Unimodality of Probability Measures:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1997
|
| Schriftenreihe: | Mathematics and Its Applications
382 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Labor omnia vincit improbus. VIRGIL, Georgica I, 144-145. In the first part of his Theoria combinationis observationum erroribus min imis obnoxiae, published in 1821, Carl Friedrich Gauss [Gau80, p.10] deduces a Chebyshev-type inequality for a probability density function, when it only has the property that its value always decreases, or at least does l not increase, if the absolute value of x increases . One may therefore conjecture that Gauss is one of the first scientists to use the property of 'single-humpedness' of a probability density function in a meaningful probabilistic context. More than seventy years later, zoologist W.F.R. Weldon was faced with 'double humpedness'. Indeed, discussing peculiarities of a population of Naples crabs, possi bly connected to natural selection, he writes to Karl Pearson (E.S. Pearson [Pea78, p.328]): Out of the mouths of babes and sucklings hath He perfected praise! In the last few evenings I have wrestled with a double humped curve, and have overthrown it. Enclosed is the diagram... If you scoff at this, I shall never forgive you. Not only did Pearson not scoff at this bimodal probability density function, he examined it and succeeded in decomposing it into two 'single-humped curves' in his first statistical memoir (Pearson [Pea94]) |
| Beschreibung: | 1 Online-Ressource (XIV, 256 p) |
| ISBN: | 9789401588089 9789048147694 |
| DOI: | 10.1007/978-94-015-8808-9 |
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| 500 | |a Labor omnia vincit improbus. VIRGIL, Georgica I, 144-145. In the first part of his Theoria combinationis observationum erroribus min imis obnoxiae, published in 1821, Carl Friedrich Gauss [Gau80, p.10] deduces a Chebyshev-type inequality for a probability density function, when it only has the property that its value always decreases, or at least does l not increase, if the absolute value of x increases . One may therefore conjecture that Gauss is one of the first scientists to use the property of 'single-humpedness' of a probability density function in a meaningful probabilistic context. More than seventy years later, zoologist W.F.R. Weldon was faced with 'double humpedness'. Indeed, discussing peculiarities of a population of Naples crabs, possi bly connected to natural selection, he writes to Karl Pearson (E.S. Pearson [Pea78, p.328]): Out of the mouths of babes and sucklings hath He perfected praise! In the last few evenings I have wrestled with a double humped curve, and have overthrown it. Enclosed is the diagram... If you scoff at this, I shall never forgive you. Not only did Pearson not scoff at this bimodal probability density function, he examined it and succeeded in decomposing it into two 'single-humped curves' in his first statistical memoir (Pearson [Pea94]) | ||
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Datensatz im Suchindex
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| discipline | Mathematik |
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| language | English |
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| spelling | Bertin, Emile M. J. Verfasser aut Unimodality of Probability Measures by Emile M. J. Bertin, Ioan Cuculescu, Radu Theodorescu Dordrecht Springer Netherlands 1997 1 Online-Ressource (XIV, 256 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 382 Labor omnia vincit improbus. VIRGIL, Georgica I, 144-145. In the first part of his Theoria combinationis observationum erroribus min imis obnoxiae, published in 1821, Carl Friedrich Gauss [Gau80, p.10] deduces a Chebyshev-type inequality for a probability density function, when it only has the property that its value always decreases, or at least does l not increase, if the absolute value of x increases . One may therefore conjecture that Gauss is one of the first scientists to use the property of 'single-humpedness' of a probability density function in a meaningful probabilistic context. More than seventy years later, zoologist W.F.R. Weldon was faced with 'double humpedness'. Indeed, discussing peculiarities of a population of Naples crabs, possi bly connected to natural selection, he writes to Karl Pearson (E.S. Pearson [Pea78, p.328]): Out of the mouths of babes and sucklings hath He perfected praise! In the last few evenings I have wrestled with a double humped curve, and have overthrown it. Enclosed is the diagram... If you scoff at this, I shall never forgive you. Not only did Pearson not scoff at this bimodal probability density function, he examined it and succeeded in decomposing it into two 'single-humped curves' in his first statistical memoir (Pearson [Pea94]) Mathematics Functional equations Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Difference and Functional Equations Mathematik Statistik Choquet-Kapazität (DE-588)4425296-1 gnd rswk-swf Choquet-Kapazität (DE-588)4425296-1 s 1\p DE-604 Cuculescu, Ioan Sonstige oth Theodorescu, Radu Sonstige oth https://doi.org/10.1007/978-94-015-8808-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bertin, Emile M. J. Unimodality of Probability Measures Mathematics Functional equations Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Difference and Functional Equations Mathematik Statistik Choquet-Kapazität (DE-588)4425296-1 gnd |
| subject_GND | (DE-588)4425296-1 |
| title | Unimodality of Probability Measures |
| title_auth | Unimodality of Probability Measures |
| title_exact_search | Unimodality of Probability Measures |
| title_full | Unimodality of Probability Measures by Emile M. J. Bertin, Ioan Cuculescu, Radu Theodorescu |
| title_fullStr | Unimodality of Probability Measures by Emile M. J. Bertin, Ioan Cuculescu, Radu Theodorescu |
| title_full_unstemmed | Unimodality of Probability Measures by Emile M. J. Bertin, Ioan Cuculescu, Radu Theodorescu |
| title_short | Unimodality of Probability Measures |
| title_sort | unimodality of probability measures |
| topic | Mathematics Functional equations Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Difference and Functional Equations Mathematik Statistik Choquet-Kapazität (DE-588)4425296-1 gnd |
| topic_facet | Mathematics Functional equations Distribution (Probability theory) Statistics Probability Theory and Stochastic Processes Statistics, general Difference and Functional Equations Mathematik Statistik Choquet-Kapazität |
| url | https://doi.org/10.1007/978-94-015-8808-9 |
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