QuantilePlot[list]
产生 list 的分位数对一个正态分布的分位数的图线.
QuantilePlot[dist]
产生分布 dist 的分位数对一个正态分布的分位数的图线.
QuantilePlot[data,rdata]
产生 data 的分位数对 rdata 的分位数的图线.
QuantilePlot[data,rdist]
产生 data 的分位数对符号分布 rdist 的分位数的图线.
QuantilePlot[{data1,data2,…},ref]
产生 datai 的分位数对参照分布 ref 的分位数的图线.
QuantilePlot
QuantilePlot[list]
产生 list 的分位数对一个正态分布的分位数的图线.
QuantilePlot[dist]
产生分布 dist 的分位数对一个正态分布的分位数的图线.
QuantilePlot[data,rdata]
产生 data 的分位数对 rdata 的分位数的图线.
QuantilePlot[data,rdist]
产生 data 的分位数对符号分布 rdist 的分位数的图线.
QuantilePlot[{data1,data2,…},ref]
产生 datai 的分位数对参照分布 ref 的分位数的图线.
更多信息和选项
- QuantilePlot 也称为单参数形式的正态量值图和双参数形式的量值-量值(Q-Q)图.
- QuantilePlot[data1,data2] 与 datai 一起使用,数据或者是一个由实值组成的数据集,或者是一个符号单变量分布组成的数据集.
- QuantilePlot 的数据可以以下列格式给出:
-
{e1,e2,…} 具有或者不具有封装的元素列表 <|k1y1,k2y2,…|> 由键值和长度组成的相关性 TimeSeries[…],EventSeries[…],TemporalData[…] 时间序列、事件序列和时间数据 WeightedData[…],EventData[…] 扩展数据集 w[{e1,e2,…},…] 应用于整个数据集的封装 w[{data1,data1,…},…] 应用于所有数据集的封装 - 对于数据集 list,使用经验性数据,而对于符号分布 dist,使用确切数据.
- 具有符号参数 θi 的 QuantilePlot[data,dist[θ1,…]] 等价于 QuantilePlot[data,EstimatedDistribution[data,dist[θ1,…]]].
- 形式 w[data] 或者 w[dist] 提供了一个封装 w 以应用于所得的图形基元.
- QuantilePlot[Tabular[…]cspec] 用列指定 cspec 从表格对象中提取值并绘制.
- 可使用以下形式的列指定 cspec 来绘制表格数据:
-
colx 绘制列 x 的值 {colx1,colx2,…} 绘制列 x1、x2、… - 可以使用以下封装:
-
Annotation[e,label] 提供一个注解 Button[e,action] 定义一个当元素被点击时执行的操作 EventHandler[e,…] 对元素顶一个一个通用事件句柄 Highlighted[datai,effect] 用某种效果动态突出显示 fi Highlighted[datai,Placed[effect,pos]] 在位置 pos 处用某种效果静态突出显示 fi Hyperlink[e,uri] 使元素作为超链接使用 PopupWindow[e,cont] 对元素附加一个弹出窗口 StatusArea[e,label] 当鼠标移过元素时,在状态栏中显示 Style[e,opts] 显示使用指定样式的元素 Tooltip[e,label] 对元素附加一个任意的工具提示条 - QuantilePlot 具有和 Graphics 相同的选项,另外有以下添加和变动: [所有选项的列表]
-
AspectRatio 1/GoldenRatio 宽高比 ClippingStyle Automatic 在曲线被剪切的位置绘制什么 ColorFunction Automatic 如何确定曲线的着色 ColorFunctionScaling True 是否对 ColorFunction 的变量进行尺度缩放 Filling None 在每条曲线下插入的填充 FillingStyle Automatic 用于填充的样式 Joined Automatic 是否对点进行连接 Mesh None 在每条曲线上绘制的网格点的数目 MeshFunctions {#1&} 如何确定网格点的位置 MeshShading None 如何对网格点之间绘制阴影区域 MeshStyle Automatic 网格点的样式 Method Automatic 使用的方法 PerformanceGoal $PerformanceGoal 尝试优化的性能方面 PlotHighlighting Automatic 曲线的突出显示效果 PlotLegends None 数据点的图例 PlotMarkers None 对数据集指定每个点时所用的记号 PlotRange Automatic 要包括的值范围 PlotRangeClipping True 是否在图线范围进行剪切 PlotStyle Automatic 用于对每个对象指定样式的图形指令 PlotTheme $PlotTheme 图线的整体主题 ReferenceLineStyle Automatic 参考线的样式 ScalingFunctions None 如何对单个坐标进行尺度缩放 WorkingPrecision MachinePrecision 对符合分布的内部计算所用的精度 - 当设置 Filling->Automatic 时,数据集合参考线之间的区域将被填充. 默认情况下,对数据集使用"stems",对符号分布使用“实心”填充. 设置 Joined->True 将对数据集强制使用“实心”填充.
