A Log-Dagum Weibull Distribution: Properties and Characterization

Aneeqa Khadim; Aamir Saghir; Tassadaq Hussain; Mohammad Shakil; Mohammad Ahsanullah

doi:doi:10.11648/j.acm.20211005.11

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A Log-Dagum Weibull Distribution: Properties and Characterization

Aneeqa Khadim, Aamir Saghir, Tassadaq Hussain, Mohammad Shakil, Mohammad Ahsanullah

Published in Applied and Computational Mathematics (Volume 10, Issue 5)

Received: 10 September 2021 Accepted: 27 September 2021 Published: 12 October 2021

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Abstract

This article proposes a new family of continuous distributions generated from a log dagum random variable (named Log-Dagum Weibull Distribution) on the basis of T-X family technique. mathematical and statistical properties including survival function, hazard and reverse hazard function, Rth moments, L-moments, incomplete rth moments, quantile points, Order Statistics, Bonferroni and Lorenz curves as well as entropy measures for this class of distributions are presented also LDW distribution characterized by truncated moments order statistics and upper record values. Simulation study of the proposed family of distribution has been derived. The model parameters are obtained by the method of maximum likelihood estimation. We illustrate the performance of the proposed new family of distributions by means of four real data sets and the data sets show the new family of distributions is more appropriate as compared to Exponentiated exponential distribution (EED), Weibull distribution (WD), Gamma distribution (GD), NEED Nadarajah Exponentiated exponential distribution and Lomax distribution (LD). Moreover, perfection of competing models is also tested via the Kolmogrov-Simnorov (K S), the Anderson Darling (A^*) and the Cramer-von Misses (W^*). The measures of goodness of fit including the Akaike information criterion (AIC), consistent Akaike information criterion (CAIC), Bayesian information criterion (BIC), Hannan-Quinn information criterion (HQIC) are computed to compare the fitted models.

Published in	Applied and Computational Mathematics (Volume 10, Issue 5)
DOI	10.11648/j.acm.20211005.11
Page(s)	100-113
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), 2024. Published by Science Publishing Group

Keywords

Probability Distributions, Log-Dagum Distribution, Parameter Estimation, Weibull Distribution

References

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APA Style

Aneeqa Khadim, Aamir Saghir, Tassadaq Hussain, Mohammad Shakil, Mohammad Ahsanullah. (2021). A Log-Dagum Weibull Distribution: Properties and Characterization. Applied and Computational Mathematics, 10(5), 100-113. https://doi.org/10.11648/j.acm.20211005.11

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ACS Style

Aneeqa Khadim; Aamir Saghir; Tassadaq Hussain; Mohammad Shakil; Mohammad Ahsanullah. A Log-Dagum Weibull Distribution: Properties and Characterization. Appl. Comput. Math. 2021, 10(5), 100-113. doi: 10.11648/j.acm.20211005.11

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AMA Style

Aneeqa Khadim, Aamir Saghir, Tassadaq Hussain, Mohammad Shakil, Mohammad Ahsanullah. A Log-Dagum Weibull Distribution: Properties and Characterization. Appl Comput Math. 2021;10(5):100-113. doi: 10.11648/j.acm.20211005.11

