A New Generalization of the Lomax Distribution with Increasing, Decreasing, and Constant Failure Rate

Oguntunde, Pelumi E.; Khaleel, Mundher A.; Ahmed, Mohammed T.; Adejumo, A. O.; Odetunmibi, Oluwole A.

doi:10.1155/2017/6043169

Cited by 43 publications

(25 citation statements)

References 17 publications

(21 reference statements)

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“…For this reason, numerous efforts have been launched to generalized these distributions in the best way possible. Among these generalizations, we would like to mention the Marshall-Olkin extended Lomax distribution by [7], the exponentiated Lomax distribution by [8], the McDonald Lomax distribution by [9], the Poisson Lomax distribution by [10], the gamma Lomax distribution by [11], the exponential Lomax distribution by [12], the transmuted Lomax distribution by [13], the weighted Lomax distribution by [14], the Weibull Lomax distribution by [15], the Gompertz Lomax distribution by [16], the Transformed-Transformer Lomax distribution by [17], and the power Lomax (PL) distribution by [18].…”

Section: From the Lomax Distribution To The Power Lomax Distributionmentioning

confidence: 99%

Type II Topp Leone Power Lomax Distribution with Applications

Al-Marzouki

Jamal²,

Chesneau

et al. 2019

Mathematics

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In many areas of applied sciences, the last step of a study often consists in analyzing in depth the collected data. Among all the kinds of data, the lifetime data are well-known to convey a great deal of information whose capture is necessary to identify one or more key phenomena. In this regards, numerous mathematical models have been proposed, including those based on lifetime distributions. In this paper, we introduce a new four-parameter lifetime distribution based on the type II Topp-Leone-G family and the power Lomax distribution. In comparison to the existing distributions, the new one is characterized by very flexible probability functions: increasing, decreasing, J, and reverse J shapes are observed for the probability density and hazard rate functions, giving first signs on the potential of adaptability of the related model. With this idea in mind, the new distribution is studied in detail, from both the theoretical and applied sides. After showing its main mathematical properties, the related model is investigated with estimation of the parameters by the maximum likelihood method. We applied it to two practical datasets, including the well-know aircraft windshield data. We show that the new model performs better than several modern adversary models, motivating its use in an applied setting.

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Section: From the Lomax Distribution To The Power Lomax Distributionmentioning

confidence: 99%

Type II Topp Leone Power Lomax Distribution with Applications

Al-Marzouki

Jamal²,

Chesneau

et al. 2019

Mathematics

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“…This data represents the strengths of 1.5 cm glass fibres. The observations are contained in Oguntunde et al (2017), Merovci et al (2016), Bourguignon et al (2014), and Smith and Naylor (1987). We provide the summary of the data in Table 3.…”

Section: Second Data Setmentioning

confidence: 99%

The inverted weighted exponential distribution with applications

Oguntunde¹,

Ilori²,

Okagbue³

2018

Int. j. adv. appl. sci.

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“…is distribution has been proved as a significant alternative to the exponential, Weibull, and gamma distributions to model heavy-tailed data sets. Due to the importance and applicability of the Lomax distribution, it has been extensively generalized and modified to obtain a more flexible extension of the Lomax distributions, for example, power Lomax distribution [2], transmuted Lomax distribution [3], exponentiated Lomax distribution [4], weighted Lomax distribution [5], exponential Lomax distribution [6], gamma Lomax distribution [7], Poisson Lomax distribution [8], an extended Lomax distribution [9], Marshall-Olkin extended Lomax [10], exponentiated Weibull Lomax [11], Kumaraswamy generalized power Lomax [12], Marshall-Olkin length biased Lomax [13], Gompertz Lomax [14], half-logistic Lomax [15], Gumbel Lomax [16], transmuted Weibull Lomax [17], and transmuted exponentiated Lomax [18].…”

Section: Introductionmentioning

confidence: 99%

The Lomax‐Claim Model: Bivariate Extension and Applications to Financial Data

et al. 2021

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The uses of statistical distributions for modeling real phenomena of nature have received considerable attention in the literature. The recent studies have pointed out the potential of statistical distributions in modeling data in applied sciences, particularly in financial sciences. Among them, the two-parameter Lomax distribution is one of the prominent models that can be used quite effectively for modeling data in management sciences, banking, finance, and actuarial sciences, among others. In the present article, we introduce a new three-parameter extension of the Lomax distribution via using a class of claim distributions. The new model may be called the Lomax-Claim distribution. The parameters of the Lomax-Claim model are estimated using the maximum likelihood estimation method. The behaviors of the maximum likelihood estimators are examined by conducting a brief Monte Carlo study. The potentiality and applicability of the Lomax claim model are illustrated by analyzing a dataset taken from financial sciences representing the vehicle insurance loss data. For this dataset, the proposed model is compared with the Lomax, power Lomax, transmuted Lomax, and exponentiated Lomax distributions. To show the best fit of the competing distributions, we consider certain analytical tools such as the Anderson–Darling test statistic, Cramer–Von Mises test statistic, and Kolmogorov–Smirnov test statistic. Based on these analytical measures, we observed that the new model outperforms the competitive models. Furthermore, a bivariate extension of the proposed model called the Farlie–Gumble–Morgenstern bivariate Lomax-Claim distribution is also introduced, and different shapes for the density function are plotted. An application of the bivariate model to GDP and export of goods and services is provided.

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A New Generalization of the Lomax Distribution with Increasing, Decreasing, and Constant Failure Rate

Cited by 43 publications

References 17 publications

Type II Topp Leone Power Lomax Distribution with Applications

Type II Topp Leone Power Lomax Distribution with Applications

The inverted weighted exponential distribution with applications

The Lomax‐Claim Model: Bivariate Extension and Applications to Financial Data

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