{"product_id":"unimodality-of-probability-measures-von-emile-m-j-bertin-i-cuculescu-radu-theodorescu","title":"Unimodality of Probability Measures","description":"\u003cp\u003eLabor 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]).\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9780792343189\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9789048147694\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Hardcover - 9780792343189","offer_id":50725957574,"sku":"9780792343189","price":160.49,"currency_code":"EUR","in_stock":true},{"title":"Softcover - 9789048147694","offer_id":39415522558045,"sku":"9789048147694","price":160.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/c0792840-3be6-47c3-bf9c-cd781d351dd1.jpg?v=1772261627","url":"https:\/\/shop.autorenwelt.de\/products\/unimodality-of-probability-measures-von-emile-m-j-bertin-i-cuculescu-radu-theodorescu","provider":"Autorenwelt Shop","version":"1.0","type":"link"}