NS: Normal Scores

In SNSchart: Sequential Normal Scores in Statistical Process Management

Description

Get conditional or unconditional normal score (NS) of observations (X) relative to previous observations (Y).

Usage

NS(
  X,
  Y = NULL,
  theta = NULL,
  Ftheta = NULL,
  scoring = "Z",
  Chi2corrector = "None",
  alignment = "unadjusted",
  constant = NULL,
  absolute = FALSE
)

Arguments

X	vector. New observations to obtain the N¡normal scores.
Y	vector. If Y is not defined (no previous observation available, NULL), NS is relative to X. Default NULL.
theta	scalar. Value corresponig with the Ftheta quantile.
Ftheta	scalar. Quantile of the data distribution. The values that take are between (0,1).
scoring	character string. If "Z" (normal scores) (default). If "Z-SQ" (normal scores squared).
Chi2corrector	character string. Only when scoring is Z-SQ. Select from "approx: Z^2*(m + 1 + 1.3)/(m+1). "exact": Z^2/mean(Z). "none": Z^2. If "approx" () (default). If "exact" (normal scores squared).
alignment	character string. Aligment of the data X and Y. Select from "unadjusted": nothing is sustracte from X and Y (default). "overallmean": overall mean is sustracted from X and Y. "overallmedian": overall median is sustracted from X and Y. "samplemean": mean from corresponding group (X and Y) is sustracted from its corresponing vector. "samplemedian": median from corresponding group (X and Y) is sustracted from its corresponing vector. "referencemean": mean from Y is subtracted from X and Y. "referencemedian": median from Y is subtracted from X and Y. "constantvalue": a constant value is subtracted from X and Y.
constant	scalar. Only used when the alignment is selected "constantvalue". Default NULL.
absolute	logical. If TRUE, the absolute aligned values are obtained. (Default FALSE)

Value

Multiple output. Select by output$

• R: vector. Ranks for the X observations. If ties occurs, average ranks are used.

• P: vector. Probability of the ranks for the X observations. Instead of Van Der Waerden normal scores where P = R/(n+1), P = (R-0.5)/n, where R stands for rank and P for the input evaluated in the inverse of a Standard Normal Distribution.

• Z: vector. Normal scores for the X observations. Z if scoring is "Z" and Z^2 if scoring is "Z-SQ".

Examples

Y <- c(10, 20, 30, 40, 50, 60, 70, 80, 90, 100)
X <- c(30, 35, 45)
theta <- 40
Ftheta <- 0.5
# EXAMPLE CONDITIONAL
NS(X = X, Y = Y, theta = theta, Ftheta = Ftheta)

# EXAMPLE UNCONDITIONAL
theta <- NULL
Ftheta <- NULL
NS(X = X, Y = Y, theta = theta, Ftheta = Ftheta)

SNSchart documentation built on April 7, 2021, 9:07 a.m.