Log-Likelihood Profile Function for Parametric Lifetime Distributions with Threshold

This function evaluates the log-likelihood with respect to a given threshold parameter of a parametric lifetime distribution. In terms of Maximum Likelihood Estimation this function can be optimized (optim) to estimate the threshold parameter.

loglik_profiling(x, ...)

# S3 method for wt_reliability_data
loglik_profiling(
  x,
  wts = rep(1, nrow(x)),
  thres,
  distribution = c("weibull3", "lognormal3", "loglogistic3", "exponential2"),
  ...
)

Arguments

x

A tibble with class wt_reliability_data returned by reliability_data.

...

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

wts

Optional vector of case weights. The length of wts must be equal to the number of observations in x.

thres

A numeric value for the threshold parameter.

distribution

Supposed parametric distribution of the random variable.

Value

Returns the log-likelihood value for the threshold parameter thres given the data.

References

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

Examples

# Reliability data preparation:
data <- reliability_data(
  alloy,
  x = cycles,
  status = status
)

# Determining the optimal loglikelihood value:
## Range of threshold parameter must be smaller than the first failure:
threshold <- seq(
  0,
  min(data$x[data$status == 1]) - 0.1,
  length.out = 50
)

## loglikelihood value with respect to threshold values:
profile_logL <- loglik_profiling(
  x = data,
  thres = threshold,
  distribution = "weibull3"
)

## Threshold value (among the candidates) that maximizes the
## loglikelihood:
threshold[which.max(profile_logL)]
#> [1] 91.98367

## plot:
plot(
  threshold,
  profile_logL,
  type = "l"
)
abline(
  v = threshold[which.max(profile_logL)],
  h = max(profile_logL),
  col = "red"
)