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@article{10.11648/j.acm.20211005.11,
  author = {Aneeqa Khadim and Aamir Saghir and Tassadaq Hussain and Mohammad Shakil and Mohammad Ahsanullah},
  title = {A Log-Dagum Weibull Distribution: Properties and Characterization},
  journal = {Applied and Computational Mathematics},
  volume = {10},
  number = {5},
  pages = {100-113},
  doi = {10.11648/j.acm.20211005.11},
  url = {https://doi.org/10.11648/j.acm.20211005.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20211005.11},
  abstract = {This article proposes a new family of continuous distributions generated from a log dagum random variable (named Log-Dagum Weibull Distribution) on the basis of T-X family technique. mathematical and statistical properties including survival function, hazard and reverse hazard function, Rth moments, L-moments, incomplete rth moments, quantile points, Order Statistics, Bonferroni and Lorenz curves as well as entropy measures for this class of distributions are presented also LDW distribution characterized by truncated moments order statistics and upper record values. Simulation study of the proposed family of distribution has been derived. The model parameters are obtained by the method of maximum likelihood estimation. We illustrate the performance of the proposed new family of distributions by means of four real data sets and the data sets show the new family of distributions is more appropriate as compared to Exponentiated exponential distribution (EED), Weibull distribution (WD), Gamma distribution (GD), NEED Nadarajah Exponentiated exponential distribution and Lomax distribution (LD). Moreover, perfection of competing models is also tested via the Kolmogrov-Simnorov (K S), the Anderson Darling (A*) and the Cramer-von Misses (W*). The measures of goodness of fit including the Akaike information criterion (AIC), consistent Akaike information criterion (CAIC), Bayesian information criterion (BIC), Hannan-Quinn information criterion (HQIC) are computed to compare the fitted models.},
 year = {2021}
}

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TY  - JOUR
T1  - A Log-Dagum Weibull Distribution: Properties and Characterization
AU  - Aneeqa Khadim
AU  - Aamir Saghir
AU  - Tassadaq Hussain
AU  - Mohammad Shakil
AU  - Mohammad Ahsanullah
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DO  - 10.11648/j.acm.20211005.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
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EP  - 113
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20211005.11
AB  - This article proposes a new family of continuous distributions generated from a log dagum random variable (named Log-Dagum Weibull Distribution) on the basis of T-X family technique. mathematical and statistical properties including survival function, hazard and reverse hazard function, Rth moments, L-moments, incomplete rth moments, quantile points, Order Statistics, Bonferroni and Lorenz curves as well as entropy measures for this class of distributions are presented also LDW distribution characterized by truncated moments order statistics and upper record values. Simulation study of the proposed family of distribution has been derived. The model parameters are obtained by the method of maximum likelihood estimation. We illustrate the performance of the proposed new family of distributions by means of four real data sets and the data sets show the new family of distributions is more appropriate as compared to Exponentiated exponential distribution (EED), Weibull distribution (WD), Gamma distribution (GD), NEED Nadarajah Exponentiated exponential distribution and Lomax distribution (LD). Moreover, perfection of competing models is also tested via the Kolmogrov-Simnorov (K S), the Anderson Darling (A*) and the Cramer-von Misses (W*). The measures of goodness of fit including the Akaike information criterion (AIC), consistent Akaike information criterion (CAIC), Bayesian information criterion (BIC), Hannan-Quinn information criterion (HQIC) are computed to compare the fitted models.
VL  - 10
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Author Information

Aneeqa Khadim

Department of Mathematics, Faculty of Sciences, Mirpur University of Science and Technology (MUST), Mirpur, Pakistan
Aamir Saghir

Department of Mathematics, Faculty of Sciences, Mirpur University of Science and Technology (MUST), Mirpur, Pakistan
Tassadaq Hussain

Department of Mathematics, Faculty of Sciences, Mirpur University of Science and Technology (MUST), Mirpur, Pakistan
Mohammad Shakil

Department of Liberal Arts and Sciences, Faculty of Mathematics, Miami Dade College, Hialeah, USA
Mohammad Ahsanullah

Department of Management Sciences, Rider University, Lawrenceville, USA

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APA Style

Aneeqa Khadim, Aamir Saghir, Tassadaq Hussain, Mohammad Shakil, Mohammad Ahsanullah. (2021). A Log-Dagum Weibull Distribution: Properties and Characterization. Applied and Computational Mathematics, 10(5), 100-113. https://doi.org/10.11648/j.acm.20211005.11

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ACS Style

Aneeqa Khadim; Aamir Saghir; Tassadaq Hussain; Mohammad Shakil; Mohammad Ahsanullah. A Log-Dagum Weibull Distribution: Properties and Characterization. Appl. Comput. Math. 2021, 10(5), 100-113. doi: 10.11648/j.acm.20211005.11

