| Unimodality of Probability Measures 1997 Edition Contributor(s): Bertin, Emile M. J. (Author), Cuculescu, I. (Author), Theodorescu, Radu (Author) |
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ISBN: 0792343182 ISBN-13: 9780792343189 Publisher: Springer OUR PRICE: $161.49 Product Type: Hardcover - Other Formats Published: November 1996 |
| Additional Information |
| BISAC Categories: - Mathematics | Probability & Statistics - General - Mathematics | Mathematical Analysis - Mathematics | Differential Equations - General |
| Dewey: 519.2 |
| LCCN: 96048825 |
| Series: Mathematics and Its Applications |
| Physical Information: 0.63" H x 6.14" W x 9.21" (1.23 lbs) 256 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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]). |