Note: This is quite unfinished. I plan on fleshing this out when I revisit my master’s project work on estimating latent failure rate distributions. I plan on generalizing the result to allow for arbitrary failure rates and to use the MLE approach to estimate the parameters of the failure rate, since the MLE approach is more general and can be used to estimate the parameters given more complicated data generating processes.
The R packge dfr_dist provides an API for specifying and estimating dynamic failure rate distributions. They can depend on the data in any way, as the failure rate is any function of time and any set of predictors, as long as the failure rate satsifies two key properties:
- It’s non-negative. It is not meaningful to have a negative failure rate; the failure rate can decrease some times, and even go to $0$, though.
- It’s cumulative hazard has a limit of infinity, $\lim_{t \to \infty} H(t, x_1, \ldots, x_p) = \infty$. If this isn’t satisfied, then the survival function is not well-defined.
This object satisfies all of the requirements of an algebraic.dist and a likelihoood model. It is also designed to work well with the algebraic.mle package, which provides a framework for performing maximum likelihood estimation (MLE) and retrieving various statistical properties of the MLEs.
