log-log: The log-log and complementary log-log functions In LaplacesDemon: Complete Environment for Bayesian Inference

Description

The log-log and complementary log-log functions, as well as the inverse functions, are provided.

Usage

 ```1 2 3 4``` ```cloglog(p) invcloglog(x) invloglog(x) loglog(p) ```

Arguments

 `x` This is a vector of real values that will be transformed to the interval [0,1]. `p` This is a vector of probabilities p in the interval [0,1] that will be transformed to the real line.

Details

The logit and probit links are symmetric, because the probabilities approach zero or one at the same rate. The log-log and complementary log-log links are asymmetric. Complementary log-log links approach zero slowly and one quickly. Log-log links approach zero quickly and one slowly. Either the log-log or complementary log-log link will tend to fit better than logistic and probit, and are frequently used when the probability of an event is small or large. A mixture of the two links, the log-log and complementary log-log is often used, where each link is weighted. The reason that logit is so prevalent is because logistic parameters can be interpreted as odds ratios.

Value

`cloglog` returns `x`, `invcloglog` and `invloglog` return probability `p`, and `loglog` returns `x`.

Author(s)

Statisticat, LLC. [email protected]

`LaplacesDemon`

Examples

 ```1 2 3 4``` ```library(LaplacesDemon) x <- -5:5 p <- invloglog(x) x <- loglog(p) ```

Example output

```
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LaplacesDemon documentation built on July 1, 2018, 9:02 a.m.