STATISTICAL INFERENCE OF EXPONENTIAL RECORD DATA UNDER KULLBACK-LEIBLER DIVERGENCE MEASURE

We consider the maximum likelihood and Bayesian estimation of parameters and prediction of future records of the Weibull distribution from δ -record data, which consists of records and near-records. We discuss existence, consistency and numerical computation of estimators and predictors. The performance of the proposed methodology is assessed by Montecarlo simulations and the analysis of monthly rainfall series. Our conclusion is that inferences for the Weibull model, based on δ -record data, clearly improve inferences based solely on records. This methodology can be recommended, more so as near-records can be collected along with records, keeping essentially the same experimental design.

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Overlap coefficients based on Kullback-Leibler divergence: Exponential populations case

International Journal of Applied Mathematical Research ◽

10.14419/ijamr.v6i4.8493 ◽

2017 ◽

Vol 6 (4) ◽

pp. 135

Author(s):

Hamza Dhaker ◽

Papa Ngom ◽

Malick Mbodj

Keyword(s):

Statistical Inference ◽

Mean Square Error ◽

Confidence Intervals ◽

Taylor Series ◽

Simulation Study ◽

Invariance Property ◽

Mean Square ◽

Taylor Series Approximation ◽

Leibler Divergence ◽

Exponential Populations

This article is devoted to the study of overlap measures of densities of two exponential populations. Various Overlapping Coefficients, namely: Matusita’s measure ρ, Morisita’s measure λ and Weitzman’s measure ∆. A new overlap measure Λ based on Kullback-Leibler measure is proposed. The invariance property and a method of statistical inference of these coefficients also are presented. Taylor series approximation are used to construct confidence intervals for the overlap measures. The bias and mean square error properties of the estimators are studied through a simulation study.

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A Generalized Divergence Measure for Nonnegative Matrix Factorization

Neural Computation ◽

10.1162/neco.2007.19.3.780 ◽

2007 ◽

Vol 19 (3) ◽

pp. 780-791 ◽

Cited By ~ 92

Author(s):

Raul Kompass

Keyword(s):

Matrix Factorization ◽

Nonnegative Matrix Factorization ◽

Nonnegative Matrix ◽

Auxiliary Function ◽

Divergence Measure ◽

Factorization Problem ◽

Special Cases ◽

Leibler Divergence ◽

Update Rules ◽

Quadratic Distance

This letter presents a general parametric divergence measure. The metric includes as special cases quadratic error and Kullback-Leibler divergence. A parametric generalization of the two different multiplicative update rules for nonnegative matrix factorization by Lee and Seung (2001) is shown to lead to locally optimal solutions of the nonnegative matrix factorization problem with this new cost function. Numeric simulations demonstrate that the new update rule may improve the quadratic distance convergence speed. A proof of convergence is given that, as in Lee and Seung, uses an auxiliary function known from the expectation-maximization theoretical framework.

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