This function estimates the parameters of a parametric 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).
ml_estimation(x, ...) # S3 method for wt_reliability_data ml_estimation( x, distribution = c("weibull", "lognormal", "loglogistic", "sev", "normal", "logistic", "weibull3", "lognormal3", "loglogistic3", "exponential", "exponential2"), wts = rep(1, nrow(x)), conf_level = 0.95, start_dist_params = NULL, control = list(), ... )
Further arguments passed to or from other methods. Currently not used.
Supposed distribution of the random variable.
Optional vector of case weights. The length of
Confidence level of the interval.
Optional vector with initial values of the (log-)location-scale parameters.
A list of control parameters (see 'Details' and optim).
A list with classes
coefficients : A named vector of estimated coefficients (parameters of the
assumed distribution). Note: The parameters are given in the
confint : Confidence intervals for the (log-)location-scale parameters.
shape_scale_coefficients : Only included if
"weibull3" (parameterization used in Weibull).
shape_scale_confint : Only included if
"weibull3". Confidence intervals for scale \(\eta\) and shape \(\beta\)
(and threshold \(\gamma\) if
distribution = "weibull3").
varcov : Estimated variance-covariance matrix of (log-)location-scale parameters.
logL : The log-likelihood value.
aic : Akaike Information Criterion.
bic : Bayesian Information Criterion.
data : A
tibble with class
wt_reliability_data returned by
distribution : Specified distribution.
ml_estimation, optim is called with
method = "BFGS"
control$fnscale = -1 to estimate the parameters that maximize the
log-likelihood (see loglik_function). For threshold models, the profile
log-likelihood is maximized in advance (see loglik_profiling). Once the
threshold parameter is determined, the threshold model is treated like a
distribution without threshold (lifetime is reduced by threshold estimate)
and the general optimization routine is applied.
Normal approximation confidence intervals for the parameters are computed as well.
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 ) # Example 1 - Fitting a two-parametric weibull distribution: ml_2p <- ml_estimation( data_2p, distribution = "weibull" ) # Example 2 - Fitting a three-parametric lognormal distribution: ml_3p <- ml_estimation( data_3p, distribution = "lognormal3", conf_level = 0.99 )