- 提供给函数 MeshFunctions 和 RegionFunction 的变量是
、
. 默认情况下,提供给函数 ColorFunction 的变量是这些变量尺度缩放后的版本. - 当比较两个分布时,设置 Joined->Automatic 等价于 Joined->True,在其他情况下为 Joined->False.
- PlotLegends 的典型设置包括:
-
None 不使用图例 Automatic 自动确定图例 {lbl1,lbl2,…} 将 lbl1, lbl2, … 作为图例标签使用 Placed[lspec,…] 指定图例的位置 - PlotStylesty 指定每条曲线使用的样式. 可能的设置包括:
-
{sty1,sty2,…} 针对各个数据集的一系列样式 <|"key"val,…|> 针对不同层级的数据的样式元素 - 接受的键有:
-
"Base" 所有 datai 的整体样式 "Lists" 针对每个 datai 的样式列表 styi - ColorData["DefaultPlotColors"] 给出 PlotStyle 使用的默认颜色序列.
- 当设置 ReferenceLineStyle->None 时,不绘制参考线.
- Highlighted 和 PlotHighlighting 可用的突出显示效果包括:
-

style 突出显示指定的数据 
"Ball" 突出显示并标注数据中指定的点 
"Dropline" 突出显示并标注数据中指定的点,同时绘制到坐标轴的准线 
"XSlice" 突出显示并标注垂直切片上的所有点 
"YSlice" 突出显示并标注水平切片上的所有点 
Placed[effect,pos] 静态突出显示给定位置 pos - 突出显示的位置指定 pos 包括:
-
x, {x} 在 {x,y} 处突出显示,自动选择 y {x,y} 在 {x,y} 处突出显示 {pos1,pos2,…} 多个位置 posi - 当设置 ScalingFunctions->{sx,sy} 时,
坐标使用 sx 进行尺度缩放,
坐标使用 sy 进行尺度缩放.
所有选项的列表
范例
打开所有单元 关闭所有单元基本范例 (5)
QuantilePlot[RandomVariate[UniformDistribution[{0, 1}], 100]]QuantilePlot[RandomVariate[UniformDistribution[{0, 1}], 100], UniformDistribution[{0, 1}]]data = RandomVariate[StudentTDistribution[4, 2, 3], 200];
QuantilePlot[data, StudentTDistribution[μ, σ, ν]]EstimatedDistribution[data, StudentTDistribution[μ, σ, ν]]data1 = RandomVariate[NormalDistribution[2, 3], 100];
data2 = RandomVariate[StudentTDistribution[4, 2, 3], 200];QuantilePlot[data1, data2]data1 = RandomVariate[NormalDistribution[2, 3], 100];
data2 = RandomVariate[StudentTDistribution[4, 2, 3], 200];QuantilePlot[{data1, data2}, PlotLegends -> {"normal", "Student t"}]范围 (25)
数据和分布 (11)
QuantilePlot 适用于数值数据:
QuantilePlot[RandomVariate[UniformDistribution[{0, 1}], 100]]QuantilePlot 适用于符号式分布:
QuantilePlot[UniformDistribution[{0, 1}]]QuantilePlot[{RandomVariate[NormalDistribution[], 100], RandomVariate[PoissonDistribution[1], 50], WeibullDistribution[2, 2]}]默认的参考分布是最近的估计 NormalDistribution:
data = RandomVariate[UniformDistribution[{0, 1}], 100];
ref = EstimatedDistribution[data, NormalDistribution[a, b]];{QuantilePlot[data], QuantilePlot[data, ref]}data = RandomVariate[UniformDistribution[{0, 1}], 100];{QuantilePlot[data, RandomVariate[NormalDistribution[0, 1], 100]], QuantilePlot[data, NormalDistribution[0, 1]]}data = RandomVariate[UniformDistribution[{0, 1}], 100];QuantilePlot[{data, 2 + data ^ 2}, PlotRange -> All]QuantilePlot[RandomVariate[UniformDistribution[{0, 1}], 100], WeibullDistribution[a, b, c]]data = RandomVariate[UniformDistribution[{0, 1}], 100];QuantilePlot[data, WeibullDistribution[2, 5]]QuantilePlot[data, SmoothKernelDistribution[data]]QuantilePlot[data, TruncatedDistribution[{2, 4}, ExponentialDistribution[1]]]QuantilePlot[<|"a" -> 2, "b" -> 3, "c" -> 5, "d" -> 7, "e" -> 11, "f" -> 13|>]QuantilePlot[<|2 -> 1, 3 -> 2, 5 -> 3, 7 -> 4, 11 -> 5, 13 -> 6|>]data = CountryData["UnitedStates", {{"Population"}, {1988, 2013}}]QuantilePlot[data, AxesLabel -> Automatic]忽略 WeightedData 中的权值:
