About: Location–scale family

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In probability theory, especially in mathematical statistics, a location–scale family is a family of probability distributions parametrized by a location parameter and a non-negative scale parameter. For any random variable whose probability distribution function belongs to such a family, the distribution function of also belongs to the family (where means "equal in distribution"—that is, "has the same distribution as").

Attributes	Values
rdfs:label	Lage-Skalen-Familie (de) Location–scale family (en)
rdfs:comment	In der Statistik ist eine Lage-Skalen-Familie bzw. Lage- und Skalenfamilie eine Familie von Wahrscheinlichkeitsverteilungen parametrisiert durch einen Lageparameter und einen nichtnegativen Skalenparameter. (de) In probability theory, especially in mathematical statistics, a location–scale family is a family of probability distributions parametrized by a location parameter and a non-negative scale parameter. For any random variable whose probability distribution function belongs to such a family, the distribution function of also belongs to the family (where means "equal in distribution"—that is, "has the same distribution as"). (en)
dcterms:subject	Parametric statistics Types of probability distributions Location-scale family probability distributions
Wikipage page ID	2680667 (xsd:integer)
Wikipage revision ID	1079945922 (xsd:integer)
Link from a Wikipage to another Wikipage	Probability distribution Uniform distribution (continuous) Variance Decision theory Degrees of freedom (statistics) Quantile function Continuous random variable Parametric statistics Elliptical distribution Generalized extreme value distribution Location parameter Statistics Student's t-distribution Cauchy distribution Laplace distribution Logistic distribution Univariate distribution Cumulative distribution function Expected value Normal distribution Probability density function Probability theory Random variable Types of probability distributions Location-scale family probability distributions R (programming language) Probability mass function Scale parameter Uniform distribution (discrete) Discrete random variable Random variate Two-moment decision models Cumulative distribution functions
Link from a Wikipage to an external page	http://www.randomservices.org/random/special/LocationScale.html
sameAs	Location–scale family Location–scale family Location–scale family
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:Short_description dbt:Statistics dbt:Probability_distributions
has abstract	In der Statistik ist eine Lage-Skalen-Familie bzw. Lage- und Skalenfamilie eine Familie von Wahrscheinlichkeitsverteilungen parametrisiert durch einen Lageparameter und einen nichtnegativen Skalenparameter. (de) In probability theory, especially in mathematical statistics, a location–scale family is a family of probability distributions parametrized by a location parameter and a non-negative scale parameter. For any random variable whose probability distribution function belongs to such a family, the distribution function of also belongs to the family (where means "equal in distribution"—that is, "has the same distribution as"). In other words, a class of probability distributions is a location–scale family if for all cumulative distribution functions and any real numbers and , the distribution function is also a member of . * If has a cumulative distribution function , then has a cumulative distribution function . * If is a discrete random variable with probability mass function , then is a discrete random variable with probability mass function . * If is a continuous random variable with probability density function , then is a continuous random variable with probability density function . Moreover, if and are two random variables whose distribution functions are members of the family, and assuming existence of the first two moments and has zero mean and unit variance,then can be written as , where and are the mean and standard deviation of . In decision theory, if all alternative distributions available to a decision-maker are in the same location–scale family, and the first two moments are finite, then a two-moment decision model can apply, and decision-making can be framed in terms of the means and the variances of the distributions. (en)
prov:wasDerivedFrom	wikipedia-en:Location–scale_family?oldid=1079945922&ns=0
page length (characters) of wiki page	6025 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Location–scale_family
is Link from a Wikipage to another Wikipage of	Behrens–Fisher problem Nuisance parameter Location parameter Location-scale family Location-scale
is Wikipage redirect of	Location-scale family Location-scale
is foaf:primaryTopic of	wikipedia-en:Location–scale_family

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