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AMA Style

Aneeqa Khadim, Aamir Saghir, Tassadaq Hussain, Mohammad Shakil, Mohammad Ahsanullah. A Log-Dagum Weibull Distribution: Properties and Characterization. Appl Comput Math. 2021;10(5):100-113. doi: 10.11648/j.acm.20211005.11

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@article{10.11648/j.acm.20211005.11,
  author = {Aneeqa Khadim and Aamir Saghir and Tassadaq Hussain and Mohammad Shakil and Mohammad Ahsanullah},
  title = {A Log-Dagum Weibull Distribution: Properties and Characterization},
  journal = {Applied and Computational Mathematics},
  volume = {10},
  number = {5},
  pages = {100-113},
  doi = {10.11648/j.acm.20211005.11},
  url = {https://doi.org/10.11648/j.acm.20211005.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20211005.11},
  abstract = {This article proposes a new family of continuous distributions generated from a log dagum random variable (named Log-Dagum Weibull Distribution) on the basis of T-X family technique. mathematical and statistical properties including survival function, hazard and reverse hazard function, Rth moments, L-moments, incomplete rth moments, quantile points, Order Statistics, Bonferroni and Lorenz curves as well as entropy measures for this class of distributions are presented also LDW distribution characterized by truncated moments order statistics and upper record values. Simulation study of the proposed family of distribution has been derived. The model parameters are obtained by the method of maximum likelihood estimation. We illustrate the performance of the proposed new family of distributions by means of four real data sets and the data sets show the new family of distributions is more appropriate as compared to Exponentiated exponential distribution (EED), Weibull distribution (WD), Gamma distribution (GD), NEED Nadarajah Exponentiated exponential distribution and Lomax distribution (LD). Moreover, perfection of competing models is also tested via the Kolmogrov-Simnorov (K S), the Anderson Darling (A*) and the Cramer-von Misses (W*). The measures of goodness of fit including the Akaike information criterion (AIC), consistent Akaike information criterion (CAIC), Bayesian information criterion (BIC), Hannan-Quinn information criterion (HQIC) are computed to compare the fitted models.},
 year = {2021}
}

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TY  - JOUR
T1  - A Log-Dagum Weibull Distribution: Properties and Characterization
AU  - Aneeqa Khadim
AU  - Aamir Saghir
AU  - Tassadaq Hussain
AU  - Mohammad Shakil
AU  - Mohammad Ahsanullah
Y1  - 2021/10/12
PY  - 2021
N1  - https://doi.org/10.11648/j.acm.20211005.11
DO  - 10.11648/j.acm.20211005.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 100
EP  - 113
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20211005.11
AB  - This article proposes a new family of continuous distributions generated from a log dagum random variable (named Log-Dagum Weibull Distribution) on the basis of T-X family technique. mathematical and statistical properties including survival function, hazard and reverse hazard function, Rth moments, L-moments, incomplete rth moments, quantile points, Order Statistics, Bonferroni and Lorenz curves as well as entropy measures for this class of distributions are presented also LDW distribution characterized by truncated moments order statistics and upper record values. Simulation study of the proposed family of distribution has been derived. The model parameters are obtained by the method of maximum likelihood estimation. We illustrate the performance of the proposed new family of distributions by means of four real data sets and the data sets show the new family of distributions is more appropriate as compared to Exponentiated exponential distribution (EED), Weibull distribution (WD), Gamma distribution (GD), NEED Nadarajah Exponentiated exponential distribution and Lomax distribution (LD). Moreover, perfection of competing models is also tested via the Kolmogrov-Simnorov (K S), the Anderson Darling (A*) and the Cramer-von Misses (W*). The measures of goodness of fit including the Akaike information criterion (AIC), consistent Akaike information criterion (CAIC), Bayesian information criterion (BIC), Hannan-Quinn information criterion (HQIC) are computed to compare the fitted models.
VL  - 10
IS  - 5
ER  -

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