{"product_id":"9789048147694","title":"Unimodality of Probability Measures (Mathematics and Its Applications)","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.\n\u003cbr\u003eNot 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","brand":"Springer","offers":[{"title":"Default Title","offer_id":49170432983267,"sku":"00000_00000_00000_00000","price":169.99,"currency_code":"USD","in_stock":true}],"url":"https:\/\/usa.kinokuniya.com\/products\/9789048147694","provider":"Books Kinokuniya USA","version":"1.0","type":"link"}