Alpha Power Transformed Log-Logistic Distribution with Application to Breaking Stress Data

Aldahlan, Maha A.

doi:10.1155/2020/2193787

Cited by 17 publications

(12 citation statements)

References 13 publications

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“…In terms of applications, the log-logistic distribution and its generalizations have become the most popular models for survival and reliability data. Some recent applications have included: modeling for AIDS and Melanoma data (de Santana, Ortega, Cordeiro, & Silva, 2012); used for minification process (Gui, 2013); modeling breast cancer data (Ramos et al 2013); (Tahir et al 2014); modeling on censored survival data (Lemonte, 2014); modeling time up to first calving of cows (Louzada & Granzotto, 2016); modeling, inference, and use to a polled Tabapua Race Time up to First Calving Data (Granzotto et al 2017); modeling positive real data in many areas (Lima & Cordeiro, 2017); analysing a right-censored data (Shakhatreh, 2018); modeling lung cancer data (Alshangiti, et al 2016); and modeling of breaking stress data (Aldahlan, 2020).…”

Section: Extensions Of Log-logistic Distributionmentioning

confidence: 99%

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On the Log-Logistic Distribution and Its Generalizations: A Survey

Muse¹,

Mwalili²,

Ngesa³

2021

IJSP

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In this paper, we present a review on the log-logistic distribution and some of its recent generalizations. We cite more than twenty distributions obtained by different generating families of univariate continuous distributions or compounding methods on the log-logistic distribution. We reviewed some log-logistic mathematical properties, including the eight different functions used to define lifetime distributions. These results were used to obtain the properties of some log-logistic generalizations from linear representations. A real-life data application is presented to compare some of the surveyed distributions.

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Section: Extensions Of Log-logistic Distributionmentioning

confidence: 99%

“…The Alpha Power Transformed Log-logistic distribution Aldahlan (2020) proposed an Alpha Power Transformed Log-logistic distribution (APTLL) and studied the mathematical and statistical properties of the new distribution. Aldahlan (2020) extended the two-parameter log-logistic distribution.…”

Section: The Marshall-olkin Family Of Distributionsmentioning

confidence: 99%

On the Log-Logistic Distribution and Its Generalizations: A Survey

Muse¹,

Mwalili²,

Ngesa³

2021

IJSP

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“…In the statistical literature, with the aim of increasing the versatility of the log-logistic distribution in modelling survival time data, different generalized forms of the distribution have recently been proposed, including a new extension of the LL distribution with applications to actuarial data sets [ 7 ], alpha power transformed LL distribution [ 8 , 9 ], transmuted four-parameter generalized LL distribution [ 10 , 11 ], a new three-parameter LL distribution [ 12 ], extended log-logistic distribution [ 13 ], exponentiated LL geometric distribution [ 14 ], the LL Weibull distribution [ 15 ], beta LL distribution [ 16 ], McDonald LL distribution [ 2 ], transmuted LL distribution [ 17 ], Marshal-Olkin LL distribution [ 18 ], the Zografos-Balakrishnan LL distribution [ 19 ], and exponentiated LL distribution [ 20 ]. More details about the modifications and recent generalizations of the log-logistic distribution can be found in [ 21 ].…”

Section: Introductionmentioning

confidence: 99%

Bayesian and Classical Inference for the Generalized Log‐Logistic Distribution with Applications to Survival Data

Muse¹,

Mwalili

Ngesa³

et al. 2021

Computational Intelligence and Neuroscience

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The generalized log-logistic distribution is especially useful for modelling survival data with variable hazard rate shapes because it extends the log-logistic distribution by adding an extra parameter to the classical distribution, resulting in greater flexibility in analyzing and modelling various data types. We derive the fundamental mathematical and statistical properties of the proposed distribution in this paper. Many well-known lifetime special submodels are included in the proposed distribution, including the Weibull, log-logistic, exponential, and Burr XII distributions. The maximum likelihood method was used to estimate the unknown parameters of the proposed distribution, and a Monte Carlo simulation study was run to assess the estimators’ performance. This distribution is significant because it can model both monotone and nonmonotone hazard rate functions, which are quite common in survival and reliability data analysis. Furthermore, the proposed distribution’s flexibility and usefulness are demonstrated in a real-world data set and compared to its submodels, the Weibull, log-logistic, and Burr XII distributions, as well as other three-parameter parametric survival distributions, such as the exponentiated Weibull distribution, the three-parameter log-normal distribution, the three-parameter (or the shifted) log-logistic distribution, the three-parameter gamma distribution, and an exponentiated Weibull distribution. The proposed distribution is plausible, according to the goodness-of-fit, log-likelihood, and information criterion values. Finally, for the data set, Bayesian inference and Gibb’s sampling performance are used to compute the approximate Bayes estimates as well as the highest posterior density credible intervals, and the convergence diagnostic techniques based on Markov chain Monte Carlo techniques were used.

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“…In the literature, several studies have applied this technique to introduce some new distributions. These include the study of [12], in which the APT technique was applied to the exponential distribution; the study of [13], which introduced the alpha power Weibull distribution; the study of [14], which introduced the alpha power transformed Lindley distribution; the study of [15], which introduced the alpha power Pareto distribution; the study of [16], which presented the alpha power transformed inverse Lindley distribution; the study of [17], which presented the alpha power Gompertz distribution, and the study of [18], which presented the alpha power transformed log-logistic distribution.…”

Section: Introductionmentioning

confidence: 99%

A New Technique for Generating Distributions Based on a Combination of Two Techniques: Alpha Power Transformation and Exponentiated T-X Distributions Family

Klakattawi

Aljuhani

2021

Symmetry

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In the following article, a new five-parameter distribution, the alpha power exponentiated Weibull-exponential distribution is proposed, based on a newly developed technique. It is of particular interest because the density of this distribution can take various symmetric and asymmetric possible shapes. Moreover, its related hazard function is tractable and showing a great diversity of asymmetrical shaped, including increasing, decreasing, near symmetrical, increasing-decreasing-increasing, increasing-constant-increasing, J-shaped, and reversed J-shaped. Some properties relating to the proposed distribution are provided. The inferential method of maximum likelihood is employed, in order to estimate the model’s unknown parameters, and these estimates are evaluated based on various simulation studies. Moreover, the usefulness of the model is investigated through its application to three real data sets. The results show that the proposed distribution can, in fact, better fit the data, when compared to other competing distributions.

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Alpha Power Transformed Log-Logistic Distribution with Application to Breaking Stress Data

Cited by 17 publications

References 13 publications

On the Log-Logistic Distribution and Its Generalizations: A Survey

On the Log-Logistic Distribution and Its Generalizations: A Survey

Bayesian and Classical Inference for the Generalized Log‐Logistic Distribution with Applications to Survival Data

A New Technique for Generating Distributions Based on a Combination of Two Techniques: Alpha Power Transformation and Exponentiated T-X Distributions Family

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