Convert All Moments Up to Order K Across Origins

Transforms a vector of raw moments about origin a to moments about target origin k using the generalized binomial transformation (Theorem 1, Mahmud 2025).

Usage

conv_moment_all(x, a, k)

Arguments

x

Numeric vector of raw moments about origin a (orders 1, 2, ..., K).

a

Initial origin (numeric).

k

Target origin (numeric).

Value

Numeric vector of moments about k (orders 1..K).

Examples

# Raw moments about a=2: mu'_1=-1, mu'_2=7, mu'_3=39
x <- c(-1, 7, 39)
conv_moment_all(x, a = 2, k = 5)  # -> c(-4, 22, -78)
#> [1]  -4  22 -78