Package DTDA.ni
Doubly truncated data analysis, non iterative
Description [package]
This package implements a non-iterative estimator for the cumulative distribution of a doubly truncated variable, see de Uña-Álvarez (2018). The package is restricted to interval sampling.
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, pp. 387-400.
DTDAni(x, u , tau)
Description [function DTDAni]
This function calculates the non-iterative estimator for the cumulative distribution of a doubly truncated variable proposed by de Uña-Álvarez (2018). The package works for interval sampling.
Details [function DTDAni]
The function DTDAni is adapted to the presence of ties. It can be used to compute the direct (Fd) and the reverse (Fr) estimators; see the example below. Both curves are valid estimators for the cumulative distribution (F) of the doubly truncated variable. Weighted estimators Fw = w * Fd + (1 − w) * Fr with 0 < w < 1 are valid too, the choice w = 1/2 being recommended in practice (de Uña-Álvarez, 2018).
Usage
In order to use this package, install it and load the library with:
library(DTDA.ni)
Parameters
- 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.
Return
- 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.
Usage
# Loading the package:
library(DTDA.ni)
# 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 wit DTDAni function
res <- DTDAni(x, u, tau)
#> Call:
#> DTDAni(x = x, u = u, tau = tau)
plot(res, ecdf = T) # Plot with ecdf = T (default = FALSE)
# Calculating the reverse estimator:
plot(res)
res2 <- DTDAni(-x, -u - 0.75, 0.75)
#> Call:
#> DTDAni(x = -x, u = -u - 0.75, tau = 0.75)
lines(-res2$x, 1 - res2$cumprob, type = "s", col = "blue", lty = 2)
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).
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