The Gamma-Weibull-G Family of Distributions with Applications

Oluyede, Broderick O.

doi:10.17713/ajs.v47i1.155

Cited by 32 publications

(28 citation statements)

References 14 publications

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“…Remark 1. One can remark that he OGWG distribution is special case of the general gamma-Weibull-Weibull distribution introduced by ([7], Section 6) (with the notations of [7], it corresponds to β = 1, simplifying the complexity of the distribution, α = 1/(1 − p), λ = 1/β and k = c). It is also an extension of the so-called exponentiated exponential power distribution thanks to the presence of the parameter p.…”

Section: Main Probability Functionsmentioning

confidence: 99%

“…As a final approach, one can use the result of Proposition 1 and more specially, the result (7). Hereafter, let X r,s be a random variable following the Weibull distribution with parameters (r + s + 1) 1/c β and c, i.e., with the pdf given by r,s (x) = c(r + s + 1)β c x c−1 e −[(r+s+1) 1/c βx] c , x > 0.…”

Section: Proposition 2 Let Us Setmentioning

confidence: 99%

“…It is well defined for t ∈ R. By applying the change of variable y = (e (βx) c − 1)/(1 − p), we can express M(t) as For given parameters c, α, p, β and t, the integrals above can be computed numerically. A series expansion of M(t) can be derived from (7). Indeed, we have…”

Section: Moment Generating Functionmentioning

confidence: 99%

“…This is supported by [5] with the uniform distribution as baseline and by [6] with the exponentiated version of the uniform distribution and the exponentiated version of the Weibull distribution as baselines. See also more general distributions in [7]. In terms of modelling, it is shown that they enjoy better goodness of fit properties to other useful competitors.On the other side, Ref.[8] introduced and studied another generalization of the Weibull distribution called the Weibull-geometric distribution.…”

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confidence: 98%

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The Odd Gamma Weibull-Geometric Model: Theory and Applications

2019

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In this paper, we study a new four-parameter distribution called the odd gamma Weibull-geometric distribution. Having the qualities suggested by its name, the new distribution is a special member of the odd-gamma-G family of distributions, defined with the Weibull-geometric distribution as baseline, benefiting of their respective merits. Firstly, we present a comprehensive account of its mathematical properties, including shapes, asymptotes, quantile function, quantile density function, skewness, kurtosis, moments, moment generating function and stochastic ordering. Then, we focus our attention on the statistical inference of the corresponding model. The maximum likelihood estimation method is used to estimate the model parameters. The performance of this method is assessed by a Monte Carlo simulation study. An empirical illustration of the new distribution is presented by the analyses two real-life data sets. The results of the proposed model reveal to be better as compared to those of the useful beta-Weibull, gamma-Weibull and Weibull-geometric models.Mathematics 2019, 7, 399 2 of 18 where γ(α, z) = z 0 t α−1 e −t dt, α > 0, z ≥ 0 is the lower incomplete gamma function and Γ(α) = +∞ 0 t α−1 e −t dt is the gamma function. The corresponding pdf is given byThis modification can significantly enriches the former model related to G(x). This is supported by [5] with the uniform distribution as baseline and by [6] with the exponentiated version of the uniform distribution and the exponentiated version of the Weibull distribution as baselines. See also more general distributions in [7]. In terms of modelling, it is shown that they enjoy better goodness of fit properties to other useful competitors.On the other side, Ref.[8] introduced and studied another generalization of the Weibull distribution called the Weibull-geometric distribution. As indicated by the name, it is obtained by compounding the Weibull and geometric distributions. The corresponding cdf is given bywhere β > 0, c > 0 and p ∈ [0, 1). The corresponding pdf is given byOne can remark that the Weibull distribution arises as a special case when p = 0. It is shown in [8] that the Weibull-geometric pdf and hrf take more general forms that the standard Weibull distribution. Among others, thanks to the presence of the parameter p, the related model is of interest for modeling unimodal failure rates (contrary to the standard Weibull model).In this paper, we focus our attention on a new distribution with cdf defined by the compounding of the odd-gamma-G cdf given by (1) and the Weibull-geometric cdf given by (2). The obtained distribution is then called the odd gamma Weibull-geometric distribution (OGWG for short). We thus aim to benefit of the respective merits of the two compounded distributions to create a new one having a great flexibility in modelling. Among others, we show that the OGWG pdf can have reversed-J, right skewed shapes, left-skewed and approximately symmetric, and the OGWG hrf can have increasing failure rate, decreasing failure rate and bathtub...

