# loglik_profiling: Log-Likelihood Profile Function for Parametric Lifetime... In weibulltools: Statistical Methods for Life Data Analysis

## Description

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

## Usage

 1 2 3 4 5 6 loglik_profiling( x, status, thres, distribution = c("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. status A vector of binary data (0 or 1) indicating whether unit i is a right censored observation (= 0) or a failure (= 1). thres A numeric value for the threshold parameter. distribution Supposed three-parametric distribution of the random variable.

## Value

Returns the log-likelihood value for the data with respect to the threshold parameter thres.

## 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 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 # Vectors: cycles <- alloy\$cycles status <- alloy\$status # Determining the optimal loglikelihood value: ## Range of threshold parameter must be smaller than the first failure: threshold <- seq( 0, min(cycles[status == 1]) - 0.1, length.out = 50 ) ## loglikelihood value with respect to threshold values: profile_logL <- loglik_profiling( x = cycles, status = status, thres = threshold, distribution = "weibull3" ) ## Threshold value (among the candidates) that maximizes the ## loglikelihood: threshold[which.max(profile_logL)] ## plot: plot( threshold, profile_logL, type = "l" ) abline( v = threshold[which.max(profile_logL)], h = max(profile_logL), col = "red" )

weibulltools documentation built on Jan. 16, 2021, 5:21 p.m.