Open Access
ARTICLE
A New Logarithmic Family of Distributions: Properties and Applications
Yanping Wang1,2, Zhengqiang Feng1, Almaspoor Zahra3,*
1 Central South University Business School, Changsha, China
2 Hunan International Business Vocational College, Changsha, China
3 Department of Statistics, Yazd University, Yazd, Iran
* Corresponding Author: Almaspoor Zahra. Email:
Computers, Materials & Continua 2021, 66(1), 919-929. https://doi.org/10.32604/cmc.2020.012261
Received 22 June 2020; Accepted 19 September 2020; Issue published 30 October 2020
Abstract
In recent years, there has been an increased interest among the researchers to propose new families of distributions to provide the best fit to lifetime data
with monotonic (increasing, decreasing, constant) and non-monotonic (unimodal,
modified unimodal, bathtub) hazard functions. We further carry this area of
research and propose a new family of lifetime distributions called a new logarithmic family via the T-
X family approach. For the proposed family, explicit expressions for some mathematical properties along with the estimation of parameters
through Maximum likelihood method are discussed. A sub-model, called a new
logarithmic Weibull distribution is taken up. The proposed model is very flexible
and can be used to model data with increasing, decreasing, modified unimodal or
bathtub shaped hazard rates. The maximum likelihood estimators of the model
parameters are obtained. To assess the behavior of the maximum likelihood estimators, a comprehensive Monte Carlo simulation study has been carried out.
Finally, the potentiality of the new model is shown via analyzing two real data
sets taken from reliability engineering and biomedical fields. The comparison
of the proposed model is made with the other well-known competitors such as
(i) the three parameters exponentiated Weibull and Marshall–Olkin Weibull distributions and (ii) a four-parameter beta Weibull distribution. The practical applications show that the proposed model performs much better than the competitive
models and can be used as a good candidate model to analyze data in engineering,
medical sciences and other related fields.
Keywords
Cite This Article
Y. Wang, Z. Feng and A. Zahra, "A new logarithmic family of distributions: properties and applications,"
Computers, Materials & Continua, vol. 66, no.1, pp. 919–929, 2021. https://doi.org/10.32604/cmc.2020.012261