Estimation and bimodality testing in the cusp model

Jan Voříšek

Kybernetika (2018)

  • Volume: 54, Issue: 4, page 798-814
  • ISSN: 0023-5954

Abstract

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The probability density function of the stochastic cusp model belongs to the class of generalized exponential distributions. It accommodates variable skewness, kurtosis, and bimodality. A statistical test for bimodality of the stochastic cusp model using the maximum likelihood estimation and delta method for Cardan's discriminant is introduced in this paper, as is a necessary condition for bimodality, which can be used for simplified testing to reject bimodality. Numerical maximum likelihood estimation of the cusp model is simplified by analytical reduction of the parameter space dimension, and connection to the method of moment estimates is shown. A simulation study is used to determine the size and power of the proposed tests and to compare pertinence among different tests for various parameter settings.

How to cite

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Voříšek, Jan. "Estimation and bimodality testing in the cusp model." Kybernetika 54.4 (2018): 798-814. <http://eudml.org/doc/294693>.

@article{Voříšek2018,
abstract = {The probability density function of the stochastic cusp model belongs to the class of generalized exponential distributions. It accommodates variable skewness, kurtosis, and bimodality. A statistical test for bimodality of the stochastic cusp model using the maximum likelihood estimation and delta method for Cardan's discriminant is introduced in this paper, as is a necessary condition for bimodality, which can be used for simplified testing to reject bimodality. Numerical maximum likelihood estimation of the cusp model is simplified by analytical reduction of the parameter space dimension, and connection to the method of moment estimates is shown. A simulation study is used to determine the size and power of the proposed tests and to compare pertinence among different tests for various parameter settings.},
author = {Voříšek, Jan},
journal = {Kybernetika},
keywords = {multimodal distributions; cusp model; bimodality test; reduced maximum likelihood estimation},
language = {eng},
number = {4},
pages = {798-814},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Estimation and bimodality testing in the cusp model},
url = {http://eudml.org/doc/294693},
volume = {54},
year = {2018},
}

TY - JOUR
AU - Voříšek, Jan
TI - Estimation and bimodality testing in the cusp model
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 4
SP - 798
EP - 814
AB - The probability density function of the stochastic cusp model belongs to the class of generalized exponential distributions. It accommodates variable skewness, kurtosis, and bimodality. A statistical test for bimodality of the stochastic cusp model using the maximum likelihood estimation and delta method for Cardan's discriminant is introduced in this paper, as is a necessary condition for bimodality, which can be used for simplified testing to reject bimodality. Numerical maximum likelihood estimation of the cusp model is simplified by analytical reduction of the parameter space dimension, and connection to the method of moment estimates is shown. A simulation study is used to determine the size and power of the proposed tests and to compare pertinence among different tests for various parameter settings.
LA - eng
KW - multimodal distributions; cusp model; bimodality test; reduced maximum likelihood estimation
UR - http://eudml.org/doc/294693
ER -

References

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