loglik_function {weibulltools} | R Documentation |
Log-Likelihood Function for Parametric Lifetime Distributions
Description
This function computes the log-likelihood value with respect to a given set of parameters. 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, ...)
## S3 method for class 'wt_reliability_data'
loglik_function(
x,
wts = rep(1, nrow(x)),
dist_params,
distribution = c("weibull", "lognormal", "loglogistic", "sev", "normal", "logistic",
"weibull3", "lognormal3", "loglogistic3", "exponential", "exponential2"),
...
)
Arguments
x |
A |
... |
Further arguments passed to or from other methods. Currently not used. |
wts |
Optional vector of case weights. The length of |
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
Returns the log-likelihood value for the parameters in dist_params
given
the data.
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 | - |
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
)
# Example 1 - Evaluating Log-Likelihood function of two-parametric weibull:
loglik_weib <- loglik_function(
x = data,
dist_params = c(5.29, 0.33),
distribution = "weibull"
)
# Example 2 - Evaluating Log-Likelihood function of three-parametric weibull:
loglik_weib3 <- loglik_function(
x = data,
dist_params = c(4.54, 0.76, 92.99),
distribution = "weibull3"
)