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The notions of completely and absolutely monotone function/sequence play an important role in several areas of mathematics. For example, in classical analysis they occur in the proof of the positivity of integrals involving Bessel functions or the positivity of Cesàro means of certain Jacobi series. [ 6 ]
Monotone likelihood-functions are used to construct median-unbiased estimators, using methods specified by Johann Pfanzagl and others. [ 2 ] [ 3 ] One such procedure is an analogue of the Rao–Blackwell procedure for mean-unbiased estimators : The procedure holds for a smaller class of probability distributions than does the Rao–Blackwell ...
In real analysis, a branch of mathematics, Bernstein's theorem states that every real-valued function on the half-line [0, ∞) that is totally monotone is a mixture of exponential functions. In one important special case the mixture is a weighted average , or expected value .
In the mathematical field of numerical analysis, monotone cubic interpolation is a variant of cubic interpolation that preserves monotonicity of the data set being interpolated. Monotonicity is preserved by linear interpolation but not guaranteed by cubic interpolation .
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Download QR code; Print/export Download as PDF; Printable version; In other projects ... where X is a real Hilbert space is said to be strongly monotone if
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