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(), ... )

x | A |
---|---|

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

distribution | Supposed distribution of the random variable. |

wts | Optional vector of case weights. The length of |

conf_level | Confidence level of the interval. |

start_dist_params | Optional vector with initial values of the (log-)location-scale parameters. |

control | A list of control parameters (see 'Details' and optim). |

A list with classes `wt_model`

, `wt_ml_estimation`

and `wt_model_estimation`

which contains:

`coefficients`

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

: Confidence intervals for the (log-)location-scale parameters.`shape_scale_coefficients`

: Only included if`distribution`

is`"weibull"`

or`"weibull3"`

(parameterization used in Weibull).`shape_scale_confint`

: Only included if`distribution`

is`"weibull"`

or`"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.

Within `ml_estimation`

, optim is called with `method = "BFGS"`

and `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 )