如何在fitdistrplus中用尺度和位置参数拟合t分布

library(fitdistrplus)

# 生成一组样本数据
data <- rt(n = 100, df = 10)

# 定义t分布的概率密度函数
dt <- function(x, df, mean, sd) {
  (gamma((df + 1) / 2) / (sqrt(df * pi) * gamma(df / 2))) * 
    (1 + ((x - mean) ^ 2 / (df * sd ^ 2))) ^ (-(df + 1) / 2)
}

# 定义t分布的对数似然函数
logLik_t <- function(params) {
  df <- params[1]
  mean <- params[2]
  sd <- params[3]
  
  sum(log(dt(data, df, mean, sd)))
}

# 初始参数值
start_params <- c(df = 10, mean = mean(data), sd = sd(data))

# 拟合t分布
fit <- fitdist(data, "t", start = start_params, method = "BFGS", lower = c(0, -Inf, 0))

# 输出拟合结果
summary(fit)