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

| Peer-Reviewed

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

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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), 2021. Published by Science Publishing Group

Keywords

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

References

[1]	Alzaghal, A., Lee C., and Famoye, C. F. (2013). Exponentiated T-X family of distributions with some applications. International Journal of Probability Statistics, 2, 31-49.
[2]	Ahmad, Z.(2018). A new generalized class of distributions properties and estimation based on type I censored samples. Annals of Data Science https://doi.org/10.1007/s40745-018-0160-5.
[3]	Alzaatreh, A., Famoye, F., and Lee, C. (2013). A new method for generating families of continuous distributions. Metron, 71, 63-79.
[4]	Alzaatreh, A., Famoye, F. and Lee, C. (2014). The gamma-normal distribution properties and applications. Computational statistics and data analysis, 69, 67–80.
[5]	Alexander, C., Cordeiro, G., Ortega, E., and Sarabia, C. (2012). Generalized beta- generated distributions. Computational statistics and data analysis, 56, 1880-1897.
[6]	Aslam, M., Asghar, Z., Hussain, Z., and Farooq, S. S. (2020). A modified T-X family of distributions classical and bayesian analysis. Journal of Taibah University for Science, 1, 254–264.
[7]	Amini, M., Mir Mostafaee, S. J., and Ahmadi, J. (2014). Log-gamma-generated families of distributions. Statistics, 2014, 748-775.
[8]	Ahsanullah, M. (1995). Record Statistics, Nova Science Publishers, New York, USA.
[9]	Ahsanullah, M., Nevzorov, V. B., and Shakil, M. (2013a). An Introduction to Order Statistics Press, Paris, France.
[10]	Ahsanullah, M., Shakil, M., and Kibria, B. (2016). Characterizations of Continuous Distributions by Truncated Moment, Journal of Modern Applied Statistical Methods, 1, 316-331.
[11]	Ahsanullah, M., (2017). Characterization of Univariate Continuous Distributions, Atlantis-Press, Paris, France.
[12]	Arnold, B. C., Balakrishnan, and Nagaraja, H. N., (2005). First Course in Order Statistics Wiley, New York, USA.
[13]	Bourguignon, M., Silva, R., and Cordeiro, G., (2014). The Weibull-G family of probability distribution. Journal of data Science, 12, 53-68.
[14]	Cordeiro, G., de Castro, M., (2011). A new family of generalized distributions. Computational statistics and data analysis, 81, 883-893.
[15]	Cordeiro, G., Ortega, E., Da Cunha, D., (2013). The exponentiated generalized class of distributions. Journal of data Science, 11, 1-27.
[16]	Cordeiro, G. M., Alizadeh, M., and Diniz, M. P. R., (2016). The type I half-logistic family of distributions. Journal of statistical computation and simulation, 86, 707–728.
[17]	Cordeiro, G. M., Alizadeh, M., and Ortega, E. M. M. (2014). The exponentiated half-logistic family of distribution properties and applications. Journal of probability and statistics.
[18]	David, H. A., and Nagaraja, H. N. (2003). Order Statistics, Third Edition, Wiley, New York, USA.
[19]	Eugene, N., Lee, C., and Famoye, F. (2002). Beta-normal distribution and its applications. Communications in statistics Theory and Methods, 31, 497–512.
[20]	Jamal, F., and Nasir, M. (2019). Some new members of The T-X family of distributions. 17th International conference on statistical sciences Lahore, Pakistan, hal-01965176v3.
[21]	Hamed, D., and Alzaghal, A. (2021). New Class of Lindley Distribution. J. Stat. Distrib. App 8, 11.
[22]	Handique, L., Akbar, M., Mohsin, M., and Jamal, F. (2021). Properties and applications of a new member of the T-X family of distributions. Thailand statistician, 19, 248-260.
[23]	Hassan, A. S., Elgarhy, M. (2016). Kumaraswamy weibull-generated family of distributions with applications. Advances and applications in statistics, 48, 205–239.
[24]	Nevzorov, V. B. (2001). Records: Mathematical Theory-Translation of Mathematical Monograph, American Mathematical Society, Rhode Island, USA.
[25]	Nasiru, S., Mwita, N. P., and Ngesa, O. (2017). Exponentiated generalized exponential dagum distribution, Journal of King Saud University – Science, 31, 362–371.
[26]	Ristic, M., Balakrishnan N. (2012). The gamma-exponentiated exponential distribution. Journal of Statistical Computation and Simulation, 82, 1191-1206.
[27]	Rafique, A., and Saud, N. (2021). Some Characterizations of Unimodal, Reserve J-Shaped Distribution. 18th International Conference on Statistical Sciences Lahore, Pakistan, 35, 18-20.
[28]	Shakil, M., Ahsanullah, M., and Kibria, B. M. (2014). A new characterization of skew normal distribution by truncated moment. Applications and Applied Mathematics, 9, 28-38.
[29]	Shakil, M., Ahsanullah, M., and Kibria, B. M. (2018). On the Characterizations of Chen’s Two-Parameter Exponential Power Life-Testing Distribution. Journal of Statistical Theory and Applications, 3, 393-407.
[30]	Shakil, M., Kibria, B. M., and Ahsanullah M. (2021). Some Inferences on Dagum (4P) Distribution, Statistical Distribution and their Applications, 154, 1-33.
[31]	Shakil, M., Kibria, B. M., Singh, J. N., and Ahsanullah M. (2021). On Burr (4P) Distribution Application of Breaking Stress Data, Statistical Distributions and their Applications, 2, 190-199.
[32]	Torabi, and Montazari, N. (2014). The logistic-uniform distribution application. Communications in Statistics - Simulation and Computation, 43, 2551-2569.
[33]	Torabi, Montazari, N., (2012). The gamma-uniform distribution and its application. Kybernetika, 48, 16-30.
[34]	Tahir, M. H., Zubair, M., Mansoor, M., Cordeiro, G. M., Alizadeh, M., and Hamedani, G. H. (2016). A new Weibull-G family of distributions. Hacettepe Journal of Mathematics and Statistics, 45, 629–647.
[35]	Zografos, K., and Balakrishnan, N. (2009). On families of beta- and generalized gamma- generated distributions and associated inference. Stat. Methodology 6, 344-362.

Cite This Article

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

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  -

Copy | Download

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

Download PDF

Sections

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

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  -

Copy | Download