Package DTDA.ni"

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

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 $Fw = wFd + (1-w)Fr$ 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

Return

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)
plot(res, ecdf = FALSE) # Plot without ecdf (Default)
abline(a = 0, b = 1, col = "green")  # The true cumulative distribution
# Calculating the reverse estimator:
plot(res)

res2 <- DTDAni(-x, -u - 0.75, 0.75)
abline(a = 0, b = 1, col = "green") 
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])

plot(res)
abline(a = 0, b = 1, col = "green") 
lines(-res2$x, 1 - res2$cumprob, type = "s", col = "blue", lty = 2)
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

Author(s)

Maintainer: José Carlos Soage González (jsoage@uvigo.es)

Acknowledgements

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



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DTDA.ni documentation built on May 2, 2019, 3:50 a.m.