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

Rana Muhammad Imran Arshad; Muhammad Hussain Tahir; Christophe Chesneau; Farrukh Jamal

doi:10.21307/stattrans-2020-053

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

Rana Muhammad Imran Arshad Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan ORCID:https://orcid.org/0000-0002-5687-4634 , Muhammad Hussain Tahir Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan ORCID:https://orcid.org/0000-0002-2157-3997 , Christophe Chesneau Department of Mathematics, Universit´e de Caen, LMNO, Campus II, Science 3, 14032 Caen, France ORCID:https://orcid.org/0000-0002-1522-9292 , Farrukh Jamal Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan ORCID:https://orcid.org/0000-0001-6192-9890 Statistics in Transition new series, vol. 21, 2020, 5, pages: 17-40 Published online: 4 December 2020 DOI 10.21307/stattrans-2020-053

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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

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