# Finite-Sample Distribution

A Finite-Sample Distribution is a probability distribution of a given statistic based on a random population sample.

**AKA:**Sampling Distribution**Example(s):**- The probability distribution of all possible values of a chi-square statistic is a chi-square distribution. The sampling distribution of the chi-square statistic approaches the chi-square distribution as sample size becomes a large number.

**See:**Test Statistic, Population Sample, Sample Mean.

## References

### 2016

- (Stat Trek, 2016) ⇒ http://stattrek.com/sampling/sampling-distribution.aspx
*Retrieved: 2016-10-09*- QUOTE: Suppose that we draw all possible samples of size n from a given population. Suppose further that we compute a statistic (e.g., a mean, proportion, standard deviation) for each sample. The probability distribution of this statistic is called a sampling distribution. And the standard deviation of this statistic is called the standard error.

### 2011

- http://en.wikipedia.org/wiki/Sampling_distribution
- In statistics, a
**sampling distribution**or finite-sample distribution is the probability distribution of a given statistic based on a random sample. Sampling distributions are important in statistics because they provide a major simplification on the route to statistical inference. More specifically, they allow analytical considerations to be based on the sampling distribution of a statistic, rather than on the joint probability distribution of all the individual sample values.The

**sampling distribution**of a statistic is distribution of that statistic, considered as a random variable, when derived from a random sample of size*n*. It may be considered as the distribution of the statistic for*all possible samples from the same population*of a given size. The sampling distribution depends on the underlying distribution of the population, the statistic being considered, the sampling procedure employed and the sample size used. There is often considerable interest in whether the sampling distribution can be approximated by an asymptotic distribution, which corresponds to the limiting case as n → ∞*.*

- In statistics, a

### 2008

- (Upton & Cook, 2008) ⇒ Graham Upton, and Ian Cook. (2008). “A Dictionary of Statistics, 2nd edition revised." Oxford University Press. ISBN:0199541450
- QUOTE: sampling distribution: Distribution that describes the variation in the values of a statistic over all possible samples. For example, if [math]n[/math] values are sampled from a population and if [math]X_1, X_2, … , X_?[/math], are the random variables representing the individual sample values, then the sample mean X, given by [math]t[/math] is a random variable. The variability of the n values about their mean, is also a random variable. The form of the sampling distributions of X and V2 will depend on the population, but statements can nevertheless be made about their moments.

### 2003

- (Jaynes, 2003) ⇒ Edwin T. Jaynes. (2003). “Probability Theory: The Logic of Science." Cambridge University Press.