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Section: Main Probability Functionsmentioning

confidence: 99%

Section: Proposition 2 Let Us Setmentioning

confidence: 99%

Section: Moment Generating Functionmentioning

confidence: 99%

mentioning

confidence: 98%

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The Odd Gamma Weibull-Geometric Model: Theory and Applications

2019

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“…Additional generalized distributions include the exponentiated Weibull (EW) (Gupta and Kundu (2001)), the modified Weibull (MW) (Lai, Xie & Murthy (2003)) and the beta exponential (BE) (Nadarajah & Kotz (2005)). Recent extensions are the generalized modified Weibull (GMW) (Carrasco, Ortega & Cordeiro (2008)), the beta modified Weibull (BMW) (Nadarajah Cordeiro & Ortega (2011)), (Siva, Ortega & Cordeiro (2010)), the Weibull-G family (Bourguignon, Silva & Cordeiro (2014)), the gamma-exponentiated Weibull (GEW) (Pinho, Cordeiro & Nobre (2012)), gamma Weibull-G family (Oluyede, Pu, Makubate & Qui (2018)) and the gamma generalized modified Weibull (GGMW) (Oluyede, Huang & Yang (2015)). A new statistical distribution for characterizing the random strength of brittle materials was developed in Gurvich et al (1997).…”

Section: Introductionmentioning

confidence: 99%

A New Generalized Log-logistic and Modified Weibull Distribution with Applications

Oluyede¹,

Bindele²,

Makubate³

et al. 2018

IJSP

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A new generalized distribution called the log-logistic modified Weibull (LLoGMW) distribution is presented. This distribution includes many submodels such as the log-logistic modified Rayleigh, log-logistic modified exponential, log-logistic Weibull, log-logistic Rayleigh, log-logistic exponential, log-logistic, Weibull, Rayleigh and exponential distributions as special cases. Structural properties of the distribution including the hazard function, reverse hazard function, quantile function, probability weighted moments, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics, L-moments and Rényi entropy are derived. Model parameters are estimated based on the method of maximum likelihood. Finally, real data examples are presented to illustrate the usefulness and applicability of the model.

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Bayesian estimation of Marshall Olkin extended inverse Weibull under progressive type II censoring

Lin

Okasha

Basheer³

et al. 2023

Quality & Reliability Eng

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The estimations of parameters and percentiles for a three-parameter Marshall Olkin extended inverse Weibull distribution based on progressively type-II censored sample are concerned. The Bayesian, least-squares, maximum likelihood and percentiles estimate methods for the model parameters have been developed.Comparing all estimate methods, the least-squares, maximum likelihood and percentiles estimate methods are shown not stable due to the identification problem in the extended parametric space. Therefore, the Bayes estimate methods are focused. Three Bayesian estimations of the distribution parameters and 𝑝 percentiles for 𝑝 = 2.5, 50 and 97.5 under the squared error loss, absolute error loss and LINEX loss functions are respectively calculated by using the Markov chain Monte Carlo sampling procedure. Moreover, two real data sets are presented for the application illustration. Finally, concluding remarks are addressed.

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The Gamma-Weibull-G Family of Distributions with Applications

Cited by 32 publications

References 14 publications

The Odd Gamma Weibull-Geometric Model: Theory and Applications

The Odd Gamma Weibull-Geometric Model: Theory and Applications

A New Generalized Log-logistic and Modified Weibull Distribution with Applications

Bayesian estimation of Marshall Olkin extended inverse Weibull under progressive type II censoring

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