# rank_regression: Rank Regression for Parametric Lifetime Distributions In weibulltools: Statistical Methods for Life Data Analysis

## Description

This function fits an x on y regression to a linearized two- or three-parameter lifetime distribution for complete and (multiple) right censored data. The parameters are determined in the frequently used (log-)location-scale parameterization.

For the Weibull, estimates are additionally transformed such that they are in line with the parameterization provided by the stats package (see Weibull).

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10``` ```rank_regression(x, ...) ## S3 method for class 'wt_cdf_estimation' rank_regression( x, distribution = c("weibull", "lognormal", "loglogistic", "normal", "logistic", "sev", "weibull3", "lognormal3", "loglogistic3"), conf_level = 0.95, ... ) ```

## Arguments

 `x` Object of class `wt_cdf_estimation` returned from `estimate_cdf`. `...` Further arguments passed to or from other methods. Currently not used. `distribution` Supposed distribution of the random variable. `conf_level` Confidence level of the interval. If `distribution` is `"weibull"` this must be one of `0.9`, `0.95` or `0.99`.

## Details

If `distribution` is `"weibull"` or `"weibull3"`, the approximated confidence intervals for the parameters can only be estimated on the following confidence levels (see 'References' (Mock, 1995)):

• `conf_level` = 0.90,

• `conf_level` = 0.95,

• `conf_level` = 0.99.

If the distribution is not the Weibull, the confidence intervals of the parameters are computed on the basis of a heteroscedasticity-consistent covariance matrix. Here it should be said that there is no statistical foundation to determine the standard errors of the parameters using Least Squares in context of Rank Regression. For an accepted statistical method use maximum likelihood.

## Value

Returns a list with classes `wt_model`, `wt_rank_regression` and `wt_model_estimation` containing the following elements:

• `coefficients` : A named vector of estimated coefficients (parameters of the assumed distribution). Note: The parameters are given in location-scale-parameterization.

• `confint` : Confidence intervals for parameters. If `distribution` is `"lognormal3"` or `"loglogistic3"` no confidence interval for the threshold parameter is computed.

• `varcov` : Provided, if `distribution` is not `"weibull"` or `"weibull3"`. Estimated heteroscedasticity-consistent variance-covariance matrix for the (log-)location-scale parameters.

• `shape_scale_coefficients` : Only included if `distribution` is `"weibull"` or `"weibull3"` (parameterization used in `stats::Weibull`).

• `shape_scale_confint` : Only included if `distribution` is `"weibull"` or `"weibull3"`. Approximated confidence intervals for scale η and shape β (and threshold γ) if `distribution` is `"weibull3"`.

• `r_squared` : Coefficient of determination.

• `data` : A tibble with class `wt_cdf_estimation` returned from `estimate_cdf`.

• `distribution` : Specified distribution.

If more than one method was specified in `estimate_cdf`, the resulting output is a list with class `wt_model_estimation_list`. In this case each list element has classes `wt_rank_regression` and `wt_model_estimation` and the items listed above, are included.

## References

• Mock, R., Methoden zur Datenhandhabung in Zuverlässigkeitsanalysen, vdf Hochschulverlag AG an der ETH Zürich, 1995

• 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 45 46 47 48 49 50 51``` ```# 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", "kaplan") ) # Example 1 - Fitting a two-parametric weibull distribution: rr_2p <- rank_regression( x = prob_tbl_2p, distribution = "weibull" ) # Example 2 - Fitting a three-parametric lognormal distribution: rr_3p <- rank_regression( x = prob_tbl_3p, distribution = "lognormal3", conf_level = 0.99 ) # Example 3 - Fitting a three-parametric loglogistic distribution if multiple # methods in estimate_cdf were specified: rr_lists <- rank_regression( x = prob_tbl_mult, distribution = "loglogistic3", conf_level = 0.90 ) ```

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