Performance Analysis of Powers of Skewness and Kurtosis Based Multivariate Normality Tests and Use of Extended Monte Carlo Simulation for Proposed Novelty Algorithm

Vishwa Nath Maurya; Ram Bilas Misra; Chandra K. Jaggi; Avadhesh Kumar Maurya

doi:doi:10.11648/j.ajtas.s.2015040201.12

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Performance Analysis of Powers of Skewness and Kurtosis Based Multivariate Normality Tests and Use of Extended Monte Carlo Simulation for Proposed Novelty Algorithm

Vishwa Nath Maurya, Ram Bilas Misra, Chandra K. Jaggi, Avadhesh Kumar Maurya

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 2-1)

Received: 12 December 2014 Accepted: 13 December 2014 Published: 11 March 2015

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Abstract

An ample study of the comparative powers of a number of omnibus multivariate normality tests is main object in this paper. Since testing for multivariate normality tests is considerably more challenging process than for testing of univariate one and therefore, study of testing for multivariate normality tests has its increasing demand. Through this paper, we have explored several techniques for assessing multivariate normality (MVN) and as well as comparative analysis for their competence have also been demonstrated. The results of extensive Monte Carlo simulation study of the size corrected power of various tests of multivariate normality for drawn samples from contaminated normal distributions have been explored as well. Moreover, a novel algorithm has been proposed in order to evaluate the size corrected powers for testing multivariate normality. The algorithm proposed herein is a fast easily implementable algorithm and it can be applied for both types of univariate and multivariate normality tests. Using Different omnibus tests for sample size 50 and 200, graphs for empirical powers of multivariate normal data with lower and upper contamination have been presented. Finally, some significant conclusions of our present study have been drawn.

Published in	American Journal of Theoretical and Applied Statistics (Volume 4, Issue 2-1) This article belongs to the Special Issue Scope of Statistical Modeling and Optimization Techniques in Management Decision Making Process
DOI	10.11648/j.ajtas.s.2015040201.12
Page(s)	11-18
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Multivariate Normality Tests, Goodness-of-Fit Tests, Correlation Coefficient, Skewness, Kurtosis, Monte Carlo Simulation Technique

References

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APA Style

Vishwa Nath Maurya, Ram Bilas Misra, Chandra K. Jaggi, Avadhesh Kumar Maurya. (2015). Performance Analysis of Powers of Skewness and Kurtosis Based Multivariate Normality Tests and Use of Extended Monte Carlo Simulation for Proposed Novelty Algorithm. American Journal of Theoretical and Applied Statistics, 4(2-1), 11-18. https://doi.org/10.11648/j.ajtas.s.2015040201.12

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ACS Style

Vishwa Nath Maurya; Ram Bilas Misra; Chandra K. Jaggi; Avadhesh Kumar Maurya. Performance Analysis of Powers of Skewness and Kurtosis Based Multivariate Normality Tests and Use of Extended Monte Carlo Simulation for Proposed Novelty Algorithm. Am. J. Theor. Appl. Stat. 2015, 4(2-1), 11-18. doi: 10.11648/j.ajtas.s.2015040201.12

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AMA Style

Vishwa Nath Maurya, Ram Bilas Misra, Chandra K. Jaggi, Avadhesh Kumar Maurya. Performance Analysis of Powers of Skewness and Kurtosis Based Multivariate Normality Tests and Use of Extended Monte Carlo Simulation for Proposed Novelty Algorithm. Am J Theor Appl Stat. 2015;4(2-1):11-18. doi: 10.11648/j.ajtas.s.2015040201.12

