Add Confidence Region(s) for Quantiles and Probabilities

Source: R/plot_functions.R

This function is used to add estimated confidence region(s) to an existing probability plot which also includes the estimated regression line.

# S3 method for default
plot_conf(
  p_obj,
  x,
  y,
  distribution = c("weibull", "lognormal", "loglogistic", "sev", "normal", "logistic",
    "weibull3", "lognormal3", "loglogistic3", "exponential", "exponential2"),
  direction = c("y", "x"),
  title_trace = "Confidence Limit",
  ...
)

Arguments

p_obj

A plot object returned by plot_mod.

x

A list containing the x-coordinates of the confidence region(s). The list can be of length 1 or 2. For more information see Details.

y

A list containing the y-coordinates of the Confidence Region(s). The list can be of length 1 or 2. For more information see Details.

distribution

Supposed distribution of the random variable.

direction

A character string specifying the direction of the plotted interval(s). "y" for failure probabilities or "x" for quantiles.

title_trace

A character string which is assigned to the legend trace.

...

Further arguments passed to or from other methods. Currently not used.

Value

A plot object containing the probability plot with plotting positions, the estimated regression line and the estimated confidence region(s).

Details

It is important that the length of the vectors provided as lists in x and y match with the length of the vectors x and y in the function plot_mod. For this reason the following procedure is recommended:

  • Calculate confidence intervals with the function confint_betabinom or confint_fisher and store it in a data.frame. For instance call it df.

  • Inside plot_mod use the output df$x for x and df$prob for y of the function(s) named before.

  • In Examples the described approach is shown with code.

References

Meeker, William Q; Escobar, Luis A., Statistical methods for reliability data, New York: Wiley series in probability and statistics, 1998

See also

plot_conf

Examples

# Vectors:
cycles <- alloy$cycles
status <- alloy$status

prob_tbl <- estimate_cdf(x = cycles, status = status, method = "johnson")

# Example 1 - Probability Plot, Regression Line and Confidence Bounds for Three-Parameter-Weibull:
rr <- rank_regression(
  x = prob_tbl$x,
  y = prob_tbl$prob,
  status = prob_tbl$status,
  distribution = "weibull3"
)

conf_betabin <- confint_betabinom(
  x = prob_tbl$x,
  status = prob_tbl$status,
  dist_params = rr$coefficients,
  distribution = "weibull3"
)

plot_weibull <- plot_prob(
  x = prob_tbl$x,
  y = prob_tbl$prob,
  status = prob_tbl$status,
  id = prob_tbl$id,
  distribution = "weibull"
)

plot_reg_weibull <- plot_mod(
  p_obj = plot_weibull,
  x = conf_betabin$x,
  y = conf_betabin$prob,
  dist_params = rr$coefficients,
  distribution = "weibull3"
)

plot_conf_beta <- plot_conf(
  p_obj = plot_reg_weibull,
  x = list(conf_betabin$x),
  y = list(conf_betabin$lower_bound, conf_betabin$upper_bound),
  direction = "y",
  distribution = "weibull3"
)

# Example 2 - Probability Plot, Regression Line and Confidence Bounds for Three-Parameter-Lognormal:
rr_ln <- rank_regression(
  x = prob_tbl$x,
  y = prob_tbl$prob,
  status = prob_tbl$status,
  distribution = "lognormal3"
)

conf_betabin_ln <- confint_betabinom(
  x = prob_tbl$x,
  status = prob_tbl$status,
  dist_params = rr_ln$coefficients,
  distribution = "lognormal3"
)

plot_lognormal <- plot_prob(
  x = prob_tbl$x,
  y = prob_tbl$prob,
  status = prob_tbl$status,
  id = prob_tbl$id,
  distribution = "lognormal"
)

plot_reg_lognormal <- plot_mod(
  p_obj = plot_lognormal,
  x = conf_betabin_ln$x,
  y = conf_betabin_ln$prob,
  dist_params = rr_ln$coefficients,
  distribution = "lognormal3"
)

plot_conf_beta_ln <- plot_conf(
  p_obj = plot_reg_lognormal,
  x = list(conf_betabin_ln$x),
  y = list(conf_betabin_ln$lower_bound, conf_betabin_ln$upper_bound),
  direction = "y",
  distribution = "lognormal3"
)