Polish Statistical Association

Central Statistical Office of Poland

**Subject:** Economics, Statistics & Probability

**ISSN:** 1234-7655

**eISSN:** 2450-0291

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

**Keywords : **
Kumaraswamy distribution,
gamma distribution,
generalised family,
moments,
stochastic ordering,
maximum likelihood method,
data analysis

**Citation Information : **
Statistics in Transition New Series. Volume 21,
Issue 5,
Pages 17-40,
DOI: https://doi.org/10.21307/stattrans-2020-053

**License : **
(CC BY-NC-ND 4.0)

**Received Date : **30-May-2020
/
**Accepted: **03-September-2020
/
**Published Online: ** 20-December-2020

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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.

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