A bimodal Weibull distribution: properties and inference

Vila, Roberto; Çankaya, Mehmet Niyazi

doi:10.1080/02664763.2021.1931822

Cited by 9 publications

(9 citation statements)

References 36 publications

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“…In what follows we present some comparisons between the rates of random variables with known distributions: Inverse-gamma, Log-normal, Generalized-Pareto, BWeibull (see Vila et al 2020 [18]), BGamma (see Vila et al 2020 [17]), BG, exponential and Normal;…”

Section: Rate Of a Random Variable With Bg Distributionmentioning

confidence: 99%

“…Our approach consists of introduce bimodality in (1.1) as Elal-Olivero (2010) [3]. Results involving bimodality in other related probabilistic models can be found, for example, in Martinez et al (2013) [9], C ¸ankaya et al (2015) [2]; and more recently, in ) [16,17,18,19]. The advantage of our model in comparison to other generalizations of the Gumbel distribution is the number of parameters and the fact that it can be used to model extreme data with one or two modes.…”

Section: Introductionmentioning

confidence: 99%

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On the bimodal Gumbel model with application to environmental data

Otiniano¹,

Vila²,

Brom³

et al. 2021

Preprint

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The Gumbel model is a very popular statistical model due to its wide applicability for instance in the course of certain survival, environmental, financial or reliability studies. In this work, we have introduced a bimodal generalization of the Gumbel distribution that can be an alternative to model bimodal data. We derive the analytical shapes of the corresponding probability density function and the hazard rate function and provide graphical illustrations. Furthermore, We have discussed the properties of this density such as mode, bimodality, moment generating function and moments. Our results were verified using the Markov chain Monte Carlo simulation method. The maximum likelihood method is used for parameters estimation. Finally, we also carry out an application to real data that demonstrates the usefulness of the proposed distribution.

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Section: Rate Of a Random Variable With Bg Distributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the bimodal Gumbel model with application to environmental data

Otiniano¹,

Vila²,

Brom³

et al. 2021

Preprint

Self Cite

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“…On the basis of the zero truncated Poisson model, [ 9 ] proposed a new compound distribution called the quasi Poisson Burr X exponentiated Weibull distribution, which accommodated many important failure rates. Moreover, in a recent study, [ 10 ] have derived a bimodal form of the Weibull distribution.…”

Section: Introductionmentioning

confidence: 99%

Survival analysis of cancer patients using a new extended Weibull distribution

Klakattawi

2022

PLoS ONE

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One of the most important applications of statistical analysis is in health research and applications. Cancer studies are mostly required special statistical considerations in order to find the appropriate model for fitting the survival data. Existing classical distributions rarely fit such data well and an increasing interest has been shown recently in developing more flexible distributions by introducing some additional parameters to the basic model. In this paper, a new five-parameters distribution referred as alpha power Kumaraswamy Weibull distribution is introduced and studied. Particularly, this distribution extends the Weibull distribution based on a novel technique that combines two well known generalisation methods, namely, alpha power and T-X transformations. Different characteristics of the proposed distribution, including moments, quantiles, Rényi entropy and order statistics are obtained. The method of maximum likelihood is applied in order to estimate the model parameters based on complete and censored data. The performance of these estimators are examined via conducting some simulation studies. The potential importance and applicability of the proposed distribution is illustrated empirically by means of six datasets that describe the survival of some cancer patients. The results of the analysis indicated to the promising performance of the alpha power Kumaraswamy Weibull distribution in practice comparing to some other competing distributions.

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“…In other words, there can be a mixing of some populations even if same experiment is conducted while getting outputs of the corresponding experiment [1,4,5,6]. In such a situation, location and scale parameters of the mixed populations are important to get the central tendency and disperson (statistics) of the mixed form of the population in the experiment after shape, scale and bimodality parameters of function in the statistical theory are necessary components of a function which is used for conducting an efficient modelling [2,3,4,8,9,12,17].…”

Section: Introductionmentioning

confidence: 99%

“…The bimodality parameters ρ and δ with shape parameter α of Maxwell distribution in [18] are tools for us to generate different forms of modality. There are different degrees of mixing via Maxwell distribution and the expression which can help us to have different forms of modality of function for generating modality via compounding distributions [9,12]. The bimodal form on the positive part of the real line produces a trimodal form when it is reflected to the negative part of the real line via mirror imaging [1,13,14,15].…”

Section: Introductionmentioning

confidence: 99%

A General Class of Trimodal Distributions: Properties and Inference

Vila¹,

Victor²,

Çankaya³

et al. 2022

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The modality is important topic for modelling. Using parametric models is an efficient way when real data set shows trimodality. In this paper we propose a new class of trimodal probability distributions, that is, probability distributions that have up to three modes. Trimodality itself is achieved by applying a proper transformation to density function of certain continuous probability distributions. At first, we obtain preliminary results for an arbitratry density function g(x) and, next, we focus on the Gaussian case, studying trimodal Gaussian model more deeply. The Gaussian distribution is applied to produce the trimodal form of Gaussian known as normal distribution. The tractability of analytical expression of normal distribution, and properties of the trimodal normal distribution are important reasons why we choose normal distribution. Furthermore, the existing distributions should be improved to be capable of modelling efficiently when there exists a trimodal form in a data set. After new density function is proposed, estimating its parameters is important. Since Mathematica 12.0 software has optimization tools and important modelling techniques, computational steps are performed by using this software. The bootstrapped form of real data sets are applied to show the modelling ability of the proposed distribution when real data sets show trimodality.

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A bimodal Weibull distribution: properties and inference

Cited by 9 publications

References 36 publications

On the bimodal Gumbel model with application to environmental data

On the bimodal Gumbel model with application to environmental data

Survival analysis of cancer patients using a new extended Weibull distribution

A General Class of Trimodal Distributions: Properties and Inference

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