confint_betabinom {weibulltools} | R Documentation |
Beta Binomial Confidence Bounds for Quantiles and Probabilities
Description
This function computes the non-parametric beta binomial confidence bounds (BB) for quantiles and failure probabilities.
Usage
confint_betabinom(x, ...)
## S3 method for class 'wt_model'
confint_betabinom(
x,
b_lives = c(0.01, 0.1, 0.5),
bounds = c("two_sided", "lower", "upper"),
conf_level = 0.95,
direction = c("y", "x"),
...
)
Arguments
x |
A list with class |
... |
Further arguments passed to or from other methods. Currently not used. |
b_lives |
A numeric vector indicating the probabilities |
bounds |
A character string specifying the bound(s) to be computed. |
conf_level |
Confidence level of the interval. |
direction |
A character string specifying the direction of the confidence
interval. |
Details
The procedure is similar to the Median Ranks method but with the difference that instead of finding the probability for the j-th rank at the 50% level the probability (probabilities) has (have) to be found at the given confidence level.
Value
A tibble with class wt_confint
containing the following columns:
-
x
: An ordered sequence of the lifetime characteristic regarding the failed units, starting atmin(x)
and ending up atmax(x)
. Withb_lives = c(0.01, 0.1, 0.5)
the 1%, 10% and 50% quantiles are additionally included inx
, but only if the specified probabilities are in the range of the estimated probabilities. -
rank
: Interpolated ranks as a function of probabilities, computed with the converted approximation formula of Benard. -
prob
: An ordered sequence of probabilities with specifiedb_lives
included. -
lower_bound
: Provided, ifbounds
is one of"two_sided"
or"lower"
. Lower confidence limits with respect todirection
, i.e. limits for quantiles or probabilities. -
upper_bound
: Provided, ifbounds
is one of"two_sided"
or"upper"
. Upper confidence limits with respect todirection
, i.e. limits for quantiles or probabilities. -
cdf_estimation_method
: Method for the estimation of failure probabilities which was specified in estimate_cdf.
Further information is stored in the attributes of this tibble:
-
distribution
: Distribution which was specified in rank_regression. -
bounds
: Specified bound(s). -
direction
: Specified direction. -
model_estimation
: Input list with classwt_model
.
Examples
# Reliability data preparation:
## Data for two-parametric model:
data_2p <- reliability_data(
shock,
x = distance,
status = status
)
## Data for three-parametric model:
data_3p <- reliability_data(
alloy,
x = cycles,
status = status
)
# Probability estimation:
prob_tbl_2p <- estimate_cdf(
data_2p,
methods = "johnson"
)
prob_tbl_3p <- estimate_cdf(
data_3p,
methods = "johnson"
)
prob_tbl_mult <- estimate_cdf(
data_3p,
methods = c("johnson", "mr")
)
# Model estimation with rank_regression():
rr_2p <- rank_regression(
prob_tbl_2p,
distribution = "weibull"
)
rr_3p <- rank_regression(
prob_tbl_3p,
distribution = "lognormal3",
conf_level = 0.90
)
rr_lists <- rank_regression(
prob_tbl_mult,
distribution = "loglogistic3",
conf_level = 0.90
)
# Example 1 - Two-sided 95% confidence interval for probabilities ('y'):
conf_betabin_1 <- confint_betabinom(
x = rr_2p,
bounds = "two_sided",
conf_level = 0.95,
direction = "y"
)
# Example 2 - One-sided lower/upper 90% confidence interval for quantiles ('x'):
conf_betabin_2_1 <- confint_betabinom(
x = rr_2p,
bounds = "lower",
conf_level = 0.90,
direction = "x"
)
conf_betabin_2_2 <- confint_betabinom(
x = rr_2p,
bounds = "upper",
conf_level = 0.90,
direction = "x"
)
# Example 3 - Two-sided 90% confidence intervals for both directions using
# a three-parametric model:
conf_betabin_3_1 <- confint_betabinom(
x = rr_3p,
bounds = "two_sided",
conf_level = 0.90,
direction = "y"
)
conf_betabin_3_2 <- confint_betabinom(
x = rr_3p,
bounds = "two_sided",
conf_level = 0.90,
direction = "x"
)
# Example 4 - Confidence intervals if multiple methods in estimate_cdf, i.e.
# "johnson" and "mr", were specified:
conf_betabin_4 <- confint_betabinom(
x = rr_lists,
bounds = "two_sided",
conf_level = 0.99,
direction = "y"
)