Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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## rational *h-*index

^{th} ranked publication needs to reach \(h+1\) citations).
### Example

### History

## References

The rational *h-*index (Ruane and Tol 2008) (*h*^{Δ} or *h*_{rat}) is a continuous version of *h* which not only measures the standard *h-*index but includes the fractional progress toward the next higher value of *h.* It is calculated as

Publications are ordered by number of citations, from highest to lowest.

Citations (C)_{i} | 42 | 36 | 14 | 11 | 9 | 9 | 3 | 2 | 2 | 2 | 1 | 1 | 1 | 0 | 0 | 0 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Rank (i) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

h = 6 |

The *h-*index is 6. To reach an *h* of 7, we would need to add 0 citations to the publications within the core and 4 citations to the 7^{th} publication (for a total of 4). The maximum number of citations that could be required is 13 (if all 6 core publications had exactly 6 citations and the 7^{th} publication had zero), thus the rational *h* is 6 + 1 - 4/13 = 6.6923.

Year | h^{Δ} |
---|---|

1997 | 1.3333 |

1998 | 2.8000 |

1999 | 3.7143 |

2000 | 5.8182 |

2001 | 6.6923 |

2002 | 7.8667 |

2003 | 9.8947 |

2004 | 11.9565 |

2005 | 13.8889 |

2006 | 15.9355 |

2007 | 17.9429 |

2008 | 19.9744 |

2009 | 23.8936 |

2010 | 24.9388 |

2011 | 26.8868 |

2012 | 27.9818 |

2013 | 29.9831 |

2014 | 32.9692 |

2015 | 34.9565 |

2016 | 35.8732 |

2017 | 35.8732 |

- Ruane, F., and R.S.J. Tol (2008) Rational (successive)
*h-*indices: An application to economics in the Republic of Ireland.*Scientometrics*75(2):395–405.