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In mathematics, the trigonometric moment problem is formulated as follows: given a sequence {}, does there exist a distribution function on the interval [,] such that: [1] [2] = (), with = ¯ for . In case the sequence is finite, i.e., { c k } k = 0 n < ∞ {\displaystyle \{c_{k}\}_{k=0}^{n<\infty }} , it is referred to as the truncated ...
The p-th central moment of a measure μ on the measurable space (M, B(M)) about a given point x 0 ∈ M is defined to be (,) (). μ is said to have finite p-th central moment if the p-th central moment of μ about x 0 is finite for some x 0 ∈ M.
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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
In the case m 0 = 1, this is equivalent to the existence of a random variable X supported on [0, 1], such that E[X n] = m n. The essential difference between this and other well-known moment problems is that this is on a bounded interval, whereas in the Stieltjes moment problem one considers a half-line [0, ∞), and in the Hamburger moment ...
In trigonometry, the Snellius–Pothenot problem is a problem first described in the context of planar surveying.Given three known points A, B, C, an observer at an unknown point P observes that the line segment AC subtends an angle α and the segment CB subtends an angle β; the problem is to determine the position of the point P.
In econometrics, the method of simulated moments (MSM) (also called simulated method of moments [1]) is a structural estimation technique introduced by Daniel McFadden. [2] It extends the generalized method of moments to cases where theoretical moment functions cannot be evaluated directly, such as when moment functions involve high-dimensional integrals.
In mathematics, the Hamburger moment problem, named after Hans Ludwig Hamburger, is formulated as follows: given a sequence (m 0, m 1, m 2, ...), does there exist a positive Borel measure μ (for instance, the measure determined by the cumulative distribution function of a random variable) on the real line such that