log-log {LaplacesDemon} | R Documentation |

## The log-log and complementary log-log functions

### Description

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

### Usage

```
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. software@bayesian-inference.com

### See Also

### Examples

```
library(LaplacesDemon)
x <- -5:5
p <- invloglog(x)
x <- loglog(p)
```

*LaplacesDemon*version 16.1.6 Index]