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第987行： − + − + − 具有尺度 x _ m 和形状 α 的帕累托分布相当于位置 mu = x _ m，尺度 σ = x _ m/α，形状 xi = 1/α 的广义帕累托分布。反之亦然，人们可以通过 x _ m = sigma/xi 和 α = 1/xi 从 GPD 得到帕累托分布。+
→Relation to the exponential distribution与指数分布的关系
The Pareto distribution is a special case of the generalized Pareto distribution, which is a family of distributions of similar form, but containing an extra parameter in such a way that the support of the distribution is either bounded below (at a variable point), or bounded both above and below (where both are variable), with the Lomax distribution as a special case. This family also contains both the unshifted and shifted exponential distributions.
The Pareto distribution is a special case of the generalized Pareto distribution, which is a family of distributions of similar form, but containing an extra parameter in such a way that the support of the distribution is either bounded below (at a variable point), or bounded both above and below (where both are variable), with the Lomax distribution as a special case. This family also contains both the unshifted and shifted exponential distributions.
'''<font color="#ff8000"> 帕累托分布Pareto distribution </font>'''是'''<font color="#ff8000"> 广义帕累托分布Generalized Pareto distribution </font>'''的一个特例，它是一族形式相似的分布，但包含一个额外的参数，使得分布的支撑要么在下面有界(在一个可变点) ，要么在上面和下面都有界(两者都是可变的) ，'''<font color="#ff8000"> 洛马克斯分布Lomax distribution </font>'''是一个特例。该族同时包含'''<font color="#ff8000">无移位和移位指数分布Unshifted and Shifted exponential distributions</font>'''
'''<font color="#ff8000"> 帕累托分布Pareto distribution </font>'''是'''<font color="#ff8000"> 广义帕累托分布Generalized Pareto distribution </font>'''的一个特例，它是一族形式相似的分布，但包含一个额外的参数，使得分布的支撑要么有下界(在一个可变点处) ，要么上下都有界(两者都可变) ，'''<font color="#ff8000"> 洛马克斯分布Lomax distribution </font>'''是一个特例。该族同时包含'''<font color="#ff8000">无移位和移位指数分布Unshifted and Shifted exponential distributions</font>'''
The Pareto distribution is related to the [[exponential distribution]] as follows. If ''X'' is Pareto-distributed with minimum ''x''<sub>m</sub> and index ''α'', then
The Pareto distribution is related to the [[exponential distribution]] as follows. If ''X'' is Pareto-distributed with minimum ''x''<sub>m</sub> and index ''α'', then
帕累托分布与[[指数分布]]相关如下。如果“X”是帕累托分布，最小“X”<sub>m</sub>和索引“α”，则
帕累托分布与[[指数分布]]的关系如下。如果“X”是帕累托分布，具有最小''x''<sub>m</sub> 和指数 ''α''，则
The Pareto distribution with scale x_m and shape \alpha is equivalent to the generalized Pareto distribution with location \mu=x_m, scale \sigma=x_m/\alpha and shape \xi=1/\alpha. Vice versa one can get the Pareto distribution from the GPD by x_m = \sigma/\xi and \alpha=1/\xi.
The Pareto distribution with scale x_m and shape \alpha is equivalent to the generalized Pareto distribution with location \mu=x_m, scale \sigma=x_m/\alpha and shape \xi=1/\alpha. Vice versa one can get the Pareto distribution from the GPD by x_m = \sigma/\xi and \alpha=1/\xi.
具有规模 x_m 和形状 \alpha的帕累托分布相当于位置 mu = x _ m，规模 \sigma=x_m/\alpha 和 形状 \xi=1/\alpha 的广义帕累托分布。反之亦然，人们可以通过 x_m = \sigma/\xi 和 \alpha=1/\xi 从 GPD 得到帕累托分布。
: <math> Y = \log\left(\frac{X}{x_\mathrm{m}}\right) </math>
: <math> Y = \log\left(\frac{X}{x_\mathrm{m}}\right) </math>