Rényi information, loglikelihood and an intrinsic distribution measure

By Kai-Sheng Song. 2001

148 citations recorded by the source corpus.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/64767f9e0b49f09cef8acafecfb252a1e3a34ef7

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Citations in the corpus

General results for the Marshall and Olkin's family of distributions (2013, unknown): “It is a location and scale-free positive functional and measures the intrinsic shape of a distribution (see, Song 2001). ej = ej (α) = αδ (1– α) j Г (2 δ + j) Г (2 δ)j!”
The Relation between Evenness and Diversity (2010, unknown): “The logarithm of the diversity profile is known in statistics as the Renyi entropy spectrum of the community [24].”
An extended Lomax distribution (2013, background): “For further details, the reader is referred to 31 .”
Exponentiated $T$-$X$ Family of Distributions with Some Applications (2013, methodology): “The result follows from Theorem 1 by using the mean μT = γ Γ(1 + 1/α) and the Shannon entropy ηT = υ(1 − 1/α) − log(α/γ) + 1 for the Weibull distribution (Song, 2001).”
Limit theory for point processes in manifolds (2011, background): “The gradient limρ→1(dH ∗/dρ) equals (−1/2)Var[logκ(Y1)], a measure of the shape of the distribution [29, 43] which also appears in the statement of Theorem 2.”
Rényi divergence measures for commonly used univariate continuous distributions (2013, methodology): “Closed-form expressions for differential Shannon and Rényi entropies for several univariate continuous distributions are presented in the work by Song [30].”
A generalized normal distribution (2005, background): “Song (2001) observed that the gradient of the Renyi entropy <inline-graphic xmlns:xlink="http://www.”
A new lifetime model with decreasing failure rate (2010, methodology): “ession for the Renyi entropy because it serves as a measure of the shape of a distribution and can be used to compare the tails and shapes of various frequently used densities; for more details, see Song (2001). 5 Estimation and inference Let X 1;:::;X n be a random sample from EPL(;) distribution w”
The Heavy-Tailed Exponential Distribution: Risk Measures, Estimation, and Application to Actuarial Data (2020, methodology): “Furthermore, Song [24] developed a log-likelihood-based distribution measure using the Rényi information which exists for all distributions and allows for meaningful comparisons between distributions than the traditional kurtosis measure.”