.
4. Statistics: In statistics, geometric distribution is also widely used to infer sample data. For example, in the approximate calculation of binomial distribution, geometric distribution can be used to describe the estimation error of success probability in sample data. In addition, the application of geometric distribution often involves the calculation of confidence interval and confidence.