weibulltools (version 1.0.1)

loglik_function: Log-Likelihood Function for (Log-) Location-Scale Distributions (with Threshold)

Description

This function computes the log-likelihood value with respect to a given set of parameters. For two-parametric models the location and scale parameters are required. If a three-parametric lifetime distribution is needed an additional threshold parameter is required. In terms of Maximum Likelihood Estimation this function can be optimized (optim) to estimate the parameters and variance-covariance matrix of the parameters.

Usage

loglik_function(x, event, wts = rep(1, length(x)), pars,
  distribution = c("weibull", "lognormal", "loglogistic", "normal",
  "logistic", "sev", "weibull3", "lognormal3", "loglogistic3"))

Arguments

x

a numeric vector which consists of lifetime data. Lifetime data could be every characteristic influencing the reliability of a product, e.g. operating time (days/months in service), mileage (km, miles), load cycles.

event

a vector of binary data (0 or 1) indicating whether unit i is a right censored observation (= 0) or a failure (= 1).

wts

optional vector of case weights. The length of wts must be the same as the number of observations x. Default is that wts is a vector with all components being 1 (same weights).

pars

a numeric vector of parameters. The first element is the location parameter (\(\mu\)), the second is the scale parameter (\(\sigma\)) and if a three-parametric model is used the third element is the threshold parameter (\(\gamma\)).

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.

References

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

Examples

# NOT RUN {
# 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))

# Example 1: Evaluating Log-Likelihood function of two-parametric weibull:
loglik_weib <- loglik_function(x = cycles, event = state, pars = c(5.29, 0.33),
                               distribution = "weibull")

# Example 2: Evaluating Log-Likelihood function of three-parametric weibull:
loglik_weib3 <- loglik_function(x = cycles, event = state,
                                pars = c(4.54, 0.76, 92.99),
                                distribution = "weibull3")
# }