Prediction of Failure Probabilities for Parametric Lifetime Distributions

This function predicts the (failure) probabilities of a parametric lifetime distribution using the (log-)location-scale parameterization.

predict_prob(
  q,
  dist_params,
  distribution = c("weibull", "lognormal", "loglogistic", "sev", "normal", "logistic",
    "weibull3", "lognormal3", "loglogistic3", "exponential", "exponential2")
)

Arguments

q: A numeric vector of quantiles.
dist_params: A vector of parameters. An overview of the distribution-specific parameters can be found in section 'Distributions'.
distribution: Supposed distribution of the random variable.

Value

A vector with predicted (failure) probabilities.

Details

For a given set of parameters and specified quantiles the probabilities of the chosen model are determined.

Distributions

The following table summarizes the available distributions and their parameters

location parameter \(\mu\),
scale parameter \(\sigma\) or \(\theta\) and
threshold parameter \(\gamma\).

The order within dist_params is given in the table header.

`distribution`	`dist_params[1]`	`dist_params[2]`	`dist_params[3]`
`"sev"`	\(\mu\)	\(\sigma\)	-
`"weibull"`	\(\mu\)	\(\sigma\)	-
`"weibull3"`	\(\mu\)	\(\sigma\)	\(\gamma\)
`"normal"`	\(\mu\)	\(\sigma\)	-
`"lognormal"`	\(\mu\)	\(\sigma\)	-
`"lognormal3"`	\(\mu\)	\(\sigma\)	\(\gamma\)
`"logistic"`	\(\mu\)	\(\sigma\)	-
`"loglogistic"`	\(\mu\)	\(\sigma\)	-
`"loglogistic3"`	\(\mu\)	\(\sigma\)	\(\gamma\)
`"exponential"`	\(\theta\)	-	-
`"exponential2"`	\(\theta\)	\(\gamma\)	-

Examples

# Example 1 - Predicted probabilities for a two-parameter weibull distribution:
probs_weib2 <- predict_prob(
  q = c(15, 48, 124),
  dist_params = c(5, 0.5),
  distribution = "weibull"
)

# Example 2 - Predicted quantiles for a three-parameter weibull distribution:
probs_weib3 <- predict_prob(
  q = c(25, 58, 134),
  dist_params = c(5, 0.5, 10),
  distribution = "weibull3"
)