The gamma-normal distribution: Properties and applications

Alzaatreh, Ayman; Famoye, Felix; Lee, Carl

doi:10.1016/j.csda.2013.07.035

Cited by 105 publications

(89 citation statements)

References 21 publications

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“…Some generalizations of the gamma distribution that fall into the T -R{Y } framework include the family of generalized gamma-generated distributions by Zografos and Balakrishnan (2009), the gamma-Pareto distribution by Alzaatreh et al (2012) and the gamma-normal distribution by Alzaatreh et al (2014a). These distributions belong to the gamma-R{exponential} family.…”

Section: To the T -R(w ) Family The Cumulative Distribution Functionmentioning

confidence: 99%

Family of generalized gamma distributions: Properties and applications

Alzaatreh¹,

Lee

Famoye

2015

HJMS

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In this paper, a family of generalized gamma distributions, T -gamma family, has been proposed using the T -R{Y } framework. The family of distributions is generated using the quantile functions of uniform, exponential, log logistic, logistic and extreme value distributions. Several general properties of the T -gamma family are studied in details including moments, mean deviations, mode and Shannon's entropy. Three new generalizations of the gamma distribution which are members of the T -gamma family are developed and studied. The distributions in the T -gamma family are very flexible due to their various shapes. The distributions can be symmetric, skewed to the right, skewed to the left, or bimodal. Four data sets with various shapes are fitted by using members of the T -gamma family of distributions.

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Section: To the T -R(w ) Family The Cumulative Distribution Functionmentioning

confidence: 99%

Family of generalized gamma distributions: Properties and applications

Alzaatreh¹,

Lee

Famoye

2015

HJMS

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“…Among all families (a) to (f), the family of distributions in (b) appeared to have been studied more widely and has many references in the literature. For more details about this family, one may refer to Pinho et al (2012), Zografos and Balakrishnan (2009) and Alzaatreh et al (2012Alzaatreh et al ( , 2013aAlzaatreh et al ( , 2013bAlzaatreh et al ( , 2014a.…”

Section: B) T-weibull{exponential}mentioning

confidence: 99%

“…Alzaatreh et al (2013a) studied some properties of the family in (1.4). A number of new distributions under this family were developed and studied including: Weibull-Pareto distribution by Alzaatreh et al (2013b), gamma-Pareto distribution by Alzaatreh et al (2012) and gamma-normal distribution by Alzaatreh et al (2014a). A large number of distributions can be generated by using (.)…”

Section: Introductionmentioning

confidence: 99%

Some Generalized Families of Weibull Distribution: Properties and Applications

AlMheidat¹,

Famoye²,

Lee³

2015

IJSP

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The Weibull distribution has been applied in various fields, especially to fit life time data. Some of these applications are limited partly due to the fact that the distribution has monotonically increasing, monotonically decreasing or constant hazard rate. This limitation undoubtedly inspired researchers to develop generalized Weibull distribution that can exhibit unimodal or bathtub hazard rate. In this article, we introduce six new families of T-Weibull{Y} distributions arising from the quantile function of a random variable Y. These six families are: The T-Weibull{uniform}, T-Weibull{exponential}, T-Weibull{log-logistic}, T-Weibull{Fré chet}, T-Weibull{logistic} and T-Weibull{extreme value}. Some properties of these families are discussed and general expressions for the quantile function, the Shannon's entropy, the non-central moments and the mean deviations are provided. Different new members of the T-Weibull{Y} families are derived and some of their properties are discussed. Two real data sets are used to illustrate the potential usefulness of the T-Weibull{Y} distributions and the results are compared with the results from some existing distributions.

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“…The beta normal (Eugene et al 2002), Kumaraswamy normal (Cordeiro and de Castro 2011), and generalized beta-generated normal (Alexander et al 2012) belong to the T-normal{standard uniform} families. The gamma-normal distribution studied by Alzaatreh, et al (2014) is a member of T-normal{standard exponential} family. For distribution "parsimony", we will focus on the quantile functions of standard distributions in order to limit the number of parameters.…”

Section: Remarkmentioning

confidence: 99%

T-normal family of distributions: a new approach to generalize the normal distribution

Alzaatreh

Lee

Famoye

2014

J Stat Distrib Appl

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The idea of generating skewed distributions from normal has been of great interest among researchers for decades. This paper proposes four families of generalized normal distributions using the T-X framework. These four families of distributions are named as T-normal families arising from the quantile functions of (i) standard exponential, (ii) standard log-logistic, (iii) standard logistic and (iv) standard extreme value distributions. Some general properties including moments, mean deviations and Shannon entropy of the T-normal family are studied. Four new generalized normal distributions are developed using the T-normal method. Some properties of these four generalized normal distributions are studied in detail. The shapes of the proposed T-normal distributions can be symmetric, skewed to the right, skewed to the left, or bimodal. Two data sets, one skewed unimodal and the other bimodal, are fitted by using the generalized T-normal distributions.

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The gamma-normal distribution: Properties and applications

Cited by 105 publications

References 21 publications

Family of generalized gamma distributions: Properties and applications

Family of generalized gamma distributions: Properties and applications

Some Generalized Families of Weibull Distribution: Properties and Applications

T-normal family of distributions: a new approach to generalize the normal distribution

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