The Gamma Kumaraswamy-G family of distributions: theory, inference and applications

Imran Arshad Rana Muhammad (), Tahir Muhammad Hussain (), Chesneau Christophe () and Jamal Farrukh ()
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Imran Arshad Rana Muhammad: Department of Statistics, The Islamia University of Bahawalpur, Punjab, 63100, Pakistan .
Tahir Muhammad Hussain: Department of Statistics, The Islamia University of Bahawalpur, Punjab, 63100, Pakistan .
Chesneau Christophe: Department of Mathematics, Université de Caen, LMNO, Campus II, Science 3, 14032 Caen, France .
Jamal Farrukh: Department of Statistics, The Islamia University of Bahawalpur, Punjab, 63100, Pakistan .

Statistics in Transition New Series, 2020, vol. 21, issue 5, 17-40

Abstract: In this paper, we introduce a new family of univariate continuous distributions called the Gamma Kumaraswamy-generated family of distributions. Most of its properties are studied in detail, including skewness, kurtosis, analytical comportments of the main functions, moments, stochastic ordering and order statistics. The next part of the paper focuses on a particular member of the family with four parameters, called the gamma Kumaraswamy exponential distribution. Among its advantages, the following should be mentioned: the corresponding probability density function can have symmetrical, left-skewed, right-skewed and reversed-J shapes, while the corresponding hazard rate function can have (nearly) constant, increasing, decreasing, upside-down bathtub, and bathtub shapes. Subsequently, the inference on the gamma Kumaraswamy exponential model is performed. The method of maximum likelihood is applied to estimate the model parameters. In order to demonstrate the importance of the new model, analyses on two practical data sets were carried out. The results proved more favourable for the studied model than for any of the other eight competitive models.

Keywords: Kumaraswamy distribution; gamma distribution; generalised family; moments; stochastic ordering; maximum likelihood method; data analysis. (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:stintr:v:21:y:2020:i:5:p:17-40:n:8

DOI: 10.21307/stattrans-2020-053

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