Statistic Function

A Statistic Function is a multiset scoring function that summarizes some numerical property of a multiset.

• AKA: Scalar Statistic, Aggregation Function.
• Context:
  • range: a Statistic Value.
  • It can range from being a Population Statistic Function to being a Sample Statistic Function.
• Example(s):
  • any Population Aggregation Function, such as an arithmetic mean function or an arithmetic median function.
  • any Sample Statistic Function, such as a Sample Mean, Sample Median.
  • a Count Function, for count values.
  • a Maximum Function, for a maximum value.
  • a Minimum Function, for a minimum value.
  • a Sum Function, for a sum value.
  • a P Value Function, for p values.
  • …
• Counter-Example(s):
  • a Population Parameter.
  • a Probability Function.
• See: Metric Function, Random Variable, Moment, Aggregate Function, Point Estimator.

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References

2009

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Aggregate_function
  • In Computer Science, an aggregate function is a function that returns a single value from a collection of input values such as a set, a bag or a list.
  • Common aggregate functions include:
    • Average()
    • Count()
    • Maximum()
    • Minimum()
    • Sum()
  • Aggregate functions are common in numerous Programming Languages such as Ruby, in spreadsheets, and in Relational Algebra.
• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Summary_statistics
  • In Descriptive Statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount as simply as possible. Statisticians commonly try to describe the observations in
    • a measure of location, or Central Tendency, such as the Arithmetic Mean, Median, mode, or Interquartile Mean.
    • a measure of Statistical Dispersion like the Standard Deviation, Variance, range, or Interquartile Range, or Absolute Deviation.
    • a measure of the shape of the distribution like Skewness or Kurtosis.
  • A common collection of Order Statistics used as summary statistics are the Five-Number Summary, sometimes extended to a Seven-Number Summary, and the associated Box Plot.

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