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@article{10.11648/j.ajtas.s.2015040201.12,
  author = {Vishwa Nath Maurya and Ram Bilas Misra and Chandra K. Jaggi and Avadhesh Kumar Maurya},
  title = {Performance Analysis of Powers of Skewness and Kurtosis Based Multivariate Normality Tests and Use of Extended Monte Carlo Simulation for Proposed Novelty Algorithm},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {2-1},
  pages = {11-18},
  doi = {10.11648/j.ajtas.s.2015040201.12},
  url = {https://doi.org/10.11648/j.ajtas.s.2015040201.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.s.2015040201.12},
  abstract = {An ample study of the comparative powers of a number of omnibus multivariate normality tests is main object in this paper. Since testing for multivariate normality tests is considerably more challenging process than for testing of univariate one and therefore, study of testing for multivariate normality tests has its increasing demand. Through this paper, we have explored several techniques for assessing multivariate normality (MVN) and as well as comparative analysis for their competence have also been demonstrated. The results of extensive Monte Carlo simulation study of the size corrected power of various tests of multivariate normality for drawn samples from contaminated normal distributions have been explored as well. Moreover, a novel algorithm has been proposed in order to evaluate the size corrected powers for testing multivariate normality. The algorithm proposed herein is a fast easily implementable algorithm and it can be applied for both types of univariate and multivariate normality tests. Using Different omnibus tests for sample size 50 and 200, graphs for empirical powers of multivariate normal data with lower and upper contamination have been presented. Finally, some significant conclusions of our present study have been drawn.},
 year = {2015}
}

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TY  - JOUR
T1  - Performance Analysis of Powers of Skewness and Kurtosis Based Multivariate Normality Tests and Use of Extended Monte Carlo Simulation for Proposed Novelty Algorithm
AU  - Vishwa Nath Maurya
AU  - Ram Bilas Misra
AU  - Chandra K. Jaggi
AU  - Avadhesh Kumar Maurya
Y1  - 2015/03/11
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.s.2015040201.12
DO  - 10.11648/j.ajtas.s.2015040201.12
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 11
EP  - 18
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.s.2015040201.12
AB  - An ample study of the comparative powers of a number of omnibus multivariate normality tests is main object in this paper. Since testing for multivariate normality tests is considerably more challenging process than for testing of univariate one and therefore, study of testing for multivariate normality tests has its increasing demand. Through this paper, we have explored several techniques for assessing multivariate normality (MVN) and as well as comparative analysis for their competence have also been demonstrated. The results of extensive Monte Carlo simulation study of the size corrected power of various tests of multivariate normality for drawn samples from contaminated normal distributions have been explored as well. Moreover, a novel algorithm has been proposed in order to evaluate the size corrected powers for testing multivariate normality. The algorithm proposed herein is a fast easily implementable algorithm and it can be applied for both types of univariate and multivariate normality tests. Using Different omnibus tests for sample size 50 and 200, graphs for empirical powers of multivariate normal data with lower and upper contamination have been presented. Finally, some significant conclusions of our present study have been drawn.
VL  - 4
IS  - 2-1
ER  -

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Author Information

Vishwa Nath Maurya

Department of Pure & Applied Mathematics and Statistics, School of Science & Technology, The University of Fiji, Lautoka, Fiji Islands
Ram Bilas Misra

Division of Applied Mathematics, State University of New York, Incheon, Republic of Korea & Ex-Vice Chancellor, Dr. R. M. L. Avadh University, Faizabad, UP, India
Chandra K. Jaggi

Department of Operations Research, University of Delhi, New Delhi, India
Avadhesh Kumar Maurya

Department of Electronics & Communication Engineering, Lucknow Institute of Technology, U. P. Technical University, Lucknow, India

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Vishwa Nath Maurya, Ram Bilas Misra, Chandra K. Jaggi, Avadhesh Kumar Maurya. (2015). Performance Analysis of Powers of Skewness and Kurtosis Based Multivariate Normality Tests and Use of Extended Monte Carlo Simulation for Proposed Novelty Algorithm. American Journal of Theoretical and Applied Statistics, 4(2-1), 11-18. https://doi.org/10.11648/j.ajtas.s.2015040201.12

