Weighted Distributions: A Brief Review, Perspective and Characterizations

Saghir, Aamir; Hamedani, G. G.; Tazeem, Sadaf; Khadim, Aneeqa

doi:10.5539/ijsp.v6n3p109

Cited by 29 publications

(15 citation statements)

References 17 publications

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“…Let us recall that the cdf of the OGWG distribution is defined by (1) with G(x) given (2). By noticing that odd G (x) = (e (βx) c − 1)/(1 − p), the corresponding cdf is given by…”

Section: Main Probability Functionsmentioning

confidence: 99%

“…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%

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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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“…Let us recall that the cdf of the OGWG distribution is defined by (1) with G(x) given (2). By noticing that odd G (x) = (e (βx) c − 1)/(1 − p), the corresponding cdf is given by…”

Section: Main Probability Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Odd Gamma Weibull-Geometric Model: Theory and Applications

2019

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“…Recent weighted exponential distributions with great ability in statistical applications include the exponentiated exponential (EE) distribution introduced by [9], the weighted exponential (WE) distribution introduced by [7], the Gamma exponentiated exponential (GEE) distribution introduced by [14], the weighted generalized exponential (WGE) distribution introduced by [10] and the exponentiated weighted exponential (EWE) distribution introduced by [13]. A brief review on weighted distributions (exponential or non-exponential) can be found in [15]. The statistical literature on proposing new weighted exponential distributions is vast and growing fast.…”

Section: Introductionmentioning

confidence: 99%

On a weighted exponential distribution with a logarithmic weight: theory and applications

et al. 2021

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A new weighted exponential distribution is proposed using a logarithmic weight function. Mathematical properties are studied, including moments, residual life function, order statistics and record values. A parametric estimation is performed using the maximum likelihood method, the weighted least-square method and the maximum product of spacing estimators method. Applications are provided using four real data sets. It is shown that our new distribution works better than a number of classical and recent distributions.

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“…Further details on such family of distributions can be found in [19]. On the other side, [5] introduced the transmuted exponential distribution defined by the following cdf:…”

Section: Introductionmentioning

confidence: 99%

A weighted transmuted exponential distributions with environmental applications

Chesneau¹,

Bakouch²,

Khan³

2020

Stat., optim. inf. comput.

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In this paper, we introduce a new three-parameter distribution based on the combination of re-parametrization of the so-called EGNB2 and transmuted exponential distributions. This combination aims to modify the transmuted exponential distribution via the incorporation of an additional parameter, mainly adding a high degree of flexibility on the mode and impacting the skewness and kurtosis of the tail. We explore some mathematical properties of this distribution including the hazard rate function, moments, the moment generating function, the quantile function, various entropy measures and (reversed) residual life functions. A statistical study investigates estimation of the parameters using the method of maximum likelihood. The distribution along with other existing distributions are fitted to two environmental data sets and its superior performance is assessed by using some goodness-of-fit tests. As a result, some environmental measures associated with these data are obtained such as the return level and mean deviation about this level.

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Weighted Distributions: A Brief Review, Perspective and Characterizations

Cited by 29 publications

References 17 publications

The Odd Gamma Weibull-Geometric Model: Theory and Applications

The Odd Gamma Weibull-Geometric Model: Theory and Applications

On a weighted exponential distribution with a logarithmic weight: theory and applications

A weighted transmuted exponential distributions with environmental applications

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