depthDistribution: The distributions of the sign depths

In melaniehorn/GSignTest: Robust Tests for Regression-Parameters via Sign Depth

Description

Density, distribution function and quantile function for the distribution of the K-sign depth.

Usage

qdepth(p, N, K = 3, transform = FALSE)

pdepth(q, N, K = 3, transform = FALSE)

ddepth(x, N, K = 3, transform = FALSE)

Arguments

p	[numeric] vector of probabilities.
N	[integer(1)] number of data points.
K	[integer(1)] parameter of the sign depth. Currently only K = 2, 3, 4, 5 is supported. Default is K = 3.
transform	[logical(1)] Shall the values be transformed so that the distribution converges for large N?
x, q	[numeric] vector of quantiles.

Details

For N = K, …, 25 the depth distributions are calculated exactly. For N = 26, …, 100 the distributions were simulated. For N > 100 the values of N = 100 are token.

If y is a non-transformed value of one of these functions, N * (y - 0.5^(K-1)) is the transformed value. For further understanding of the transformed statistic, see references.

Value

ddepth gives the density, pdepth the distribution function and qdepth the quantile function.

References

Kustosz C., Leucht A. and Mueller Ch. H. (2016). Tests based on Simplicial depth for AR(1) models with explosion. Journal of Time Series Analysis. In press.

Examples

qdepth(0.05, 20)
ddepth(0.25, 100)
pdepth(0.25, 50)

melaniehorn/GSignTest documentation built on July 11, 2021, 1:18 a.m.