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ACS Style

Vishwa Nath Maurya; Ram Bilas Misra; Chandra K. Jaggi; Avadhesh Kumar Maurya. Performance Analysis of Powers of Skewness and Kurtosis Based Multivariate Normality Tests and Use of Extended Monte Carlo Simulation for Proposed Novelty Algorithm. Am. J. Theor. Appl. Stat. 2015, 4(2-1), 11-18. doi: 10.11648/j.ajtas.s.2015040201.12

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AMA Style

Vishwa Nath Maurya, Ram Bilas Misra, Chandra K. Jaggi, Avadhesh Kumar Maurya. Performance Analysis of Powers of Skewness and Kurtosis Based Multivariate Normality Tests and Use of Extended Monte Carlo Simulation for Proposed Novelty Algorithm. Am J Theor Appl Stat. 2015;4(2-1):11-18. doi: 10.11648/j.ajtas.s.2015040201.12

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@article{10.11648/j.ajtas.s.2015040201.12,
  author = {Vishwa Nath Maurya and Ram Bilas Misra and Chandra K. Jaggi and Avadhesh Kumar Maurya},
  title = {Performance Analysis of Powers of Skewness and Kurtosis Based Multivariate Normality Tests and Use of Extended Monte Carlo Simulation for Proposed Novelty Algorithm},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {2-1},
  pages = {11-18},
  doi = {10.11648/j.ajtas.s.2015040201.12},
  url = {https://doi.org/10.11648/j.ajtas.s.2015040201.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.s.2015040201.12},
  abstract = {An ample study of the comparative powers of a number of omnibus multivariate normality tests is main object in this paper. Since testing for multivariate normality tests is considerably more challenging process than for testing of univariate one and therefore, study of testing for multivariate normality tests has its increasing demand. Through this paper, we have explored several techniques for assessing multivariate normality (MVN) and as well as comparative analysis for their competence have also been demonstrated. The results of extensive Monte Carlo simulation study of the size corrected power of various tests of multivariate normality for drawn samples from contaminated normal distributions have been explored as well. Moreover, a novel algorithm has been proposed in order to evaluate the size corrected powers for testing multivariate normality. The algorithm proposed herein is a fast easily implementable algorithm and it can be applied for both types of univariate and multivariate normality tests. Using Different omnibus tests for sample size 50 and 200, graphs for empirical powers of multivariate normal data with lower and upper contamination have been presented. Finally, some significant conclusions of our present study have been drawn.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Performance Analysis of Powers of Skewness and Kurtosis Based Multivariate Normality Tests and Use of Extended Monte Carlo Simulation for Proposed Novelty Algorithm
AU  - Vishwa Nath Maurya
AU  - Ram Bilas Misra
AU  - Chandra K. Jaggi
AU  - Avadhesh Kumar Maurya
Y1  - 2015/03/11
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.s.2015040201.12
DO  - 10.11648/j.ajtas.s.2015040201.12
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 11
EP  - 18
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.s.2015040201.12
AB  - An ample study of the comparative powers of a number of omnibus multivariate normality tests is main object in this paper. Since testing for multivariate normality tests is considerably more challenging process than for testing of univariate one and therefore, study of testing for multivariate normality tests has its increasing demand. Through this paper, we have explored several techniques for assessing multivariate normality (MVN) and as well as comparative analysis for their competence have also been demonstrated. The results of extensive Monte Carlo simulation study of the size corrected power of various tests of multivariate normality for drawn samples from contaminated normal distributions have been explored as well. Moreover, a novel algorithm has been proposed in order to evaluate the size corrected powers for testing multivariate normality. The algorithm proposed herein is a fast easily implementable algorithm and it can be applied for both types of univariate and multivariate normality tests. Using Different omnibus tests for sample size 50 and 200, graphs for empirical powers of multivariate normal data with lower and upper contamination have been presented. Finally, some significant conclusions of our present study have been drawn.
VL  - 4
IS  - 2-1
ER  -

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