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

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Arshad R. M. I., Tahir M. H., Chesneau C., Jamal F.

Statistics in Transition new series

2020

vol. 21

issue 5

17-40

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.

Analysis of COVID-19 and cancer data using new half-logistic generated family of distributions

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Khan S., Tahir M. H., Jamal F.

Operations Research and Decisions

2023

vol. 33

issue 4

We focus on a specific sub-model of the proposed family that we call the new half logistic-Fréchet. This sub-model stems from a new generalisation of the half-logistic distribution which we call the new half-logistic-G. The novelty of proposing this new family is that it does not include any additional parameters and instead relies on the baseline parameter. Standard statistical formulas are used to show the forms of the density and failure rate functions, ordinary and incomplete moments with generating functions, and random variate generation. The maximum likelihood estimation procedure is used to estimate the set of parameters. We conduct a simulation analysis to ensure that our calculations are converging with lower mean square error and biases. We use three real-life data sets to equate our model to well-established existing models. The proposed model outperforms the well-established four parameters beta Fréchet and exponentiated generalized Fréchet for some real- -life results, with three parameters such as half-logistic Fréchet, exponentiated Fréchet, Zografos–Balakrishnan gamma Fréchet, Topp–Leonne Fréchet, and Marshall–Olkin Fréchet and two-parameter classical Fréchet distribution.

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1 Operations Research and Decisions

1 Statistics in Transition new series

2 Jamal F.

2 Tahir M. H.

1 Arshad R. M. I.

1 Chesneau C.

1 Khan S.

1 2023

1 2020

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

Analysis of COVID-19 and cancer data using new half-logistic generated family of distributions