# On the distribution of the largest part of unrestricted partitions of small integers

Brown, Simon
(2009)
*On the distribution of the largest part of unrestricted partitions of small integers.*
Electronic Journal of Applied Statistical Analysis, 1 (1). pp. 1-10.

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## Abstract

Several theoretical estimates of the distribution of the parts of integer partitions have been published. Generally these are asymptotically correct for large integers, but practical applications require that the distribution be known for small integers (n ≤ 1000). The largest part (or the number of parts) of an unrestricted partition of the integer n has the extreme value distribution, in agreement with the theoretical estimates. Expressions approximating the mode and variance of the distribution are given for n ≤ 1000 that represent significant improvements over the asymptotically correct theoretical expressions.

Item ID: | 53063 |
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Item Type: | Article (Research - C1) |

ISSN: | 2070-5948 |

Keywords: | integer partition; extreme value distribution; approximation |

Date Deposited: | 09 Apr 2018 05:53 |

FoR Codes: | 01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010101 Algebra and Number Theory @ 50% 01 MATHEMATICAL SCIENCES > 0104 Statistics > 010401 Applied Statistics @ 50% |

SEO Codes: | 97 EXPANDING KNOWLEDGE > 970101 Expanding Knowledge in the Mathematical Sciences @ 100% |

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