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In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph.If the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total mass) is the center of mass, and the second moment is the moment of inertia.
Moments are usually defined with respect to a fixed reference point and refer to physical quantities located some distance from the reference point. For example, the moment of force, often called torque, is the product of a force on an object and the distance from the reference point to the object. In principle, any physical quantity can be ...
Example: Given the mean and variance (as well as all further cumulants equal 0) the normal distribution is the distribution solving the moment problem. In mathematics , a moment problem arises as the result of trying to invert the mapping that takes a measure μ {\displaystyle \mu } to the sequence of moments
The essential difference between this and other well-known moment problems is that this is on a half-line [0, ∞), whereas in the Hausdorff moment problem one considers a bounded interval [0, 1], and in the Hamburger moment problem one considers the whole line (−∞, ∞).
The Stieltjes moment problems and the Hamburger moment problems, if they are solvable, may have infinitely many solutions (indeterminate moment problem) whereas a Hausdorff moment problem always has a unique solution if it is solvable (determinate moment problem). In the indeterminate moment problem case, there are infinite measures ...
Some Questions in the Theory of Moments. Translations of mathematical monographs. American Mathematical Society. ISBN 978-0-8218-1552-6. Geronimus, J. (1946). "On the Trigonometric Moment Problem". Annals of Mathematics. 47 (4): 742– 761. doi:10.2307/1969232. ISSN 0003-486X. JSTOR 1969232. Schmüdgen, Konrad (2017). The Moment Problem ...
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Pages in category "Moment (mathematics)" The following 25 pages are in this category, out of 25 total. ... Moment measure; Moment problem; Moment-generating function; O.
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