| Title: | Doubly Truncated Data Analysis, Non Iterative |
| Version: | 1.0.1 |
| Maintainer: | José Carlos Soage González <jsoage@uvigo.es> |
| Description: | Non-iterative estimator for the cumulative distribution of a doubly truncated variable. de Uña-Álvarez J. (2018) <doi:10.1007/978-3-319-73848-2_37>. |
| Depends: | R (≥ 3.3.0) |
| License: | GPL-2 |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.1.2 |
| Suggests: | knitr, rmarkdown |
| VignetteBuilder: | knitr |
| URL: | https://github.com/sidoruvigo/DTDA.ni |
| NeedsCompilation: | no |
| Author: | Jacobo de Uña Álvarez [aut], José Carlos Soage González [cre] |
| Packaged: | 2022-04-12 08:12:26 UTC; User |
| Repository: | CRAN |
| Date/Publication: | 2022-04-12 08:32:29 UTC |
Package ‘DTDA.ni’
Description
Non-iterative estimator for the cumulative distribution of a doubly truncated variable, see de Uña-Álvarez (2018). Restricted to interval sampling.
Details
Documentation for package ‘DTDA.ni’ version 1.0
Package: DTDA.ni
Version: 1.0
Maintainer: José Carlos Soage González jsoage@uvigo.es
License: GPL-2
Value
DTDAni: Implements a non-iterative estimator for the cumulative distribution of a doubly truncated variable
plot.DTDAni: S3 method to plot a DTDAni object by using the generic plot function.
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.
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, pp. 387-400.
See Also
Useful links:
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 (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).
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)
plot.DTDAni
Description
S3 method to plot a DTDAni object by using the generic plot function.
Usage
## S3 method for class 'DTDAni'
plot(x, ecdf = FALSE, ...)
Arguments
x |
DTDAni object. |
ecdf |
Whether to display the ordinary empirical cumulative distribution function or not. Default = FALSE. |
... |
Aditional parameters. |
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, pp. 387-400.
Examples
## Not run:
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
res <- DTDAni(x, u , tau)
plot(res)
plot(res, ecdf = TRUE)
## End(Not run)