Statistical Inference And R Package Of Bernoulli Distribution

Bernoulli distribution and binomial distribution are one of the most widely used discrete distributions in mathematical statistics.Their application fields include industrial experiments,quality control,biomedical research,etc.In this paper,we systematically summarize the interval estimation and hypothesis testing problems in the statistical inference of Bernoulli distribution and binomial distribution,including the case of a single sample,the case of two samples and the case of multiple samples.We compared the coverage probability and the length of different confidence intervals,compared the test power and type I error probability of different test methods,and analyzed the advantages and disadvantages of different methods.There are many confidence interval methods for p and p₁-p₂,each has its advantages and disadvantages.In the case of a single sample or two samples,the confidence interval and test constructed by the Fiducial method has obvious advantages over other methods.The coverage and length of the MOVER interval forp₁-p₂ performed well.For two kinds of test problems with multiple samples,the mid p-value and PB algorithms perform well,and Monte Carlo method is better than the chi-square test.The purpose of this paper is to create a R package named“Bernoulli”about Bernoulli distribution and binomial distribution on the basis of summarizing and comparing the methods proposed by predecessors,We write the better interval estimation and hypothesis testing methods in the literature as functions and put them into the package.We can call the corresponding function to get the point estimate of the parameter,the confidence interval and the hypothesis test inference result.This paper also introduces the existing R packages and related functions about Bernoulli distribution,binomial distribution statistical inference problem.However,the existing functions are few and the methods are relatively single.The newly created R package realizes the confidence interval and hypothesis testing of parameters in different sample cases,which is more comprehensive and systematic than the existing R package method.We illustrate the correlation functions in the package with concrete examples.