Lorentzian function

Article summary

the probability density function of the Cauchy distribution

Key claims

1. P18: http://commons.wikimedia.org/wiki/Special:FilePath/Cauchy%20pdf.svg — source: Wikidata · confidence 0.95
2. P2534: <math class="mwe-math-element mwe-math-element-inline mathjax_ignore" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo>;</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>,</mo><mi>γ</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>π</mi><mi>γ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mn>1</mn><mo stretchy="false">+</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>x</mi><mo stretchy="false">−</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>γ</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">]</mo></mrow></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>π</mi></mrow></mfrac><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mfrac><mrow><mi>γ</mi></mrow><mrow><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">−</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac><mo data-mjx-texclass="CLOSE">]</mo></mrow></mstyle></mrow></math> — source: Wikidata · confidence 0.95
3. P2671: /g/121kwxxp — source: Wikidata · confidence 0.95
4. P279: Q5189500 — source: Wikidata · confidence 0.95
5. P7235: <math class="mwe-math-element mwe-math-element-inline mathjax_ignore" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>f</mi></mstyle></mrow></math> — source: Wikidata · confidence 0.95
6. P7235: <math class="mwe-math-element mwe-math-element-inline mathjax_ignore" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mstyle></mrow></math> — source: Wikidata · confidence 0.95
7. P7235: <math class="mwe-math-element mwe-math-element-inline mathjax_ignore" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>x</mi></mstyle></mrow></math> — source: Wikidata · confidence 0.95
8. P7235: <math class="mwe-math-element mwe-math-element-inline mathjax_ignore" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>γ</mi></mstyle></mrow></math> — source: Wikidata · confidence 0.95

Discussion questions

1. Summarise the article in your own words. Which single claim would you verify first, and why?
2. The record states that the P18 is "http://commons.wikimedia.org/wiki/Special:FilePath/Cauchy%20pdf.svg". What evidence would count against this claim?
3. The record states that the P2534 is "<math class="mwe-math-element mwe-math-element-inline mathjax_ignore" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo>;</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>,</mo><mi>γ</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>π</mi><mi>γ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mn>1</mn><mo stretchy="false">+</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>x</mi><mo stretchy="false">−</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>γ</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">]</mo></mrow></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>π</mi></mrow></mfrac><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mfrac><mrow><mi>γ</mi></mrow><mrow><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">−</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac><mo data-mjx-texclass="CLOSE">]</mo></mrow></mstyle></mrow></math>". What evidence would count against this claim?
4. The record states that the P2671 is "/g/121kwxxp". What evidence would count against this claim?
5. The record states that the P279 is "Q5189500". What evidence would count against this claim?
6. The record states that the P7235 is "<math class="mwe-math-element mwe-math-element-inline mathjax_ignore" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>f</mi></mstyle></mrow></math>". What evidence would count against this claim?
7. The record states that the P7235 is "<math class="mwe-math-element mwe-math-element-inline mathjax_ignore" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mstyle></mrow></math>". What evidence would count against this claim?
8. The record states that the P7235 is "<math class="mwe-math-element mwe-math-element-inline mathjax_ignore" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>x</mi></mstyle></mrow></math>". What evidence would count against this claim?
9. The record states that the P7235 is "<math class="mwe-math-element mwe-math-element-inline mathjax_ignore" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>γ</mi></mstyle></mrow></math>". What evidence would count against this claim?
10. Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
11. If two sources disagreed about one of these facts, what would you need in order to trust one over the other?

Bibliography

No sources recorded.