예제: 코쉬 분포

함수 > 통계 > 확률 분포 > 예제: 코쉬 분포

예제: 코쉬 분포

1. 코쉬 분포의 정의를 표시합니다.

여기서

◦ l은 위치 매개변수(평균)입니다.

◦ s는 배율 매개변수(분산의 제곱근)이며 s > 0입니다.

2. 위치 및 배율 매개변수 집합 세 개를 정의한 다음 위치 및 배율 매개변수 l0 및 s0에서 곡선의 진폭(또는 높이)을 계산합니다.

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3. dcauchy 함수를 사용하여 서로 다른 값의 위치 매개변수와 고정 배율 매개변수에서 값 x에 대한 확률 밀도를 구합니다.

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 l<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript>
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 <id xml:space="preserve">
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 </id>
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 <math resultRef="257">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
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서로 다른 위치 매개변수 값은 X축 방향으로 곡선을 이동합니다.

4. 고정된 위치 매개변수와 서로 다른 배율 매개변수 값을 사용하여 dcauchy 함수를 도표화합니다.

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서로 다른 배율 매개변수 값은 곡선의 높이를 변경합니다.

5. 서로 다른 위치 매개변수와 배율 매개변수 값을 사용하여 dcauchy 함수를 도표화합니다.

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서로 다른 배율 및 위치 매개변수는 곡선을 이동하고 곡선의 높이를 변경합니다.

6. 서로 다른 값의 위치 매개변수와 고정 배율 매개변수를 사용하여 pcauchy 함수를 도표화합니다.

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◦ 서로 다른 위치 매개변수 값은 X축 방향으로 곡선을 이동합니다.

◦ pcauchy의 모든 y 값은 0과 1 사이에 있습니다.

7. 고정된 위치 매개변수와 서로 다른 배율 매개변수 값을 사용하여 pcauchy 함수를 도표화합니다.

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◦ 서로 다른 배율 매개변수 값은 곡선을 수평 방향으로 평평하게 만들지만 모든 곡선은 y=0.5에서 교차합니다.

◦ pcauchy의 모든 y 값은 0과 1 사이에 있습니다.

8. 서로 다른 값의 위치 매개변수와 고정 배율 매개변수를 사용하여 qcauchy 함수를 도표화합니다.

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 <id xml:space="preserve">x</id>
 <id xml:space="preserve">
 l<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript>
 </id>
 <id xml:space="preserve">
 s<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript>
 </id>
 </sequence>
 </apply>
 </math>
 <math resultRef="422">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 <plotEquation>
 <math resultRef="423">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id labels="FUNCTION" xml:space="preserve">qcauchy</id>
 <sequence>
 <id xml:space="preserve">x</id>
 <id xml:space="preserve">
 l<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript>
 </id>
 <id xml:space="preserve">
 s<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript>
 </id>
 </sequence>
 </apply>
 </math>
 <math resultRef="424">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 </plotEquations>
 <xyDomain scale-type="linear" auto-scale="true">
 <startValue resultRef="414">
 <real xmlns="http://schemas.mathsoft.com/math50">-15</real>
 </startValue>
 <secondTickValue resultRef="416">
 <real xmlns="http://schemas.mathsoft.com/math50">-10</real>
 </secondTickValue>
 <endValue resultRef="418">
 <real xmlns="http://schemas.mathsoft.com/math50">15</real>
 </endValue>
 </xyDomain>
 </yAxis>
 </axes>
 </xyPlot>
 </plot>
</region>

◦ 서로 다른 위치 매개변수 값은 Y축 방향으로 곡선을 이동합니다.

◦ qcauchy의 모든 x 값은 0과 1 사이에 있습니다.

9. 고정 위치 및 배율 매개변수를 사용하여 rcauchy 함수를 계산합니다.

<region id="ID0EKPRBB" top="3648.0000000000005" left="38.400000000000006" height="27.791200000000003" width="169.31666666666666" xmlns="http://schemas.mathsoft.com/worksheet50">
 <math resultRef="442">
 <define xmlns="http://schemas.mathsoft.com/math50">
 <id labels="VARIABLE" xml:space="preserve">R</id>
 <parens>
 <apply>
 <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">rcauchy</id>
 <sequence>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">m</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 l<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript>
 </id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">
 s<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript>
 </id>
 </sequence>
 </apply>
 </parens>
 </define>
 <resultFormat>
 <matrix size="12,12" offset="0,0" show-indices="true" expand-nested-arrays="true" />
 </resultFormat>
 </math>
</region>

함수 rcauchy는 코쉬 분포에 따라 난수 m개의 벡터를 구합니다.

10. rcauchy 함수로 구한 난수를 도표화합니다.

<region id="ID0EKRRBB" top="3744.0000000000005" left="38.400000000000006" height="288" width="576.39999999999986" xmlns="http://schemas.mathsoft.com/worksheet50">
 <plot background-type="white" origin-positioning="true">
 <xyPlot>
 <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
 <legend />
 <traces>
 <trace resultRef="444">
 <traceStyle color="#FFED1D2F" symbol="filledStar" line-weight="2" line-style="None">lines</traceStyle>
 </trace>
 </traces>
 <graph-size width="476.4" height="230.4" />
 <axes>
 <xAxis rank="1" legend-position="PlotBoundaryBottom" start="0" end="50">
 <axisLine position="origin" positionticmark="6" legendWidth="61.7533333333333" />
 <axisGrid>
 <gridFrequency>6</gridFrequency>
 <gridLabels display="true" />
 <gridLines />
 <tickMarks display="true" />
 </axisGrid>
 <axisLabel />
 <markers />
 <plotEquations>
 <plotEquation>
 <math resultRef="451">
 <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">n</id>
 </math>
 <math resultRef="452">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 </plotEquations>
 <xyDomain scale-type="linear" auto-scale="true">
 <startValue resultRef="446">
 <real xmlns="http://schemas.mathsoft.com/math50">0</real>
 </startValue>
 <secondTickValue resultRef="448">
 <real xmlns="http://schemas.mathsoft.com/math50">10</real>
 </secondTickValue>
 <endValue resultRef="450">
 <real xmlns="http://schemas.mathsoft.com/math50">50</real>
 </endValue>
 </xyDomain>
 </xAxis>
 <yAxis rank="1" legend-position="PlotBoundaryLeft" start="-12" end="8">
 <axisLine position="origin" positionticmark="0" legendWidth="69.59" />
 <axisGrid>
 <gridFrequency>11</gridFrequency>
 <gridLabels display="true" />
 <gridLines />
 <tickMarks display="true" />
 </axisGrid>
 <axisLabel />
 <markers />
 <plotEquations>
 <plotEquation>
 <math resultRef="453">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <indexer />
 <id xml:space="preserve">R</id>
 <id xml:space="preserve">n</id>
 </apply>
 </math>
 <math resultRef="454">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 </plotEquations>
 <xyDomain scale-type="linear" auto-scale="true">
 <startValue>
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </startValue>
 <endValue>
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </endValue>
 </xyDomain>
 </yAxis>
 </axes>
 </xyPlot>
 </plot>
</region>

워크시트를 다시 계산하면 rcauchy 함수가 새 난수 집합을 구하고, 그에 따라 도표가 업데이트됩니다.