The gamma-exponentiated exponential distribution

Ristić, Miroslav M.; Balakrishnan, N.

doi:10.1080/00949655.2011.574633

Cited by 294 publications

(177 citation statements)

References 12 publications

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“…However, in some situations, the observed data have uncommon behavior, so the LL distribution is not suitable to describe and predict the phenomenon of interest. Recent developments have been made to define new generated families to control skewness and kurtosis through the tail weights and provide great flexibility in modeling skewed data in practice, the generators pioneered by Ristic and Balakrishnan (2012) proposed a family of univariate distributions generated by gamma random variables. For any baseline cdf G(t), they defined the gamma-G distribution with pdf f (t) and cdf F(t) by…”

Section: The Log-gamma-logistic Distributionmentioning

confidence: 99%

The Log-gamma-logistic Regression Model: Estimation, Sensibility and Residual Analysis

Hashimoto¹,

Ortega²,

Cordeiro³

et al. 2017

JSTA

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In this paper, we formulate and develop a log-linear model using a new distribution called the log-gammalogistic. We show that the new regression model can be applied to censored data since it represents a parametric family of models that includes as sub-models several widely-known regression models and therefore can be used more effectively in the analysis of survival data. We obtain maximum likelihood estimates of the model parameters by considering censored data and evaluate local influence on the estimates of the parameters by taking different perturbation schemes. Some global-influence measurements are also investigated. Further, for different parameter settings, sample sizes and censoring percentages, various simulations are performed. In addition, the empirical distributions of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to modified deviance residuals in the proposed regression model applied to censored data. We demonstrate that our extended regression model is very useful to the analysis of real data and may give more realistic fits than other special regression models.

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Section: The Log-gamma-logistic Distributionmentioning

confidence: 99%

The Log-gamma-logistic Regression Model: Estimation, Sensibility and Residual Analysis

Hashimoto¹,

Ortega²,

Cordeiro³

et al. 2017

JSTA

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“…The associated probability density function (pdf) corresponding to (3) is as follows On the basis of cdf (2) (see Ristic and Balakrishnan, 2011), we use the half logistic generator instead of gamma generator to obtain type II half logistic family which is denoted by TIIHL G  . Hence the cdf of TIIHL G  family can be expressed as follows…”

Section: Type II Half Logistic Familymentioning

confidence: 99%

Type II Half Logistic Family of Distributions with Applications

Hassan¹,

Elgarhy

Shakil³

2017

Pak.j.stat.oper.res.

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A new family of distributions called the type II half logistic is introduced and studied. Four new special models are presented. Some mathematical properties of the type II half logistic family are studied. Explicit expressions for the moments, probability weighted, quantile function, mean deviation, order statistics and Rényi entropy are investigated. Parameter estimates of the family are obtained based on maximum likelihood procedure. Two real data sets are employed to show the usefulness of the new family.

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“…There has been an increased interest in defining new classes of univariate continuous distributions introducing additional shape parameters to the baseline model. In many applied areas such as lifetime analysis (Gupta and Kundu, 2001), environmental (Ristić and Balakrishnan, 2012), medical (Ortega et al, 2012), economy (McDonald and Xu, 1993), there is a clear need for extended forms of the classical distributions, that is, new distributions which are more flexible to model real data in these areas since the data can present a high degree of skewness and kurtosis. In the context of extreme values, Papastathopoulos and Tawn (2013) studied three extensions of the generalised Pareto distribution.…”

Section: Introductionmentioning

confidence: 99%

Extended generalized extreme value distribution with applications in environmental data

Nascimento¹,

Bourguignon²,

Leão³

2015

HJMS

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In probability theory and statistics, the generalized extreme value (GEV) distribution is a family of continuous probability distributions developed within extreme value theory, which has wide applicability in several areas including hydrology, engineering, science, ecology and finance. In this paper, we propose three extensions of the GEV distribution that incorporate an additional parameter. These extensions are more flexible than the GEV distribution, i.e., the additional parameter introduces skewness and to vary tail weight. In these three cases, the GEV distribution is a particular case. The parameter estimation of these new distributions is done under the Bayesian paradigm, considering vague priors for the parameters. Simulation studies show the efficiency of the proposed models. Applications to river quotas and rainfall show that the generalizations can produce more efficient results than is the standard case with GEV distribution.

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The gamma-exponentiated exponential distribution

Cited by 294 publications

References 12 publications

The Log-gamma-logistic Regression Model: Estimation, Sensibility and Residual Analysis

The Log-gamma-logistic Regression Model: Estimation, Sensibility and Residual Analysis

Type II Half Logistic Family of Distributions with Applications

Extended generalized extreme value distribution with applications in environmental data

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