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).
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Object of class
Further arguments passed to or from other methods. Currently not used.
Supposed distribution of the random variable.
Confidence level of the interval. If
"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.
Returns a list with classes
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
confidence interval for the threshold parameter is computed.
varcov : Provided, if
distribution is not
"weibull3". Estimated heteroscedasticity-consistent
variance-covariance matrix for the (log-)location-scale parameters.
shape_scale_coefficients : Only included if
(parameterization used in
shape_scale_confint : Only included if
"weibull3". Approximated confidence intervals
for scale η and shape β (and threshold γ)
r_squared : Coefficient of determination.
data : A tibble with class
wt_cdf_estimation returned from
distribution : Specified distribution.
If more than one method was specified in
the resulting output is a list with class
In this case each list element has classes
wt_model_estimation and the items listed above, are included.
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
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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 ) # 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 )
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