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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.
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
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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.
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
In probability and statistics, a moment measure is a mathematical quantity, function or, more precisely, measure that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both.