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Central limit theorems of pedigrees
Journal of Mathematical Biology, 1978Two multivariate central limit theorems are proved for polygenic trait values over a pedigree or collection of pedigrees. These theorems presuppose Hardy-Weinberg and linkage equilibrium for all loci, absence of assortative mating and epistasis, and a small variance for each locus compared to the total variance over many loci.
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2008
At the end of the 17th century, the mathematician Abraham de Moivre first used the normal distribution as an approximation for the percentage of successes in a large number of experiments. Later on, Laplace generalized his results, but it took 20th century mathematics to give an exact and complete description of this subject. So let me now describe the
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At the end of the 17th century, the mathematician Abraham de Moivre first used the normal distribution as an approximation for the percentage of successes in a large number of experiments. Later on, Laplace generalized his results, but it took 20th century mathematics to give an exact and complete description of this subject. So let me now describe the
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Conditional Central Limit Theorem
Theory of Probability & Its Applications, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1981
Here we present some non-trivial limit theorems where the limit is a non-Gaussian self-similar field. The results of the previous chapters may explain at a heuristic level why such results should hold. But a rigorous proof demands much extra work whose consequences may be interesting in themselves.
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Here we present some non-trivial limit theorems where the limit is a non-Gaussian self-similar field. The results of the previous chapters may explain at a heuristic level why such results should hold. But a rigorous proof demands much extra work whose consequences may be interesting in themselves.
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A Counterexample in the Central Limit Theorem
Bulletin of the London Mathematical Society, 1999We construct a \(c_0\)-valued random variable \(X\) such that \((S_n/\sqrt{n})_{n\in N}\) has a convergent subsequence, but \(X\) does not satisfy the central limit theorem (CLT), thus give a counterexample against the subsequence rule in CLT.
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Functional Central Limit Theorems
2008Central limit theorems guarantee that the distributions of properly normalized sums of certain random variables are approximately normal. In many cases, however, a more detailed analysis is necessary. When testing for structural constancy in models, we might be interested in the temporal evolution of our sums.
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1978
Central limit theorems have played a paramount role in probability theory starting—in the case of independent random variables—with the DeMoivreLaplace version and culminating with that of Lindeberg-Feller. The term “central” refers to the pervasive, although nonunique, role of the normal distribution as a limit of d.f.s of normalized sums of ...
Yuan Shih Chow, Henry Teicher
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Central limit theorems have played a paramount role in probability theory starting—in the case of independent random variables—with the DeMoivreLaplace version and culminating with that of Lindeberg-Feller. The term “central” refers to the pervasive, although nonunique, role of the normal distribution as a limit of d.f.s of normalized sums of ...
Yuan Shih Chow, Henry Teicher
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1997
A key ingredient for the asymptotic normality proof, as outlined in Chapter 8, is that the normalized score vector can be expressed as a linear function of random variables ζ n which converge in distribution, cf. Assumption 8.1(g). In this chapter we present central limit theorems (CLTs) which can be used to imply this distributional convergence of ζ n
Benedikt M. Pötscher, Ingmar R. Prucha
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A key ingredient for the asymptotic normality proof, as outlined in Chapter 8, is that the normalized score vector can be expressed as a linear function of random variables ζ n which converge in distribution, cf. Assumption 8.1(g). In this chapter we present central limit theorems (CLTs) which can be used to imply this distributional convergence of ζ n
Benedikt M. Pötscher, Ingmar R. Prucha
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Scandinavian Actuarial Journal, 1944
If X and Y are mutually independent random variables whith the d. f. 1 F 1(χ) and F 2(χ), it is known 2 that the sum X + Y has the d. f. F 2(χ), defined as the convolution where the integrals are Lebesgue-Stiltjes integrals. One uses the abbreviation More generally the sum X 1 + X 2 + … + X n of n mutually independent random variables with the d. f.
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If X and Y are mutually independent random variables whith the d. f. 1 F 1(χ) and F 2(χ), it is known 2 that the sum X + Y has the d. f. F 2(χ), defined as the convolution where the integrals are Lebesgue-Stiltjes integrals. One uses the abbreviation More generally the sum X 1 + X 2 + … + X n of n mutually independent random variables with the d. f.
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2012
The law of large numbers states that the arithmetic mean of independent, identically distributed random variables converges to the expected value. One interpretation of the central limit theorem is as a (distributional) rate result.
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The law of large numbers states that the arithmetic mean of independent, identically distributed random variables converges to the expected value. One interpretation of the central limit theorem is as a (distributional) rate result.
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