Qalpha: Q^{alpha}

In robcp: Robust Change-Point Tests

Q^{α}

Description

Estimates Q-alpha using the first k elements of a time series.

Usage

Qalpha(x, alpha = 0.8)

Arguments

x	numeric vector.
alpha	quantile. Numeric value in (0, 1]

Details

\hat{Q}^{α}_{1:k} = U_{1:k}^{-1}(α) = \inf\{x | α ≤q U_{1:k}(x)\},

where U_{1:k} is the empirical distribtion function of |x_i - x_j|, \, 1 ≤q i < j ≤q k.

Value

Numeric vector of Q^{α}-s estimated using x[1], ..., x[k], k = 1, ..., n, n being the length of x.

Examples

x <- rnorm(10)
Qalpha(x, 0.5)

robcp documentation built on Sept. 16, 2022, 5:05 p.m.