Compounding of distributions: a survey and new generalized classes

Tahir, M. H.; Cordeiro, Gauss M.

doi:10.1186/s40488-016-0052-1

Cited by 102 publications

(62 citation statements)

References 193 publications

(115 reference statements)

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“…For instance, considering Lehmann Type 1 and Type 2 alternatives, we have the CDFs given by: , where x ≥ 0, λ ≥ 2, and α > 0. Tahir and Cordeiro [4] discussed many G-family distributions that can be used to extend the proposed model. Our approach should be investigated further in these contexts.…”

Section: Discussion and Extensionsmentioning

confidence: 99%

A Distribution for Instantaneous Failures

Ramos

Louzada

2019

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A new one-parameter distribution is proposed in this paper. The new distribution allows for the occurrence of instantaneous failures (inliers) that are natural in many areas. Closed-form expressions are obtained for the moments, mean, variance, a coefficient of variation, skewness, kurtosis, and mean residual life. The relationship between the new distribution with the exponential and Lindley distributions is presented. The new distribution can be viewed as a combination of a reparametrized version of the Zakerzadeh and Dolati distribution with a particular case of the gamma model and the occurrence of zero value. The parameter estimation is discussed under the method of moments and the maximum likelihood estimation. A simulation study is performed to verify the efficiency of both estimation methods by computing the bias, mean squared errors, and coverage probabilities. The superiority of the proposed distribution and some of its concurrent distributions are tested by analyzing four real lifetime datasets.

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Section: Discussion and Extensionsmentioning

confidence: 99%

A Distribution for Instantaneous Failures

Ramos

Louzada

2019

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“…Many distributions have already been proposed using the minimum or maximum activation mechanism. Tahir and Cordeiro [22] presented an interesting discussion about compounding different distributions. [22] and references therein).…”

Section: Other Compound Models Based On the Poisson Distributionmentioning

confidence: 99%

“…Tahir and Cordeiro [22] presented an interesting discussion about compounding different distributions. [22] and references therein). Our approach can be applied in any of these distributions unifying the minimum/maximum without including an extra parameter.…”

Section: Other Compound Models Based On the Poisson Distributionmentioning

confidence: 99%

An extended poisson family of life distribution: a unified approach in competitive and complementary risks

Ramos

Dey

Louzada

et al. 2019

Journal of Applied Statistics

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In this paper, we introduce a new approach to generate flexible parametric families of distributions. These models arise on competitive and complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the minimum/maximum lifetime value among all risks. The latent variables have a zero truncated Poisson distribution. For the proposed family of distribution, the extra shape parameter has an important physical interpretation in the competing and complementary risks scenario. The mathematical properties and inferential procedures are discussed. The proposed approach is applied in some existing distributions in which it is fully illustrated by an important data set.

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“…This limitation has triggered the creation of new families of distributions, often defined as compounding or weighting existing distributions. The most useful of them can be found in the surveys of [1,2]. In particular, the families of distributions defined with gamma generators has demonstrated a high ability to construct flexible models, showing nice fits for various kinds of real-life data sets.…”

Section: Introductionmentioning

confidence: 99%

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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Compounding of distributions: a survey and new generalized classes

Cited by 102 publications

References 193 publications

A Distribution for Instantaneous Failures

A Distribution for Instantaneous Failures

An extended poisson family of life distribution: a unified approach in competitive and complementary risks

The Odd Gamma Weibull-Geometric Model: Theory and Applications

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