Sample Mean Function

A Sample Mean Function is a mean function that is also sample statistic function (based on a Random Sample).

• AKA: Empirical Mean.
• Context:
  • range: Sample Mean Value.
  • …
• Counter-Example(s):
  • Population Mean Function.
  • Sample Median Function.
  • Sample Variance Function.
  • Ratio Estimator.
  • Product Estimator.
  • Ratio Type Exponential Estimator.
• See: Expected Value, Population Mean.

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References

2013

• (Wikipedia, 2013) ⇒ http://en.wikipedia.org/wiki/Sample_mean_and_sample_covariance
  • The sample mean or empirical mean and the sample covariance are statistics computed from a collection of data on one or more random variables. The sample mean is a vector each of whose elements is the sample mean of one of the random variablesTemplate:Spaced ndashthat is, each of whose elements is the arithmetic average of the observed values of one of the variables. The sample covariance matrix is a square matrix whose i, j element is the sample covariance (an estimate of the population covariance) between the sets of observed values of two of the variables and whose i, i element is the sample variance of the observed values of one of the variables. If only one variable has had values observed, then the sample mean is a single number (the arithmetic average of the observed values of that variable) and the sample covariance matrix is also simply a single value (the sample variance of the observed values of that variable).

• http://en.wikipedia.org/wiki/Sample_mean_and_sample_covariance#Sample_mean
  • Let [math]\displaystyle{ x_{ij} }[/math] be the i^th independently drawn observation (i=1,...,N) on the j^th random variable (j=1,...,K). These observations can be arranged into N column vectors, each with K entries, with the K ×1 column vector giving the i^th observations of all variables being denoted [math]\displaystyle{ \mathbf{x}_i }[/math] (i=1,...,N).

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