Historical Research Of Binomial Distribution And Its Application

It’s well known that in the theory and application of modern statistics, normal distribution is the most important probability distributions,which was found originated in the great German mathematician Gauss error distribution of research in astronomy observations.1809 Gauss published his famous celestial mechanics " Theoria motus corporum coelestium in sectionibus conicis solem ambientum", the book demonstrates the way to unexpected astronomical observations normally distributed errors, Afterwards, the scholars through the normal research eventually led to the establishment of modern statistics.However, in the earlier history of the probability,the binomial distribution is in dominant position probability theory and applied research in statistics.In the process of discovery to establish the probability theory, law of large numbers and the central limit theorem and Bayesian thinking generated, are all related to the binomial distribution, so the study of the history of the emergence and development of binomial distribution has great importance to learn the theory and application of modern probability and statistics.This paper consists of three parts.Part I:In 1654 French mathematician Pascal and Fermat’s communication on "problem of point",and in 1712 Arbuthnot tested on the sex ratio of the population.Pascal and Fermat together solved the "problem of point",marks the formal foundation of probability theory, and Arbuthnot’population sex ratio statistical test can be seen as the source of the modem theory of statistical hypothesis testing.Part II:In 1713,Swiss mathematician Bernoulli established the general form of the binomial distribution, discovery of the law of large numbers and in 1733 the French mathematician Moivre found the central limit theorem. Bernoulli’s work appears in its posthumous publication in 1713 of "Ars conjectandi", Moivre central limit theorem, which appeared Binomial Approximation published in 1738 and 1756, "Doctrine of chance "the second and third edition, the two men’s work constitutes an important cornerstone of the modern theory of probability and statistics.Part III:After the generation of binomial distribution,there are several scholars who use binomial distribution and make contributions to the theory and application of statistical theory, including the founder of the British scholar Bayesian Bayesian theory and the French mathematician Laplace as well as the father of social statistics Belgian scholar Kettler and make significant contributions to make a breakthrough in the field of genetics British scholar Galton.Because of the relatively smaller domestic research and its application of the history of "binomial distribution", so I hope to do some efforts in this area, so that people can have a better understanding of the binomial distribution, by drawing on its methods and ideas for further development assistance.In this paper,I use the literature study method.According to the research purpose, I try to get the development of the binomial distribution through literature survey data,collect relevant facts, describes the different stages of their development, organize, analyze the contribution of different periods Contact, and the final presentation of the binomial distribution from generation to mature development context.