QuantilePlot[WeightedData[{2, 3, 5, 7, 11, 13, 17, 19, 23, 29}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}]]表格数据 (1)
iris = ResourceData["Sample Tabular Data: Fisher Iris"]QuantilePlot[iris -> "SepalWidth"]QuantilePlot[iris -> {"SepalWidth", "PetalWidth"}]用 PivotToColumns 生成每个品种的 "SepalWidth" 列:
pivot = PivotToColumns[iris, "Species" -> "SepalWidth"]QuantilePlot[pivot -> {ExtendedKey["SepalWidth", "setosa"], ExtendedKey["SepalWidth", "versicolor"], ExtendedKey["SepalWidth", "virginica"]}]QuantilePlot[pivot -> {"setosa", "versicolor", "virginica"}]QuantilePlot[pivot -> {"setosa", "versicolor", "virginica"}, PlotLegends -> {"setosa", "versicolor", "virginica"}]演示 (13)
data = {RandomVariate[NormalDistribution[], 100], RandomVariate[WeibullDistribution[1, 2], 100]};QuantilePlot[data]data = {RandomVariate[NormalDistribution[], 100], RandomVariate[WeibullDistribution[1, 2], 100]};QuantilePlot[data, PlotStyle -> {Blue, Red}]data = {RandomVariate[NormalDistribution[], 100], RandomVariate[WeibullDistribution[1, 2], 100]};QuantilePlot[data, PlotLegends -> {"one", "two"}]QuantilePlot[RandomVariate[UniformDistribution[{0, 1}], 100], FrameLabel -> {"Theoretical Quantiles", "Empirical Quantiles"}, PlotLabel -> "Q-Q Plot", PlotStyle -> Directive[PointSize[Medium], Purple]]QuantilePlot[Range[100], ReferenceLineStyle -> Directive[Dashing[{}], Red]]QuantilePlot[Range[100], ReferenceLineStyle -> None]对数据提供互动 Tooltip:
QuantilePlot[Tooltip[RandomVariate[UniformDistribution[{0, 1}], 100]], PlotStyle -> Directive[PointSize[Medium], Orange]]data = RandomVariate[UniformDistribution[{0, 1}], 100];QuantilePlot[Tooltip[data, BoxWhiskerChart[data]], PlotStyle -> Directive[PointSize[Medium], Magenta]]data1 = RandomReal[NormalDistribution[100, 400], 200];
data2 = RandomReal[UniformDistribution[{5, 400}], 500];QuantilePlot[{data1, data2}, Filling -> {1 -> {2}}, FillingStyle -> {Red, Blue}]QuantilePlot[{{1, 2, 3, 5, 8}, {2, 3, 6, 9, 10}, {4, 5, 7, 10, 12}}, PlotMarkers -> Automatic]使用 Joined 用线连接数据集:
QuantilePlot[{1, 2, 4, 7, 3, 5, 8, 10, 9}, Joined -> True, PlotStyle -> Orange]data = RandomVariate[UniformDistribution[{0, 1}], 100];QuantilePlot[data, PlotTheme -> "Marketing"]QuantilePlot[Range[50]]ListPlot[Callout[Range[50], "hello", 20]]{QuantilePlot[Range[50], PlotHighlighting -> "Dropline"], QuantilePlot[Range[50], PlotHighlighting -> "XSlice"]}选项 (84)
AspectRatio (1)
Axes (1)
AxesLabel (1)
ClippingStyle (4)
QuantilePlot[LogNormalDistribution[0, 1], ClippingStyle -> None]QuantilePlot[LogNormalDistribution[0, 1], ClippingStyle -> Automatic, PlotStyle -> Thick]QuantilePlot[LogNormalDistribution[0, 1], ClippingStyle -> Red]QuantilePlot[LogNormalDistribution[0, 1], PlotRange -> {{-2, 4}, {-2, 4}}, ClippingStyle -> Directive[Red, Thick]]ColorFunction (6)
ColorFunction 要求至少一个数据集被 Joined:
{QuantilePlot[RandomVariate[NormalDistribution[], 100], ColorFunction -> "Rainbow"], QuantilePlot[RandomVariate[NormalDistribution[], 100], ColorFunction -> "Rainbow", Joined -> True]}Table[QuantilePlot[RandomVariate[NormalDistribution[], 100], Joined -> True, ColorFunction -> Function[{x, y}, f], PlotLabel -> f, PlotStyle -> Thick], {f, {Hue[x], Hue[y]}}]QuantilePlot[RandomVariate[NormalDistribution[], 100], Joined -> True, ColorFunction -> "DarkRainbow"]QuantilePlot[RandomVariate[NormalDistribution[1, 2], 100], Joined -> True, ColorFunction -> Function[{x, y}, Hue[x]], Filling -> Automatic]对曲线进行着色时,ColorFunction 具有比 PlotStyle 更高的优先级:
QuantilePlot[RandomVariate[NormalDistribution[1, 2], 100], Joined -> True, ColorFunction -> "DarkRainbow", PlotStyle -> Directive[Red, Thick]]用 MeshShading 中的 Automatic 来使用 ColorFunction:
QuantilePlot[RandomVariate[NormalDistribution[1, 2], 100], Joined -> True, ColorFunction -> "Rainbow", PlotStyle -> Directive[Red, Thick], Mesh -> 9, MeshShading -> {Automatic, StandardGray}, MeshStyle -> None]ColorFunctionScaling (2)
QuantilePlot[RandomVariate[NormalDistribution[], 100], Joined -> True, ColorFunction -> Function[{x, y}, Hue[y]], PlotStyle -> Thick, ColorFunctionScaling -> True]QuantilePlot[RandomVariate[NormalDistribution[], 100], Joined -> True, ColorFunction -> Function[{x, y}, Hue[y]], PlotStyle -> Thick, ColorFunctionScaling -> False]Filling (7)
QuantilePlot[RandomVariate[ParetoDistribution[1, 2], 50], Filling -> Automatic]Table[QuantilePlot[RandomVariate[ParetoDistribution[1, 2], 50], Filling -> c, PlotLabel -> c], {c, {Top, Bottom, Axis, 3}}]QuantilePlot[RandomVariate[ParetoDistribution[1, 2], 50], Filling -> Automatic]QuantilePlot[RandomVariate[ParetoDistribution[1, 2], 50], Filling -> Automatic, Joined -> True]QuantilePlot[{RandomVariate[NormalDistribution[], 14], RandomVariate[PoissonDistribution[1], 10], WeibullDistribution[2, 2]}, Filling -> {3 -> Axis}]QuantilePlot[{RandomVariate[WeibullDistribution[1, 2], 100], RandomVariate[WeibullDistribution[2, 4], 100]}, Joined -> True, Filling -> {1 -> {{2}, Directive[Orange, Dashed]}}]QuantilePlot[{RandomVariate[WeibullDistribution[1, 2], 100], RandomVariate[WeibullDistribution[2, 4], 100]}, Joined -> True, Filling -> {1 -> {{2}, {Yellow, Red}}}]QuantilePlot[{RandomVariate[ParetoDistribution[1, 6], 100], RandomVariate[ParetoDistribution[1, 10], 100]}, Joined -> True, Filling -> {1 -> {{2}, Red}}]FillingStyle (3)
Table[QuantilePlot[ParetoDistribution[1, 10], Filling -> Automatic, FillingStyle -> c], {c, {Red, Green, Blue, Yellow}}]QuantilePlot[Table[ParetoDistribution[x, 4], {x, 1, 2, 1}], Filling -> Bottom, FillingStyle -> Directive[Opacity[0.5], Orange]]QuantilePlot[Range[0, 1, 0.025], Filling -> Automatic, FillingStyle -> {Red, Blue}]Joined (2)
Mesh (4)
在
方向上,使用等间距的20个网格层(mesh level):
QuantilePlot[WeibullDistribution[1, 2], NormalDistribution[], Mesh -> 20]data = RandomVariate[UniformDistribution[{1, 10}], 100];QuantilePlot[data, Joined -> True, MeshFunctions -> {#2&}, Mesh -> {Quantile[data, Range[0.1, 0.9, 0.1]]}]data = RandomVariate[UniformDistribution[{1, 10}], 100];QuantilePlot[data, Joined -> True, Mesh -> {Range[0, 12, 2]}, MeshStyle -> PointSize[Medium]]指定
