xintercept {tbea}

xintercept: Estimate the x-intercept of an empirical cdf

Description

xintercept: Estimate the x-intercept of an empirical cdf

Usage

xintercept(x, method, alpha = 0.05, p = c(0.025, 0.975), R = 1000, robust)

Arguments

x

A vector of type numeric with time data points.

method

Either "Draper-Smith" or "Bootstrap". The function will fail otherwise.

alpha

A vector of length one and type numeric with the nominal alpha value for the Draper-Smith method, defaults to 0.05.

p

A vector of length two and type numeric with the two-tail probability values for the CI. Defaults to 0.025 and 0.975.

R

The number of iterations to be used in the Bootstrap method.

robust

Logical value indicating whether to use robust regression using 'Rfit::rfit' ('robust = TRUE') or ordinary least squares 'lm' ('robust = FALSE').

Details

This function will take a vector of time points, calculate the empirical cumulative density function, and regress its values in order to infer the x-intercept and its confidence interval. For plotting purposes, it will also return the x-y empirical cumulative density values.

Value

A named list with three elements: 'param', the value of x_hat; 'ci', the lower and upper values of the confidence interval on x; 'ecdfxy', the x and y points for the empirical cumulative density curve.

Author(s)

Gustavo A. Ballen.

Examples

data(andes)
ages <- andes$ages
ages <- ages[complete.cases(ages)] # remove NAs
ages <- ages[which(ages < 10)] # remove outliers


# Draper-Smith, OLS
draperSmithNormalX0 <- xintercept(x = ages, method = "Draper-Smith", alpha = 0.05, robust = FALSE)
# Draper-Smith, Robust fit
draperSmithRobustX0 <- xintercept(x = ages, method = "Draper-Smith", alpha = 0.05, robust = TRUE)
# Bootstrap, OLS
bootstrapNormalX0 <- xintercept(x = ages, method = "Bootstrap", p = c(0.025, 0.975), robust = FALSE)
# Bootstrap, Robust fit
bootstrapRobustX0 <- xintercept(x = ages, method = "Bootstrap", p = c(0.025, 0.975), robust = TRUE)
# plot the estimations
hist(ages, probability = TRUE, col = rgb(red = 0, green = 0, blue = 1, alpha = 0.3),
     xlim = c(0, 10), main = "CDF-based on confidence intervals", xlab = "Age (Ma)")
# plot the lines for the estimator of Draper and Smith using lm
arrows(x0 = draperSmithNormalX0$ci["upper"], y0 = 0.025, x1 = draperSmithNormalX0$ci["lower"],
       y1 = 0.025, code = 3, angle = 90, length = 0.1, lwd = 3, col = "darkblue")
# plot the lines for the estimator of Draper and Smith using rfit
arrows(x0 = draperSmithRobustX0$ci["upper"], y0 = 0.05, x1 = draperSmithRobustX0$ci["lower"],
       y1 = 0.05, code = 3, angle = 90, length = 0.1, lwd = 3, col = "darkgreen")
# plot the lines for the estimator based on bootstrap
arrows(x0 = bootstrapRobustX0$ci["upper"], y0 = 0.075, x1 = bootstrapRobustX0$ci["lower"],
       y1 = 0.075, code = 3, angle = 90, length = 0.1, lwd = 3, col = "darkred")
# plot a legend
legend(x = "topright", legend = c("Draper and Smith with lm", "Draper and Smith with rfit",
                                  "Bootstrap on x0"),
       col = c("darkblue", "darkgreen", "darkred"),  lty = 1, lwd = 3)