weibulltools (version 0.5.4)

delta_method: Delta Method for Parametric Lifetime Distributions

Description

The delta method estimates the standard error for quantities that can be written as non-linear functions of ML estimators like failure probabilities or quantiles. I.e. the location-scale parameters and variance-covariance matrix of these need to be estimated by Maximum Likelihood.

Usage

delta_method(p, loc_sc_params, loc_sc_varcov, distribution = c("weibull",
  "lognormal", "loglogistic"), direction = c("y", "x"))

Arguments

p

a numeric value of a probability or a quantile. If the standard error of probability is of interest a specific quantile needs to be supplied and vice versa.

loc_sc_params

a (named) numeric vector of estimated (by Maximum Likelihood) location and scale parameters for a specified distribution. The order of elements is important. First entry needs to be the location parameter \(\mu\) and the second element needs to be the scale parameter \(\sigma\).

loc_sc_varcov

a (named) numeric matrix of estimated (by Maximum Likelihood) location and scale variances and covariances for a specified distribution. The order of elements is important. First entry of the diagonal needs to be the variance of the location parameter Var(\(\mu\)) and the second element of the diagonal needs to be the variance of the scale parameter Var(\(\sigma\)).

distribution

supposed distribution of the random variable. The value can be "weibull", "lognormal" or "loglogistic". Other distributions have not been implemented yet.

direction

a character string specifying the direction of the computed standard errors. Must be either "y" (failure probability) or "x" (quantile). If p is a quantile then direction needs to be "y" and vice versa.

Value

A numeric value with estimated standard error of failure probability or quantiles.

Examples

# NOT RUN {
obs   <- seq(10000, 100000, 10000)
state <- c(0, 1, 1, 0, 0, 0, 1, 0, 1, 0)

mle <- ml_estimation(x = obs, event = state,
                     distribution = "weibull", conf_level = 0.95)
delta_prob <- sapply(obs, delta_method,
                          loc_sc_params = mle$loc_sc_coefficients,
                          loc_sc_varcov = mle$loc_sc_vcov,
                          distribution = "weibull",
                          direction = "y")
# }