方向上的 Style 和网格层(mesh levels):
data = RandomVariate[UniformDistribution[{1, 10}], 100];QuantilePlot[data, Joined -> True, Mesh -> {Table[{x, Hue[x / (2)]}, {x, 0., 12, .5}]}]MeshFunctions (2)
Table[QuantilePlot[ParetoDistribution[1, 10], MeshFunctions -> {Function[{x, y}, Evaluate[f]]}, Mesh -> 9, PlotLabel -> f], {f, {x, y}}]在
方向上显示5个网格层(红色),在
方向上显示10个网格层(蓝色):
QuantilePlot[ParetoDistribution[1, 10], Mesh -> {5, 10}, MeshFunctions -> {#1&, #2&}, MeshStyle -> {Directive[PointSize[Medium], Red], Blue}]MeshShading (6)
QuantilePlot[RandomVariate[NormalDistribution[], 100], Joined -> True, Mesh -> 10, MeshShading -> {Red, Blue}]使用 None 来删除线段:
QuantilePlot[RandomVariate[NormalDistribution[], 100], Joined -> True, Mesh -> 10, MeshShading -> {Red, None}]MeshShading 可以与 PlotStyle 一起使用:
QuantilePlot[RandomVariate[NormalDistribution[], 100], Joined -> True, Mesh -> 10, PlotStyle -> Thick, MeshFunctions -> {#1&}, MeshShading -> {Red, Blue}]对曲线进行样式化处理时,MeshShading 具有比 PlotStyle 更高的优先级:
QuantilePlot[RandomVariate[NormalDistribution[], 100], Joined -> True, Mesh -> 10, PlotStyle -> Green, MeshFunctions -> {#1&}, MeshShading -> {Red, Blue}]通过把 MeshShading 设置为 Automatic,对某些线段使用 PlotStyle:
QuantilePlot[RandomVariate[NormalDistribution[], 100], Joined -> True, Mesh -> 10, PlotStyle -> Directive[Thick, Yellow], MeshFunctions -> {#1&}, MeshShading -> {Red, Automatic}]MeshShading 可以与 ColorFunction 一起使用:
QuantilePlot[RandomVariate[NormalDistribution[], 100], Joined -> True, Mesh -> 10, PlotStyle -> Thick, MeshFunctions -> {#1&}, MeshShading -> {StandardGray, Automatic},
ColorFunction -> Function[{x, y}, Hue[x]]]MeshStyle (4)
QuantilePlot[RandomVariate[NormalDistribution[], 100], RandomVariate[NormalDistribution[], 200], Joined -> True, Mesh -> 9, MeshStyle -> Automatic]QuantilePlot[RandomVariate[NormalDistribution[], 100], RandomVariate[NormalDistribution[], 200], Joined -> True, Mesh -> 9, MeshStyle -> Red]QuantilePlot[RandomVariate[NormalDistribution[], 100], Joined -> True, Mesh -> 9, MeshStyle -> {Red, Blue}, MeshFunctions -> {#1&, #2&}]QuantilePlot[RandomVariate[NormalDistribution[], 100], Joined -> True, Mesh -> 10, MeshStyle -> Directive[PointSize[Large], Red]]Method (4)
QuantilePlot[RandomVariate[UniformDistribution[{0, 1}], 100]]QuantilePlot[RandomVariate[UniformDistribution[{0, 1}], 100], Method -> {"ReferenceLineMethod" -> "Fit"}]QuantilePlot[RandomVariate[UniformDistribution[{0, 1}], 100], Method -> {"ReferenceLineMethod" -> "Reference"}]QuantilePlot[RandomVariate[NormalDistribution[], 100], Method -> {"ReferenceLineMethod" -> "Diagonal"}, AspectRatio -> 1, PlotRange -> {{-1, 1}, {-1, 1}}]PlotHighlighting (9)
当设置为默认的 PlotHighlightingAutomatic 时,绘图有交互式坐标标注:
QuantilePlot[Range[0, 1, 0.025]]用 PlotHighlightingNone 禁止整个绘图的突出显示:
