# confint_betabinom: Beta Binomial Confidence Bounds for Quantiles and/or... In weibulltools: Statistical Methods for Life Data Analysis

## Description

This non-parametric approach calculates confidence bounds for quantiles and/or failure probabilities using a procedure that is similar to that used in calculating median ranks. The location-scale (and threshold) parameters estimated by rank regression are needed.

## Usage

 ```1 2 3 4``` ```confint_betabinom(x, event, loc_sc_params, distribution = c("weibull", "lognormal", "loglogistic", "normal", "logistic", "sev", "weibull3", "lognormal3", "loglogistic3"), bounds = c("two_sided", "lower", "upper"), conf_level = 0.95, direction = c("y", "x")) ```

## Arguments

 `x` a numeric vector which consists of lifetime data. `x` is used to specify the range of confidence region(s). `event` a vector of binary data (0 or 1) indicating whether unit i is a right censored observation (= 0) or a failure (= 1). `loc_sc_params` a (named) numeric vector of estimated location and scale parameters for a specified distribution. The order of elements is important. First entry needs to be the location parameter μ and the second element needs to be the scale parameter σ. If a three-parametric model is used the third element is the threshold parameter γ. `distribution` supposed distribution of the random variable. The value can be `"weibull"`, `"lognormal"`, `"loglogistic"`, `"normal"`, `"logistic"`, `"sev"` (smallest extreme value), `"weibull3"`, `"lognormal3"` or `"loglogistic3"`. Other distributions have not been implemented yet. `bounds` a character string specifying the interval(s) which has/have to be computed. Must be one of "two_sided" (default), "lower" or "upper". `conf_level` confidence level of the interval. The default value is `conf_level = 0.95`. `direction` a character string specifying the direction of the computed interval(s). Must be either "y" (failure probabilities) or "x" (quantiles).

## Value

A data frame containing the lifetime characteristic, interpolated ranks as a function of probabilities, the probabilities which are used to compute the ranks and computed values for the specified confidence bound(s).

## References

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44``` ```# Example 1: Beta-Binomial Confidence Bounds for two-parameter Weibull: obs <- seq(10000, 100000, 10000) state <- c(0, 1, 1, 0, 0, 0, 1, 0, 1, 0) df_john <- johnson_method(x = obs, event = state) mrr <- rank_regression(x = df_john\$characteristic, y = df_john\$prob, event = df_john\$status, distribution = "weibull", conf_level = .95) conf_betabin <- confint_betabinom(x = df_john\$characteristic, event = df_john\$status, loc_sc_params = mrr\$loc_sc_coefficients, distribution = "weibull", bounds = "two_sided", conf_level = 0.95, direction = "y") # Example 2: Beta-Binomial Confidence Bounds for three-parameter Weibull: # Alloy T7987 dataset taken from Meeker and Escobar(1998, p. 131) cycles <- c(300, 300, 300, 300, 300, 291, 274, 271, 269, 257, 256, 227, 226, 224, 213, 211, 205, 203, 197, 196, 190, 189, 188, 187, 184, 180, 180, 177, 176, 173, 172, 171, 170, 170, 169, 168, 168, 162, 159, 159, 159, 159, 152, 152, 149, 149, 144, 143, 141, 141, 140, 139, 139, 136, 135, 133, 131, 129, 123, 121, 121, 118, 117, 117, 114, 112, 108, 104, 99, 99, 96, 94) state <- c(rep(0, 5), rep(1, 67)) df_john2 <- johnson_method(x = cycles, event = state) mrr_weib3 <- rank_regression(x = df_john2\$characteristic, y = df_john2\$prob, event = df_john2\$status, distribution = "weibull3", conf_level = .95) conf_betabin_weib3 <- confint_betabinom(x = df_john2\$characteristic, event = df_john2\$status, loc_sc_params = mrr_weib3\$loc_sc_coefficients, distribution = "weibull3", bounds = "two_sided", conf_level = 0.95, direction = "y") ```

### Example output

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weibulltools documentation built on May 2, 2019, 11:01 a.m.