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## ----setup, echo=FALSE, message=FALSE-----------------------------------------
knitr::opts_chunk$set(
collapse = TRUE,
screenshot.force = FALSE,
comment = "#>"
)
library(weibulltools)
## ----dataset_shock, message = FALSE-------------------------------------------
# Data:
shock_tbl <- reliability_data(data = shock, x = distance, status = status)
shock_tbl
## ---- Parameter estimation procedures-----------------------------------------
# Estimation of failure probabilities:
shock_cdf <- estimate_cdf(shock_tbl, methods = "johnson")
# Rank Regression:
rr_weibull <- rank_regression(shock_cdf, distribution = "weibull")
# Maximum Likelihood Estimation:
ml_weibull <- ml_estimation(shock_tbl, distribution = "weibull")
## ---- Confidence intervals for model parameters-------------------------------
# Confidence intervals based on Rank Regression:
rr_weibull$confint
# Confidence intervals based on Maximum Likelihood Estimation:
ml_weibull$confint
## ---- Confidence level--------------------------------------------------------
# Confidence intervals based on another confidence level:
ml_weibull_99 <- ml_estimation(shock_tbl, distribution = "weibull", conf_level = 0.99)
ml_weibull_99$confint
## ---- Confidence intervals for probabilities----------------------------------
# Beta-Binomial confidence bounds:
conf_bb <- confint_betabinom(
x = rr_weibull,
b_lives = c(0.01, 0.1, 0.5),
bounds = "two_sided",
conf_level = 0.95,
direction = "y"
)
conf_bb
# Fisher's normal approximation confidence intervals:
conf_fisher <- confint_fisher(x = ml_weibull)
conf_fisher
## ---- Preparation for visualization-------------------------------------------
# Probability plot
weibull_grid <- plot_prob(
shock_cdf,
distribution = "weibull",
title_main = "Weibull Probability Plot",
title_x = "Mileage in km",
title_y = "Probability of Failure in %",
title_trace = "Defectives",
plot_method = "ggplot2"
)
## ---- BBB on failure probabilities, fig.cap = "Figure 1: Beta-Binomial confidence bounds for failure probabilities.", message = FALSE----
# Beta-Binomial confidence intervals:
weibull_conf_bb <- plot_conf(
weibull_grid,
conf_bb,
title_trace_mod = "Rank Regression",
title_trace_conf = "Beta-Binomial Bounds"
)
weibull_conf_bb
## ---- FI on failure probabilities, fig.cap = "Figure 2: Fisher's normal approximation confidence intervals for failure probabilities.", message = FALSE----
# Fisher's normal approximation confidence intervals:
weibull_conf_fisher <- plot_conf(
weibull_grid,
conf_fisher,
title_trace_mod = "Maximum Likelihood",
title_trace_conf = "Fisher's Confidence Intervals"
)
weibull_conf_fisher
## ---- Confidence intervals for quantiles--------------------------------------
# Computation of confidence intervals for quantiles:
## Beta-Binomial confidence intervals:
conf_bb_x <- confint_betabinom(
x = rr_weibull,
bounds = "upper",
conf_level = 0.95,
direction = "x"
)
conf_bb_x
## Fisher's normal approximation confidence intervals:
conf_fisher_x <- confint_fisher(x = ml_weibull, bounds = "lower", direction = "x")
conf_fisher_x
## ---- BBB on quantiles, fig.cap = "Figure 3: One-sided (upper) Beta-Binomial confidence bound for quantiles.", message = FALSE----
# Visualization:
## Beta-Binomial confidence intervals:
weibull_conf_bb_x <- plot_conf(
weibull_grid,
conf_bb_x,
title_trace_mod = "Rank Regression",
title_trace_conf = "Beta-Binomial Bounds"
)
weibull_conf_bb_x
## ---- FI on quantiles, fig.cap = "Figure 4: One-sided (lower) normal approximation confidence interval for quantiles.", message = FALSE----
## Fisher's normal approximation confidence intervals:
weibull_conf_fisher_x <- plot_conf(
weibull_grid,
conf_fisher_x,
title_trace_mod = "Maximum Likelihood",
title_trace_conf = "Fisher's Confidence Intervals"
)
weibull_conf_fisher_x
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