DTDAni {DTDA.ni} | R Documentation |
Doubly Truncated Data Analysis, Non Iterative
Description
This function computes a non-iterative estimator for the cumulative distribution of a doubly truncated variable, see de Uña-Álvarez (2018). The function is restricted to interval sampling.
Usage
DTDAni(x, u, tau)
Arguments
x |
Numeric vector corresponding the variable of ultimate interest. |
u |
Numeric vector corresponding to the left truncation variable. |
tau |
Sampling interval width. The right truncation values will be internally calculated as v = u + tau. |
Details
The function DTDAni is adapted to the presence of ties.
It can be used to compute the direct and the reverse
estimators;
see the example below. Both curves are valid estimators for the cumulative
distribution (F) of the doubly truncated variable. Weighted estimators
with
are valid too, the choice
being
recommended in practice (de Uña-Álvarez, 2018).
Value
A list containing:
x |
The distinct values of the variable of interest. |
nx |
The absloute frequency of each x value. |
cumprob |
The estimated cumulative probability for each x value. |
P |
The auxiliary Pi used in the calculation of the estimator. |
L |
The auxiliary Li used in the calculation of the estimator. |
Acknowledgements
Jacobo de Uña-Álvarez was supported by Grant MTM2014-55966-P, Spanish Ministry of Economy and Competitiveness.
José Carlos Soage was supported by Red Tecnológica de Matemática Industrial (Red TMATI), Cons. de Cultura, Educación e OU, Xunta de Galicia (ED341D R2016/051) and by Grupos de Referencia Competitiva, Consolidación y Estructuración de Unidades de Investigación Competitivas del SUG, Cons. de Cultura, Educación e OU, Xunta de Galicia (GRC ED431C 2016/040).
Author(s)
de Uña-Álvarez, Jacobo.
Soage González, José Carlos.
Maintainer: José Carlos Soage González. jsoage@uvigo.es
References
de Uña-Álvarez J. (2018) A Non-iterative Estimator for Interval Sampling and Doubly Truncated Data. In: Gil E., Gil E., Gil J., Gil M. (eds) The Mathematics of the Uncertain. Studies in Systems, Decision and Control, vol 142. Springer, Cham
Examples
## Not run:
# Generating data which are doubly truncated:
N <- 250
x0 <- runif(N) # Original data
u0 <- runif(N, -0.25, 0.5) # Left-truncation times
tau <- 0.75 # Interval width
v0 <- u0 + tau
x <- x0[u0 <= x0 & x0 <= v0]
u <- u0[u0 <= x0 & x0 <= v0]
v <- v0[u0 <= x0 & x0 <= v0]
n <- length(x) # Final sample size after the interval sampling
# Create an object with DTDAni function
res <- DTDAni(x, u, tau)
plot(res)
abline(a = 0, b = 1, col = "green") #the true cumulative distribution
# Calculating the reverse estimator:
res2 <- DTDAni(-x, -u - tau, tau)
lines(-res2$x, 1 - res2$cumprob, type = "s", col = "blue", lty = 2)
# Weigthed estimator (recommended):
w <- 1/2
k <- length(res$x)
Fw <- w * res$cumprob + (1 - w) * (1 - res2$cumprob[k:1])
lines(res$x, Fw, type = "s", col = 2)
# Using res$P and res$L to compute the estimator:
k <- length(res$x)
F <- rep(1, k)
for (i in 2:k){
F[i] <- (F[i - 1] - res$P[i - 1]) / res$L[i - 1] + res$P[i - 1]
}
F0 <- F/max(F) # This is equal to res$cumprob
## End(Not run)