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Compute w₁ Distribution on Grid

Source: R/08_weights_w1.R
w1_grid.Rd

Computes CDF, PDF, and survival function on a grid of x values. Useful for visualization and comparison across different priors.

Usage

w1_grid(a, b, x_grid = seq(0.01, 0.99, length.out = 100))

Arguments

a

Numeric; shape parameter of the Gamma prior on α.

b

Numeric; rate parameter of the Gamma prior on α.

x_grid

Numeric vector; grid of x values in (0, 1). Default is seq(0.01, 0.99, length.out = 100).

Value

A data frame with columns:

x

Grid points

cdf

CDF values F(x)

pdf

Density values p(x)

survival

Survival function S(x) = 1 - F(x)

Examples

# Compute on default grid
df <- w1_grid(a = 2, b = 1)

# Plot all three functions
par(mfrow = c(1, 3))
plot(df$x, df$cdf, type = "l", main = "CDF", xlab = "x", ylab = "F(x)")
plot(df$x, df$pdf, type = "l", main = "PDF", xlab = "x", ylab = "p(x)")
plot(df$x, df$survival, type = "l", main = "Survival", xlab = "x", ylab = "S(x)")