QuantilePlot[Range[0, 1, 0.025], PlotHighlighting -> None]QuantilePlot[{Range[0, 1, 0.025], RandomReal[{0, 1}, 41]}, PlotHighlighting -> Directive[Red, AbsolutePointSize[10], DropShadowing[]]]QuantilePlot[Range[0, 1, 0.025], PlotHighlighting -> "Dropline"]QuantilePlot[Range[0, 1, 0.025], PlotHighlighting -> "Dropline"]QuantilePlot[{Range[0, 1, 0.025], RandomReal[{0, 1}, 41]}, PlotHighlighting -> "XSlice"]QuantilePlot[{Range[0, 1, 0.025], RandomReal[{0, 1}, 41]}, PlotHighlighting -> "YSlice"]QuantilePlot[{Range[0, 1, 0.025], RandomReal[{0, 1}, 41]}, PlotHighlighting -> "XNearestPoint"]QuantilePlot[{Range[0, 1, 0.025], RandomReal[{0, 1}, 41]}, PlotHighlighting -> {"XNearestPoint", <|"Style" -> Red|>}]QuantilePlot[{Range[0, 1, 0.025], RandomReal[{0, 1}, 41]}, PlotHighlighting -> "XYLabel"]用 Callout 的选项改变标签的外观:
QuantilePlot[{Range[0, 1, 0.025], RandomReal[{0, 1}, 41]}, PlotHighlighting -> {"XYLabel", <|"Appearance" -> "Corners", "CalloutMarker" -> "Circle"|>}]QuantilePlot[{Range[0, 1, 0.025], RandomReal[{0, 1}, 41]}, PlotHighlighting -> {{"XNearestPoint", <|"Style" -> Red|>}, {"XYLabel", <|"Appearance" -> "Corners", "CalloutMarker" -> "Circle"|>}}]PlotLegends (7)
QuantilePlot[{Sqrt[Range[40]], Log[Range[40]]}]QuantilePlot[{Sqrt[Range[40]], Log[Range[40]]}, PlotLegends -> {"sqrt", "log"}]QuantilePlot[{Sqrt[Range[40]], Log[Range[40]]}, PlotLegends -> "Placeholders"]QuantilePlot[{Sqrt[Range[40]], Log[Range[40]]}, PlotStyle -> {Red, Blue}, PlotLegends -> {"sqrt", "log"}]使用 Placed 来指定图例位置:
QuantilePlot[{Sqrt[Range[40]], Log[Range[40]]}, PlotLegends -> Placed[{"sqrt", "log"}, Below]]QuantilePlot[{Sqrt[Range[40]], Log[Range[40]]}, PlotLegends -> Placed[{"sqrt", "log"}, {0.75, 0.25}]]使用 LineLegend 来改变图例外观:
QuantilePlot[{Sqrt[Range[40]], Log[Range[40]]}, PlotLegends -> LineLegend[{"sqrt", "log"}, LegendFunction -> Frame, LegendMarkers -> None]]PlotMarkers (7)
QuantilePlot 通常使用不同的颜色来区别不同的数据集:
data = Table[RandomVariate[ParetoDistribution[p[[1]], p[[2]]], 20], {p, {{1, 2}, {4, 9}, {5, 7}, {7, 9}}}];QuantilePlot[data, PlotMarkers -> None]data = Table[RandomVariate[ParetoDistribution[p[[1]], p[[2]]], 20], {p, {{1, 2}, {4, 9}, {5, 7}, {7, 9}}}];QuantilePlot[data, PlotMarkers -> Automatic]data = Table[RandomVariate[ParetoDistribution[p[[1]], p[[2]]], 20], {p, {{1, 2}, {4, 9}, {5, 7}, {7, 9}}}];QuantilePlot[data, PlotMarkers -> Automatic, PlotStyle -> StandardGray]data = Table[RandomVariate[ParetoDistribution[p[[1]], p[[2]]], 20], {p, {{1, 2}, {4, 9}, {5, 7}, {7, 9}}}];Table[QuantilePlot[data, PlotMarkers -> {Automatic, s}], {s, {Tiny, Small, Medium, Large}}]data = Table[RandomVariate[ParetoDistribution[p[[1]], p[[2]]], 20], {p, {{1, 2}, {4, 9}, {5, 7}, {7, 9}}}];QuantilePlot[data, PlotMarkers -> {"1", "2", "3", "4"}]data = Table[RandomVariate[ParetoDistribution[p[[1]], p[[2]]], 20], {p, {{1, 2}, {4, 9}, {5, 7}, {7, 9}}}];QuantilePlot[data, PlotMarkers -> {[image], [image], [image], [image]}]data = Table[RandomVariate[ParetoDistribution[p[[1]], p[[2]]], 20], {p, {{1, 2}, {4, 9}, {5, 7}, {7, 9}}}];QuantilePlot[data, PlotMarkers -> {"○"}]PlotRange (3)
