# loglik_function: Log-Likelihood Function for (Log-) Location-Scale... In weibulltools: Statistical Methods for Life Data Analysis

## 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

 ```1 2 3``` ```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 (μ), the second is the scale parameter (σ) and if a three-parametric model is used the third element is the threshold parameter (γ). `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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```# 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") ```

weibulltools documentation built on May 2, 2019, 11:01 a.m.