By Norman L. Johnson, Samuel Kotz, N. Balakrishnan
This monograph offers an in depth description of significant statistical distributions which are regularly occurring in a variety of utilized parts corresponding to engineering, enterprise, economics and behavioural, organic and environmental sciences. It offers a close description of common and particular non-stop distributions. those distributions are utilized in reliability and communique engineering, enterprise and economics
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Additional resources for Continuous univariate distributions. Vol.1
Example text
Consider a diffuse prior for one dimensional parameter π(θ), θ ∈ A . If the parameter of interest θ ranges over A ∈ (−∞, a), A ∈ (b, ∞) or A ∈ (−∞, ∞) with constant values a and b, then the integral of the diffuse prior does not exist. 3. 2 The Jeffreys’ prior Jeffreys (1961) proposed a general rule for the choice of a noninformative prior. It is proportional to the square root of the determinant of the Fisher information matrix: π(θ) ∝ |J(θ)| 1/2 . The Fisher information is given as J(θ) = − ∂ 2 log f (x|θ) f (x|θ)dx, ∂θ∂θT where the expactation is taken with respect to the sampling distribution of x.
2 The Jeffreys’ prior Jeffreys (1961) proposed a general rule for the choice of a noninformative prior. It is proportional to the square root of the determinant of the Fisher information matrix: π(θ) ∝ |J(θ)| 1/2 . The Fisher information is given as J(θ) = − ∂ 2 log f (x|θ) f (x|θ)dx, ∂θ∂θT where the expactation is taken with respect to the sampling distribution of x. The Jeffreys’ prior gives an automated method for finding a noninformative prior for any parametric model. Also, it is known that the Jeffreys’ prior is invariant to transformation.
See also Pastor (2000) and Pastor and Stambaugh (2000). 4 Bioinformatics: Tumor classification with gene expression data With the recently developed microarray technology, we can measure thousands of genes’ expression profiles simultaneously. In the bioinformatics field, a prediction of the tumor type of a new individual based on the gene expression profile is one of the most important research topics. Through the instrumentality of useful information included in gene expression profiles, a number of systematic methods to identify tumor types using gene expression data have been applied to tumor classification (see for example, Alon et al.