Asymptotic normality of the test statistics for the unified relative dispersion and relative variation indexes

Touré, Aboubacar Y.; Dossou-Gbété, Simplice; Kokonendji, Célestin C.

doi:10.1080/02664763.2020.1779193

Cited by 8 publications

(10 citation statements)

References 22 publications

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“…According to [16] and following the recent univariate unification of the well-known (Fisher) dispersion and the (Jørgensen) variation indexes by Touré et al [24], the relative variability index of d-variate nonnegative orthant distributions can be written as follows. Let X and Y be two random vectors on the same support T + d ⊆ [0, ∞) d and assume m := EX = EY, Σ X := covX and V F Y (m) := cov(Y) fixed, then the relative variability index of X with respect to Y is defined as the positive quantity…”

Section: Relative Variability Indexes For Orthant Distributionsmentioning

confidence: 99%

“…It concerns three measurements (with n = 42) of drinking water pumps installed in the Sahel. The first variable X 1 represents the failure times (in months) and, also, it is recently used by Touré et al [24]. The second variable X 2 refers to the distance (in kilometers) between each water pump and the repair center in the Sahel, while the third one X 3 stands for average volume (in m 3 ) of water per day.…”

Section: Semicontinuous Datasetsmentioning

confidence: 99%

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Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Kokonendji

Somé

2021

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Multivariate nonnegative orthant data are real vectors bounded to the left by the null vector, and they can be continuous, discrete or mixed. We first review the recent relative variability indexes for multivariate nonnegative continuous and count distributions. As a prelude, the classification of two comparable distributions having the same mean vector is done through under-, equi- and over-variability with respect to the reference distribution. Multivariate associated kernel estimators are then reviewed with new proposals that can accommodate any nonnegative orthant dataset. We focus on bandwidth matrix selections by adaptive and local Bayesian methods for semicontinuous and counting supports, respectively. We finally introduce a flexible semiparametric approach for estimating all these distributions on nonnegative supports. The corresponding estimator is directed by a given parametric part, and a nonparametric part which is a weight function to be estimated through multivariate associated kernels. A diagnostic model is also discussed to make an appropriate choice between the parametric, semiparametric and nonparametric approaches. The retention of pure nonparametric means the inconvenience of parametric part used in the modelization. Multivariate real data examples in semicontinuous setup as reliability are gradually considered to illustrate the proposed approach. Concluding remarks are made for extension to other multiple functions.

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Section: Relative Variability Indexes For Orthant Distributionsmentioning

confidence: 99%

Section: Semicontinuous Datasetsmentioning

confidence: 99%

Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Kokonendji

Somé

2021

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“…, µ d ) and correlation matrix ρ. See, e.g., Appendix According to [31] and following the recent univariate unification of the wellknown (Fisher) dispersion and the (Jørgensen) variation indexes by Touré et al [55], the relative variability index of d-variate nonnegative orthant distributions can be written as follows. Let X and Y be two random vectors on the same support…”

Section: Relative Variability Indexes For Orthant Distributionsmentioning

confidence: 99%

“…It concerns three measurements (with n = 42) of drinking water pumps installed in the Sahel. The first variable X 1 represents the failure times (in months) and, also, it is recently used by Touré et al [55]. The second variable X 2 refers to the distance (in kilometers) between each water pump and the repair center in the Sahel, while the third one X 3 stands for average volume (in m 3 ) of water per day.…”

Section: Semicontinuous Datasetsmentioning

confidence: 99%

Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Kokonendji,

Somé

2021

Preprint

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Multivariate nonnegative orthant data are real vectors bounded to the left by the null vector, and they can be continuous, discrete or mixed. We first review the recent relative variability indexes for multivariate nonnegative continuous and count distributions. As a prelude, the classification of two comparable distributions having the same mean vector is done through under-, equi-and over-variability with respect to the reference distribution. Multivariate associated kernel estimators are then reviewed with new proposals that can accommodate any nonnegative orthant dataset. We focus on bandwidth matrix selections by adaptive and local Bayesian methods for semicontinuous and counting supports, respectively. We finally introduce a flexible semiparametric approach for estimating all these distributions on nonnegative supports. The corresponding estimator is directed by a given parametric part, and a nonparametric part which is a weight function to be estimated through multivariate associated kernels. A diagnostic model is also discussed to make an appropriate choice between the parametric, semiparametric and nonparametric approaches. The retention of pure nonparametric means the inconvenience of parametric part used in the modelization. Multivariate real data examples in semicontinuous setup as reliability are gradually considered to illustrate the proposed approach. Concluding remarks are made for extension to other multiple functions.

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“…The infinite number of probability distributions requires the study of different indexes for comparisons between them. Touré et al [38] restrict to the set of distributions with finite variance which is a subset of the set of all light-tailed distributions. The authors use plug-in principle and obtain estimators of relative dispersion and the relative variation indexes with respect to the relative variability of a nonnegative natural exponential family of distributions.…”

Section: Extremes and Tailsmentioning

confidence: 99%

Editorial to special issue V WCDANM 2018

Stehlík

Grilo

Jordanova

2020

Journal of Applied Statistics

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Branching processesBulgarian probabilistic school has long traditions in studying branching processes. Tchorbadjieff and Mayster [36] start with a very good summary of the contemporary results in this area. The authors study a linear birth-death process starting with a random number of particles. At first, they consider the cases when the initial distribution follows different standard probabilistic distributions -Negative Binomial and its closest Geometric, Poisson or Pólya-Aeppli distributions. They proved analytically and numerically that the random initial conditions can not change the critical parameter of branching mechanism, but they CONTACT M.

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Asymptotic normality of the test statistics for the unified relative dispersion and relative variation indexes

Cited by 8 publications

References 22 publications

Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Editorial to special issue V WCDANM 2018

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