自动计算 PlotRange:
QuantilePlot[RandomVariate[LogNormalDistribution[2, 6], 100]]QuantilePlot[RandomVariate[LogNormalDistribution[2, 6], 100], PlotRange -> All]QuantilePlot[RandomVariate[NormalDistribution[], 100], PlotRange -> {{1, 2}, {-1, 3}}]PlotStyle (3)
Table[QuantilePlot[ParetoDistribution[1, 10], PlotStyle -> ps], {ps, {Red, Thick, Dashed, Directive[Red, Thick]}}]QuantilePlot[Table[ParetoDistribution[x, 10], {x, 1, 4, 1}]]QuantilePlot[Table[ParetoDistribution[x, 10], {x, 1, 4, 1}], PlotStyle -> {Red, Green, Blue, Brown}]PlotTheme (2)
ReferenceLineStyle (4)
默认情况下,ReferenceLineStyle 使用 PlotStyle 的 Dotted 形式:
QuantilePlot[WeibullDistribution[2, 4]]QuantilePlot[WeibullDistribution[2, 4], ReferenceLineStyle -> Red]QuantilePlot[WeibullDistribution[2, 4], ReferenceLineStyle -> Directive[Red, Dashing[0]]]使用 None 关闭参考线:
QuantilePlot[WeibullDistribution[2, 4], ReferenceLineStyle -> None]ReferenceLineStyle 可与 PlotStyle 一起使用:
QuantilePlot[WeibullDistribution[2, 4], ReferenceLineStyle -> Thick]应用 (5)
data = RandomVariate[NormalDistribution[], 1000];QuantilePlot[data, NormalDistribution[]]QuantilePlot[data, ParetoDistribution[1, 2]]来自于 LinearModelFit 的残差应该是正态分布的. 这里,一些数据是模拟具有相等方差的正态和指数噪声:
xdat = RandomVariate[UniformDistribution[{0, 100}], 100];
ydat = Table[2x + 3, {x, xdat}];exp = ydat + RandomVariate[ExponentialDistribution[1 / 50], 100];
norm = ydat + RandomVariate[NormalDistribution[0, 50], 100];lmExp = LinearModelFit[Transpose[{xdat, exp}], x, x];
lmNorm = LinearModelFit[Transpose[{xdat, norm}], x, x];{Show[ListPlot[Transpose[{xdat, exp}], PlotLabel -> "Exponential", AxesOrigin -> {0, -100}], Plot[lmExp[x], {x, 0, 100}]], Show[ListPlot[Transpose[{xdat, norm}], PlotLabel -> "Normal", AxesOrigin -> {0, -100}], Plot[lmNorm[x], {x, 0, 100}]]}{QuantilePlot[lmExp["FitResiduals"]], QuantilePlot[lmNorm["FitResiduals"]]}DistributionFitTest 可用于做一个关于正态的定量声明:
DistributionFitTest[lmExp["FitResiduals"]]DistributionFitTest[lmNorm["FitResiduals"]]纽约合唱团的歌手的音高与每个歌手的声音部分一起录制. 声音部分,按音调的增加顺序,包括男低音(Bass),男高音(Tenor),女低音(Alto)和女高音(Soprano):
data = SplitBy[ExampleData[{"Statistics", "SingerHeights"}], Last];Reverse /@ (Mean /@ data)//N//TableForm绘制女高音(Soprano)1 的音高分位数图及其它声音表明音高有一加性位移:
Table[Show[QuantilePlot[i[[All, 1]], data[[1, All, 1]], PlotRange -> {{58, 78}, {58, 78}}, PlotLabel -> i[[1, 2]], ReferenceLineStyle -> None, AspectRatio -> 1, PlotStyle -> StandardGray], Graphics[{StandardGray, Line[{{58, 58}, {78, 78}}]}]], {i, data}]从52朵云中以英亩英尺记录降雨量,其中26个是随机选择的且使用具有氧化银的种子:
