Location parameter 位置参数

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最新推荐文章于 2024-03-26 16:14:45 发布

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原文链接：http://www.cnblogs.com/emanlee/archive/2011/06/26/2090761.html

本文解释了概率分布中位置参数的概念，通过实例说明位置参数如何影响分布的形状和位置，包括位置参数在不同分布类型中的应用。

In statistics, a location family is a class of probability distributions parametrized by a scalar- or vector-valued parameter μ, which determines the "location" or shift of the distribution. Formally, this means that the probability density functions or probability mass functions in this class have the form

f μ (x) = f (x - μ).

Here, μ is called the location parameter.

In other words, when you graph the function, the location parameter determines where the origin will be located. If μ is positive, the origin will be shifted to the right, and if μ is negative, it will be shifted to the left.

A location parameter can also be found in families having more than one parameter, such as location-scale families. In this case, the probability density function or probability mass function will have the form

f μ,θ (x) = f θ (x - μ)

where μ is the location parameter, θ represents additional parameters, and $f θ$ is a function of the additional parameters.

Additive noise

An alternative way of thinking of location families is through the concept of additive noise. If μ is an unknown constant and w is random noise with probability density $f (w)$ , then $x = μ + w$ has probability density $f μ (x) = f (x - μ)$ and is therefore a location family.