A new generalized gamma distribution with applications

Bourguignon, Marcelo; Lima, Maria do Carmo S.; Leão, Jeremias; Nascimento, Abraão D. C.; Pinho, Luís Gustavo Bastos; Cordeiro, Gauss M.

doi:10.1080/01966324.2015.1040178

Cited by 16 publications

(12 citation statements)

References 31 publications

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“…In [33], the authors use multivariate gamma distribution to investigate the performance of radio frequency and optical wireless communication systems. Gamma distribution and its extensions have also been used to model a variety of data and processes [1,3,21]. It is also used as a kernel function in nonparametric density estimation.…”

Section: Literaturementioning

confidence: 99%

Gamma distribution-based sampling for imbalanced data

Kamalov,

Denisov

2020

Preprint

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Imbalanced class distribution is a common problem in a number of fields including medical diagnostics, fraud detection, and others. It causes bias in classification algorithms leading to poor performance on the minority class data. In this paper, we propose a novel method for balancing the class distribution in data through intelligent resampling of the minority class instances. The proposed method is based on generating new minority instances in the neighborhood of the existing minority points via a gamma distribution. Our method offers a natural and coherent approach to balancing the data. We conduct a comprehensive numerical analysis of the new sampling technique. The experimental results show that the proposed method outperforms the existing state-of-the-art methods for imbalanced data. Concretely, the new sampling technique produces the best results on 12 out of 24 real life as well as synthetic datasets. For comparison, the SMOTE method achieves the top score on only 1 dataset. We conclude that the new technique offers a simple yet effective sampling approach to balance data.

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Section: Literaturementioning

confidence: 99%

Gamma distribution-based sampling for imbalanced data

Kamalov,

Denisov

2020

Preprint

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“…Other representations or extensions of the generalized gamma distribution exist in the literature; see, for example, the studies of Bourguignon et al, Cordeiro et al, and Nadarajah and Gupta. ()…”

Section: Series Representations For the Generalized Gamma Distributiomentioning

confidence: 99%

“…denotes the characteristic function of X, i = √ −1 and t ∈ R. Other representations or extensions of the generalized gamma distribution exist in the literature; see, for example, the studies of Bourguignon et al, Cordeiro et al, and Nadarajah and Gupta. [12][13][14] The following theorem shows that the density of a generalized gamma distribution may be represented as follows: (a) an infinite gamma-series expansion or (b) a mixture of generalized gamma distributions. Theorem 2.1.…”

Section: Series Representations For the Generalized Gamma Distributiomentioning

confidence: 99%

Series representations for densities functions of a family of distributions—Application to sums of independent random variables

Marques

Loots

Bekker

2019

Math Methods in App Sciences

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Series representations for several density functions are obtained as mixtures of generalized gamma distributions with discrete mass probability weights, by using the exponential expansion and the binomial theorem. Based on these results, approximations based on mixtures of generalized gamma distributions are proposed to approximate the distribution of the sum of independent random variables, which may not be identically distributed. The applicability of the proposed approximations are illustrated for the sum of independent Rayleigh random variables, the sum of independent gamma random variables, and the sum of independent Weibull random variables. Numerical studies are presented to assess the precision of these approximations.

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“…• The Zografos-Balakrishnan Nadarajah-Haghighi (ZBNH) distribution (Bourguignon et al, 2015) having pdf (for x > 0) given by…”

Section: Applicationsmentioning

confidence: 99%

Some Computational and Theoretical Aspects of the Exponentiated Generalized Nadarajah-Haghighi Distribution

VedoVatto,

Nascimento,

Filho

et al. 2016

Preprint

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Real data from applications in the survival context have required the use of more flexible models. A new four-parameter model called the Exponentiated Generalized Nadarajah-Haghighi (EGNH) distribution has been introduced in order to verify this requirement. We prove that its hazard rate function can be constant, decreasing, increasing, upside-down bathtub and bathtub-shape. Theoretical essays are provided about the EGNH shapes. It includes as special models the exponential, exponentiated exponential, Nadarajah-Haghighi's exponential and exponentiated Nadarajah-Haghighi distributions. We present a physical interpretation for the EGNH distribution and obtain some of its mathematical properties including shapes, moments, quantile, generating functions, mean deviations and Rényi entropy. We estimate its parameters by maximum likelihood, on which one of the estimates may be written in closed-form expression. This last result is assessed by means of a Monte Carlo simulation study. The usefulness of the introduced model is illustrated by means of two real data sets. We hope that the new distribution could be an alternative to other distributions available for modeling positive real data in many areas.

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A new generalized gamma distribution with applications

Cited by 16 publications

References 31 publications

Gamma distribution-based sampling for imbalanced data

Gamma distribution-based sampling for imbalanced data

Series representations for densities functions of a family of distributions—Application to sums of independent random variables

Some Computational and Theoretical Aspects of the Exponentiated Generalized Nadarajah-Haghighi Distribution

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