rcc = Select[ExampleData[{"Statistics", "RainfallSeeding"}], #1[[2]] === "Control"&][[All, 1]];rsc = Select[ExampleData[{"Statistics", "RainfallSeeding"}], #1[[2]] === "Seeded"&][[All, 1]];QuantilePlot[rsc, rcc, PlotMarkers -> "*", PlotStyle -> StandardGray, Method -> {"ReferenceLineMethod" -> "Diagonal"}]Show[QuantilePlot[rsc, rcc, PlotMarkers -> "*", PlotStyle -> StandardGray, ReferenceLineStyle -> None, ScalingFunctions -> {"Log", "Log"}, PlotRangePadding -> 0], Graphics[Line[{{0, 0}, {8, 8}}]], Graphics[{Dashed, Line[{{0, 1}, {8, 9}}]}]]data1 = RandomVariate[WienerProcess[0, 2][1], 10 ^ 3];
data2 = RandomVariate[WienerProcess[0, 2][15], 10 ^ 3];QuantilePlot[data1, data2]属性和关系 (9)
data = RandomVariate[NormalDistribution[1, 2], 10 ^ 3];{QuantilePlot[data], QuantilePlot[data, NormalDistribution[μ, σ]]}与 UniformDistribution[{0,1}] 进行比较等价于绘制分位数:
data = RandomVariate[ExponentialDistribution[2], 10 ^ 3];{QuantilePlot[data, UniformDistribution[{0, 1}]], Plot[Quantile[data, q], {q, 0, 1}]}ProbabilityPlot 比较数据的累积密度函数(CDF)值:
data = RandomVariate[NormalDistribution[1, 2], 10 ^ 3];ProbabilityPlot[data]ProbabilityScalePlot 缩放坐标轴,这样分布中的点可以在一条直线上:
data = RandomVariate[NormalDistribution[1, 2], 10 ^ 3];ProbabilityScalePlot[data, "Normal"]BoxWhiskerChart 和 DistributionChart 可用于可视化数据分布:
data = RandomVariate[ExponentialDistribution[2], 10 ^ 3];{BoxWhiskerChart[data], DistributionChart[data]}SmoothHistogram 和 Histogram 可用于可视化数据分布:
data = RandomVariate[ExponentialDistribution[2], 10 ^ 3];{SmoothHistogram[data], Histogram[data]}DiscretePlot 可用于可视化离散分布:
{QuantilePlot[PoissonDistribution[3]], DiscretePlot[PDF[PoissonDistribution[3], x], {x, 0, 6}, PlotStyle -> PointSize[Medium]]}使用 ListPlot 观察数据:
data = FindClusters[RandomVariate[ExponentialDistribution[1], 100]];ListPlot[data]当输入是 TimeSeries 时,QuantilePlot 忽略时间戳:
ts = TemporalData[TimeSeries, {{{-0.5225736716034766, 1.5074606136862023, -3.483598294929333,
2.0367319058597637, 2.716015157845711, -0.10037591852519645, 4.977036434534882,
1.8340102505642033, -1.0861663086526394, 3.3604299212539277, 1.135493 ... 4, 3.80797453805332, -2.096829448377324, 1.2606176721990243,
0.9316813021159356, 1.2896204751678497}}, {{0, 999, 1}}, 1, {"Continuous", 1}, {"Discrete", 1},
1, {ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 10.1];{QuantilePlot[ts], QuantilePlot[ts["Values"]]}文本
Wolfram Research (2010),QuantilePlot,Wolfram 语言函数,https://reference.wolfram.com/language/ref/QuantilePlot.html (更新于 2026 年).
CMS
Wolfram 语言. 2010. "QuantilePlot." Wolfram 语言与系统参考资料中心. Wolfram Research. 最新版本 2026. https://reference.wolfram.com/language/ref/QuantilePlot.html.
APA
Wolfram 语言. (2010). QuantilePlot. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/QuantilePlot.html 年
BibTeX
@misc{reference.wolfram_2026_quantileplot, author="Wolfram Research", title="{QuantilePlot}", year="2026", howpublished="\url{https://reference.wolfram.com/language/ref/QuantilePlot.html}", note=[Accessed: 03-November-2026]}
BibLaTeX
@online{reference.wolfram_2026_quantileplot, organization={Wolfram Research}, title={QuantilePlot}, year={2026}, url={https://reference.wolfram.com/language/ref/QuantilePlot.html}, note=[Accessed: 03-November-2026]}