In jeksterslabds/jeksterslabRmedsimple: Jekster's Lab Simple Mediation Model Utilities

knitr::opts_chunk$set(
  error = TRUE,
  collapse = TRUE,
  comment = "#>",
  out.width = "100%"
)

alpha <- beta <- 1.5
beta_mean <- alpha / (alpha + beta)
beta_variance <- (alpha * beta) / ((alpha + beta)^2 * (alpha + beta + 1))
beta_skewness <- (2 * (beta - alpha) * sqrt(alpha + beta + 1)) / ((alpha + beta + 2) * sqrt(alpha * beta))
beta_kurtosis <- (6 * ((alpha - beta)^2 * (alpha + beta + 1) - alpha * beta * (alpha + beta + 2))) / (alpha * beta * (alpha + beta + 2) * (alpha + beta + 3))

Moments <- c(
  "Mean",
  "Variance",
  "Skewness",
  "Excess Kurtosis"
)
Formula <- c(
  "$\\frac{\\alpha}{\\alpha + \\beta}$",
  "$\\frac{\\alpha \\beta}{\\left( \\alpha + \\beta \\right)^2 \\left( \\alpha + \\beta + 1 \\right)}$",
  "$\\frac{2 \\left( \\beta - \\alpha \\right) \\sqrt{\\alpha + \\beta + 1}}{\\left( \\alpha + \\beta + 2 \\right) \\sqrt{\\alpha \\beta}}$",
  "$\\frac{6 \\left[ \\left( \\alpha - \\beta \\right)^2 \\left( \\alpha + \\beta + 1 \\right) - \\alpha \\beta \\left( \\alpha + \\beta + 2 \\right) \\right]}{\\alpha \\beta \\left( \\alpha + \\beta + 2 \\right) \\left( \\alpha + \\beta + 3 \\right)}$"
)
Value <- c(
  beta_mean,
  beta_variance,
  beta_skewness,
  beta_kurtosis
)
x <- data.frame(
  Moments,
  Formula,
  Value
)

\begin{equation} X \sim Beta \left( \alpha = r alpha, \beta = r beta \right) \end{equation}

knitr::kable(
  x = x
)

x <- seq(from = 0, to = 1, length = 1000)
y <- dbeta(
  x = x,
  shape1 = alpha,
  shape2 = beta
)
plot(
  x = x,
  y = y,
  type = "l"
)

See https://en.wikipedia.org/wiki/Beta_distribution.

data(
  paramsbeta,
  package = "jeksterslabRmedsimple"
)
DT::datatable(
  paramsbeta
)

For more details see jeksterslabRmedsimple::paramsbeta.

jeksterslabds/jeksterslabRmedsimple documentation built on Oct. 16, 2020, 11:30 a.m.