# Upper bound of the uncertainty interval of the Rao-Stirling diversity index.

### Description

This function computes the upper bound of the uncertainty interval of the Rao-Stirling diversity index, as explained in Calatrava et al. (2016). The computation involves the redistribution of uncategorized references to various disciplines. In order to avoid improbable redistributions of disciplines, a set of permissible disciplines for redistribution can be defined. Furthermore, the number of disciplines redistributed to uncategorized references can be limited.

### Usage

1 2 | ```
UpperIndexBound(known.ref.counts, uncat.ref.count, similarity,
permissible.disciplines = NULL, redistribution.limit = 4)
``` |

### Arguments

`known.ref.counts` |
A vector of positive integers. Each element represents the count of references to each discipline. |

`uncat.ref.count` |
A positive integer denoting the number of references that are not categorized into disciplines. |

`similarity` |
A positive semi-definite matrix that encodes the similarity between disciplines, as explained in Porter and Rafols (2009).
The dimensions of this matrix are |

`permissible.disciplines` |
A logical vector denoting to which disciplines uncategorized references can be distributed.
Its length needs to be equal to the length of |

`redistribution.limit` |
A positive integer that limits the number of disciplines that each uncategorized reference can have redistributed. This argument is optional and leaving it unspecified will set the redistribution.limit to default. |

### Value

The upper bound of the uncertainty interval of the Rao-Stirling diversity index.

### References

Calatrava Moreno, M.C., Auzinger, T. and Werthner, H. (2016) On the uncertainty of interdisciplinarity measurements due to incomplete bibliographic data. Scientometrics. DOI:10.1007/s11192-016-1842-4

Porter, A. and Rafols, I. (2009) Is science becoming more interdisciplinary? Measuring and mapping six research fields over time. Scientometrics, Vol. 81, No. 3 (719-745). DOI:10.1007/s11192-008-2197-2

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
#Load data
data(pubdata1)
#Get counts of citations of one of the publications in the dataset
counts <- pd1.count.matrix[,1]
#Get number of uncategorized references in the publication
uncat <- pd1.uncat.refs[1]
#Get vector of permissible disciplines.
logic.disciplines <- counts > 0
permissible <- PruneDisciplines(logic.disciplines, 0.233, pd1.similarity)
UpperIndexBound(counts, uncat, pd1.similarity, permissible)
``` |