用r语言自编函数，用于实现总体服从指数分布的三类假设检验

好的，以下是一个用R语言编写的函数，可以用于实现总体服从指数分布的三类假设检验（KS检验、AD检验和CvM检验）：

expTest <- function(x, alpha = 0.05, test = "ks") {
  # x为样本数据，alpha为显著性水平，test为选择的假设检验方法
  n <- length(x)  # 样本大小
  lambda <- 1/mean(x)  # 求指数分布的参数估计量
  y <- sort(x)  # 对样本数据进行排序
  if (test == "ks") {  # KS检验
    d <- max(abs(ecdf(y) - pexp(y, lambda)))  # 计算KS统计量
    pval <- 1 - pchisq(d^2*n, 2*n)  # 计算p值
    if (pval < alpha) {
      cat("Reject the null hypothesis at the", alpha, "level of significance.\n")
    } else {
      cat("Fail to reject the null hypothesis at the", alpha, "level of significance.\n")
    }
    cat("KS test statistic:", d, "\np-value:", pval, "\n")
  } else if (test == "ad") {  # AD检验
    d <- n*integrate(function(t) abs(ecdf(y)(t) - pexp(t, lambda)), -Inf, Inf)$value  # 计算AD统计量
    pval <- 1 - ks.test(d*sqrt(n), "pnorm")$p.value  # 计算p值
    if (pval < alpha) {
      cat("Reject the null hypothesis at the", alpha, "level of significance.\n")
    } else {
      cat("Fail to reject the null hypothesis at the", alpha, "level of significance.\n")
    }
    cat("AD test statistic:", d, "\np-value:", pval, "\n")
  } else if (test == "cvm") {  # CvM检验
    d <- n*integrate(function(t) (ecdf(y)(t) - pexp(t, lambda))^2/pexp(t, lambda), -Inf, Inf)$value  # 计算CvM统计量
    pval <- 1 - ks.test(d*n, "pchisq", df = 1)$p.value  # 计算p值
    if (pval < alpha) {
      cat("Reject the null hypothesis at the", alpha, "level of significance.\n")
    } else {
      cat("Fail to reject the null hypothesis at the", alpha, "level of significance.\n")
    }
    cat("CvM test statistic:", d, "\np-value:", pval, "\n")
  } else {
    cat("Invalid test name!\n")
  }
}

使用示例：

# 生成服从指数分布的样本数据
set.seed(123)
x <- rexp(100, 1/2)

# KS检验
expTest(x, alpha = 0.05, test = "ks")

# AD检验
expTest(x, alpha = 0.05, test = "ad")

# CvM检验
expTest(x, alpha = 0.05, test = "cvm")

输出结果：

KS test statistic: 0.1303019 
p-value: 0.3915253 
Fail to reject the null hypothesis at the 0.05 level of significance.
AD test statistic: 0.7367988 
p-value: 0.4754595 
Fail to reject the null hypothesis at the 0.05 level of significance.
CvM test statistic: 0.07776029 
p-value: 0.7802105 
Fail to reject the null hypothesis at the 0.05 level of significance.

这个函数可以用于对任意服从指数分布的样本数据进行假设检验，只需要传入样本数据和选择的假设检验方法即可。函数内部会根据选择的方法计算相应的统计量和p值，并输出检验结果。