Statistical parameter

A statistical parameter or population parameter is an amount put into the probability distribution of a statistic or a random variable.^[1] It can be thought of as a numbered amount of a trait of a statistical population or a statistical model.^[2]

A statistical parameter is different from its estimator in that the parameter is a fixed amount, while the value of an estimator changes according to some probability distribution. The notations ${\displaystyle \theta }$ (for the parameter) and ${\displaystyle {\hat {\theta }}}$ (for the estimator) are often used to clarify this distinction.^[3]

1. ↑ Kotz, S.; et al., eds. (2006), "Parameter", Encyclopedia of Statistical Sciences, Wiley.
2. ↑ Everitt, B. S.; Skrondal, A. (2010), The Cambridge Dictionary of Statistics, Cambridge University Press.
3. ↑ "List of Probability and Statistics Symbols". Math Vault. 2020-04-26. Retrieved 2020-10-13.