Absolute Frequency Function

An Absolute Frequency Function is a frequency function that is restricted to counting the occurrence of some specific Multiset Member.

• AKA: Freq, Occurrence Frequency Function.
• Context:
  • domain: Multiset, and a Set Element.
  • range: Absolute Frequency Value.
  • …
• Example(s):
  • Freq({b, [math]\displaystyle{ c }[/math], a, [math]\displaystyle{ b }[/math], a}, a) ⇒ 2.
  • a Term Frequency Function.
  • an Experimental Frequency Function.
  • …
• Counter-Example(s):
  • a Multiset Cardinality Function, e.g. [math]\displaystyle{ f }[/math]({b, [math]\displaystyle{ c }[/math], a, [math]\displaystyle{ b }[/math], a}) ⇒ 5.
  • a Multiset Membership Function, e.g. [math]\displaystyle{ f }[/math]({b, [math]\displaystyle{ c }[/math], a, [math]\displaystyle{ b }[/math], a}) ⇒ {b, [math]\displaystyle{ c }[/math], a}
  • a Relative Frequency Function, e.g. [math]\displaystyle{ f }[/math](a, {b, [math]\displaystyle{ c }[/math], a, [math]\displaystyle{ b }[/math], a}) ⇒ 2/5.
  • a Frequency Table.
• See: Frequency Function, Set Cardinality Function, Relative Frequency Function, Distribution, Ranking Function, Distribution Function, Set Member Frequency, Multiset Member Frequency.

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References

2009

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Multiplicity_(mathematics)#See_also
  • In mathematics, the multiplicity of a member of a multiset is how many memberships in the multiset it has. For example, the term is used to refer to the number of times a given polynomial equation has a root at a given point.
  • The common reason to consider notions of multiplicity is to count correctly, without specifying exceptions (for example, double roots counted twice). Hence the expression counted with (sometimes implicit) multiplicity.
  • When mathematicians wish to ignore multiplicity they will refer to the number of distinct elements of a set.

Discrete Uniform Distribution

2004

• http://www.mathsteacher.com.au/year8/ch17_stat/03_freq/freq.htm
  • The frequency of a particular data value is the number of times the data value occurs. For example, if four students have a score of 80 in mathematics, and then the score of 80 is said to have a frequency of 4. The frequency of a data value is often represented by f.
  • A frequency table is constructed by arranging collected data values in ascending order of magnitude with their corresponding frequencies.

2002

• http://www.teacherlink.org/content/math/interactive/probability/glossary/glossary.html
  • Frequency: Measures how often something occurs within some given distance or time period.

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