On the Distribution of the First Product Moment-Coefficient, in Samples Drawn From an Indefinitely Large Normal Population

Pearson, Karl; Jeffery, G. B.; Elderton, Ethel M.

doi:10.1093/biomet/21.1-4.164

Cited by 27 publications

(9 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Particular cases of this result, for r < 4 , have been deduced by combinatorial and other methods (8,11,12), but the general result has apparently not been given before*, although it follows from the operative solution (12). Such independent derivation of (14) may, if we like, be regarded as an alternative argument for deducing (13) from (12) by writing re' -1 for n.…”

Section: N'mentioning

confidence: 83%

The distribution of second order moment statistics in a normal system

Wishart¹,

Bartlett

1932

Math. Proc. Camb. Phil. Soc.

View full text Add to dashboard Cite

show abstract

Section: N'mentioning

confidence: 83%

The distribution of second order moment statistics in a normal system

Wishart¹,

Bartlett

1932

Math. Proc. Camb. Phil. Soc.

View full text Add to dashboard Cite

show abstract

“…The above distribution was first introduced by Pearson et al [32] and was derived as the law of the difference of two gamma random variables by Mathai [28]. It is also discussed in [21,Sec.…”

Section: From Gamma To Bessel-k Distributionsmentioning

confidence: 99%

Two Metropolis--Hastings Algorithms for Posterior Measures with Non-Gaussian Priors in Infinite Dimensions

Hosseini¹

2019

SIAM/ASA J. Uncertainty Quantification

View full text Add to dashboard Cite

We introduce two classes of Metropolis-Hastings algorithms for sampling target measures that are absolutely continuous with respect to non-Gaussian prior measures on infinite-dimensional Hilbert spaces. In particular, we focus on certain classes of prior measures for which prior-reversible proposal kernels of the autoregressive type can be designed. We then use these proposal kernels to design algorithms that satisfy detailed balance with respect to the target measures. Afterwards, we introduce a new class of prior measures, called the Bessel-K priors, as a generalization of the gamma distribution to measures in infinite dimensions. The Bessel-K priors interpolate between well-known priors such as the gamma distribution and Besov priors and can model sparse or compressible parameters. We present concrete instances of our algorithms for the Bessel-K priors in the context of numerical examples in density estimation, finite-dimensional denoising and deconvolution on the circle.

show abstract

“…To express the distributions of mean values of random samples from exponential and Laplace populations, the functions of the form exp( -b|x|). Jx|" K n (jx|) have been used in [14].…”

Section: F(z) = (Nb X B Y )-L K 0 {Zl(b X B Y )]mentioning

confidence: 99%