# Rissanen's universal prior for integers

### Description

It returns (up to normalizing constant) the mass assigned to each positive integer or a vector of integers by Rissanen's universal prior for positive integers

### Usage

1 | ```
rissanen(n)
``` |

### Arguments

`n` |
a vector of positive integers |

### Details

Rissanen's universal prior on positive integers is one of the default options for eliciting a noninformative prior distribution on the unknown population size *N*. It is a proper prior with tails of the order between *1/N* and *1/N^2*

### Value

The mass assigned to each positive integer in the input vector of integers `n`

by Rissanen's universal prior for positive integers

*Q(n)=2^{-\log^*(n)} \qquad n>0*

where
*\log^*(x)= \log(x)+\log( \log (x)) + \log( \log (\log (x)))....* where the sum involves only the non-negative terms. Notice that masses are not normalized hence they do not add to one but to a finite positive real constant

*c = ∑_{n=1}^∞ Q(n)*

### Author(s)

Danilo Alunni Fegatelli and Luca Tardella

### References

Rissanen, J. (1983) A universal prior for integers and estimation by minimum description length. Ann. Statist. 11, no. 2, 416-431

### Examples

1 2 3 4 | ```
# Notice that masses are not normalized hence they do not add to one but to a finite
# positive real constant c
rissanen(1:5)
``` |