# simulate a sample of ISR(pi,mu)

### Description

This function simulates univariate rankings data (ordering representation) according to the ISR(pi,mu).

### Usage

1 |

### Arguments

`n` |
size of the sample. |

`pi` |
dispersion parameter: probability of correct paired comparaison according to mu. |

`mu` |
position parameter: modal ranking in ordering representation. |

### Details

The ranking representation r=(r_1,...,r_m) contains the ranks assigned to the objects, and means that the ith object is in r_ith position.

The ordering representation o=(o_1,...,o_m) means that object o_i is in the ith position.

Let us consider the following example to illustrate both notations: a judge, which has to rank three holidays destinations according to its preferences, O1 = Countryside, O2 =Mountain and O3 = Sea, ranks first Sea, second Countryside, and last Mountain. The ordering result of the judge is o = (3, 1, 2) whereas the ranking result is r = (2, 3, 1).

You can see the convertRank function to convert the simualted ranking drom ordering to ranking representation.

### Value

a matrix with simulated ranks.

### Author(s)

Julien Jacques

### References

[1] C.Biernacki and J.Jacques (2013), A generative model for rank data based on sorting algorithm, Computational Statistics and Data Analysis, 58, 162-176.

### Examples

1 | ```
x=simulISR(30,0.8,1:4)
``` |