On Burr III Marshal Olkin family: development, properties, characterizations and applications

In this paper, a flexible family of distributions with unimodel, bimodal, increasing, increasing and decreasing, inverted bathtub and modified bathtub hazard rate called Burr III-Marshal Olkin-G (BIIIMO-G) family is developed on the basis of the T-X family technique. The density function of the BIII...

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Bibliographic Details
Published in:Journal of statistical distributions and applications 2019-08, Vol.6 (1), p.1-21, Article 12
Main Authors: Bhatti, Fiaz Ahmad, Hamedani, G. G., Korkmaz, Mustafa C., Cordeiro, Gauss M., Yousof, Haitham M., Ahmad, Munir
Format: Article
Language:English
Subjects:
Humanities and Social Sciences
Mathematics and Statistics
Maximum likelihood estimates
Maximum likelihood method
Monte Carlo simulation
multidisciplinary
Parameter estimation
Quantiles
Science
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
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Summary:In this paper, a flexible family of distributions with unimodel, bimodal, increasing, increasing and decreasing, inverted bathtub and modified bathtub hazard rate called Burr III-Marshal Olkin-G (BIIIMO-G) family is developed on the basis of the T-X family technique. The density function of the BIIIMO-G family is arc, exponential, left- skewed, right-skewed and symmetrical shaped. Descriptive measures such as quantiles, moments, incomplete moments, inequality measures and reliability measures are theoretically established. The BIIIMO-G family is characterized via different techniques. Parameters of the BIIIMO-G family are estimated using maximum likelihood method. A simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of BIIIMO-G family is demonstrated by its application to real data sets.
ISSN:2195-5832
2195-5832
DOI:10.1186/s40488-019-0101-7