Examples
In general, any random variable X is a member of a location-scale family with an infinite number of members; each of these members Y is distributed the same as a + bX for real numbers a and b > 0. However, the form of the distribution function for a + bX, and hence for Y, may differ from the form of the distribution function for X. Well-known families in which the functional form of the distribution is retained throughout the family include the following:
- Normal distribution
- Elliptical distribution
- Cauchy distribution
- Uniform distribution (continuous)
- Uniform distribution (discrete)
- Logistic distribution
- Laplace distribution
- Student's t-distribution
- Generalized extreme value distribution
Read more about this topic: Location-scale Family
Famous quotes containing the word examples:
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)