R/confidence_intervals.R
confint_fisher.Rd
This function computes normal-approximation confidence intervals for quantiles and failure probabilities.
A list with classes wt_model
and wt_ml_estimation
returned by
ml_estimation.
Further arguments passed to or from other methods. Currently not used.
A numeric vector indicating the probabilities \(p\) of the \(B_p\)-lives (quantiles) to be considered.
A character string specifying the bound(s) to be computed.
Confidence level of the interval.
A character string specifying the direction of the confidence
interval. "y"
for failure probabilities or "x"
for quantiles.
A tibble with class wt_confint
containing the following columns:
x
: An ordered sequence of the lifetime characteristic regarding the
failed units, starting at min(x)
and ending up at max(x)
. With
b_lives = c(0.01, 0.1, 0.5)
the 1%, 10% and 50% quantiles are additionally
included in x
, but only if the specified probabilities are in the range of
the estimated probabilities.
prob
: An ordered sequence of probabilities with specified b_lives
included.
std_err
: Estimated standard errors with respect to direction
.
lower_bound
: Provided, if bounds
is one of "two_sided"
or "lower"
.
Lower confidence limits with respect to direction
, i.e. limits for
quantiles or probabilities.
upper_bound
: Provided, if bounds
is one of "two_sided"
or "upper"
.
Upper confidence limits with respect to direction
, i.e. limits for
quantiles or probabilities.
cdf_estimation_method
: A character that is always NA_character
. Only
needed for internal use.
Further information is stored in the attributes of this tibble:
distribution
: Distribution which was specified in ml_estimation.
bounds
: Specified bound(s).
direction
: Specified direction.
model_estimation
: Input list with classes wt_model
and wt_ml_estimation
.
The basis for the calculation of these confidence bounds are the standard errors obtained by the delta method.
The bounds on the probability are determined by the z-procedure. See 'References' for more information on this approach.
Meeker, William Q; Escobar, Luis A., Statistical methods for reliability data, New York: Wiley series in probability and statistics, 1998
# 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
)
# Model estimation with ml_estimation():
ml_2p <- ml_estimation(
data_2p,
distribution = "weibull"
)
ml_3p <- ml_estimation(
data_3p,
distribution = "lognormal3",
conf_level = 0.90
)
# Example 1 - Two-sided 95% confidence interval for probabilities ('y'):
conf_fisher_1 <- confint_fisher(
x = ml_2p,
bounds = "two_sided",
conf_level = 0.95,
direction = "y"
)
# Example 2 - One-sided lower/upper 90% confidence interval for quantiles ('x'):
conf_fisher_2_1 <- confint_fisher(
x = ml_2p,
bounds = "lower",
conf_level = 0.90,
direction = "x"
)
conf_fisher_2_2 <- confint_fisher(
x = ml_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_fisher_3_1 <- confint_fisher(
x = ml_3p,
bounds = "two_sided",
conf_level = 0.90,
direction = "y"
)
conf_fisher_3_2 <- confint_fisher(
x = ml_3p,
bounds = "two_sided",
conf_level = 0.90,
direction = "x"
)