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

• Authors: Rana Muhammad Imran Arshad , Muhammad Hussain Tahir , Christophe Chesneau , Farrukh Jamal

Abstracts

EN

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

EN

stochastic ordering; stochastic ordering; stochastic ordering; stochastic ordering; stochastic ordering; stochastic ordering; stochastic ordering

• Publisher: Główny Urząd Statystyczny
• Journal: Statistics in Transition new series
• Year: 2020
• Volume: 21
• Issue: 5
• Pages: 17-40

Contributors

author

Rana Muhammad Imran Arshad

• Department of Statistics, The Islamia University of Bahawalpur, Punjab, Pakistan

• https://orcid.org/0000000256874634

author

Muhammad Hussain Tahir

• Department of Statistics, The Islamia University of Bahawalpur, Punjab, Pakistan

• https://orcid.org/0000000221573997

author

Christophe Chesneau

• Department of Mathematics, Université de Caen, LMNO, Caen, France

• https://orcid.org/0000000215229292

author

Farrukh Jamal

• Department of Statistics, The Islamia University of Bahawalpur, Punjab, Pakistan

• https://orcid.org/0000000161929890

Identifiers

DOI

10.21307/stattrans-2020-053

Biblioteka Nauki

1059046