confint_fisher: Fisher's Confidence Bounds for Quantiles and Probabilities

Description Usage Arguments Details Value References Examples

View source: R/confidence_intervals.R

Description

This function computes normal-approximation confidence intervals for quantiles and failure probabilities.

Usage

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confint_fisher(x, ...)

## S3 method for class 'wt_model'
confint_fisher(
  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

Object with classes wt_model and wt_ml_estimation returned from ml_estimation.

...

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

b_lives

A numeric vector indicating the probabilities p of the B_p-lives (quantiles) to be considered.

bounds

A character string specifying of which bounds have to be computed. One of "two_sided", "lower" or "upper".

conf_level

Confidence level of the interval.

direction

A character string specifying the direction of the confidence interval. One of "y" (failure probabilities) or "x" (quantiles).

Details

The basis for the calculation of these confidence bounds are the standard errors determined by the delta method and hence the required (log-)location-scale parameters as well as the variance-covariance matrix of these have to be estimated with maximum likelihood.

The bounds on the probability are determined by the z-procedure. See 'References' for more information on this approach.

Value

A tibble with class wt_confint containing the following columns:

References

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

Examples

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# 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"
)

weibulltools documentation built on Jan. 16, 2021, 5:21 p.m.