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On log-bimodal alpha-power distributions with application to nickel contents and erosion data

On log-bimodal alpha-power distributions with application to nickel contents and erosion data AbstractIn this paper, we present a new parametric class of distributions based on the log-alpha-power distribution, which contains the well-known log-normal distribution as a special case. This new family is useful to deal with unimodal as well as bimodal data with asymmetry and kurtosis coefficients ranging far from that expected based on the log-normal distribution. The usual approach is considered to perform inferences, and the traditional maximum likelihood method is employed to estimate the unknown parameters. Monte Carlo simulation results indicate that the maximum likelihood approach is quite effective to estimate the model parameters. We also derive the observed and expected Fisher information matrices. As a byproduct of such study, it is shown that the Fisher information matrix is nonsingular throughout the sample space. Empirical applications of the proposed family of distributions to real data are provided for illustrative purposes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematica Slovaca de Gruyter

On log-bimodal alpha-power distributions with application to nickel contents and erosion data

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Publisher
de Gruyter
Copyright
© 2021 Mathematical Institute Slovak Academy of Sciences
ISSN
0139-9918
eISSN
1337-2211
DOI
10.1515/ms-2021-0072
Publisher site
See Article on Publisher Site

Abstract

AbstractIn this paper, we present a new parametric class of distributions based on the log-alpha-power distribution, which contains the well-known log-normal distribution as a special case. This new family is useful to deal with unimodal as well as bimodal data with asymmetry and kurtosis coefficients ranging far from that expected based on the log-normal distribution. The usual approach is considered to perform inferences, and the traditional maximum likelihood method is employed to estimate the unknown parameters. Monte Carlo simulation results indicate that the maximum likelihood approach is quite effective to estimate the model parameters. We also derive the observed and expected Fisher information matrices. As a byproduct of such study, it is shown that the Fisher information matrix is nonsingular throughout the sample space. Empirical applications of the proposed family of distributions to real data are provided for illustrative purposes.

Journal

Mathematica Slovacade Gruyter

Published: Dec 20, 2021

Keywords: bimodality; maximum likelihood estimation; parametric inference; Primary 60E05; 62F10

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