Mc-Donald modified Burr-III distribution: properties and applications

Mukhtar, Samia; Ali, Azeem; Mutairi, Alya Al

doi:10.1080/16583655.2018.1553501

Cited by 6 publications

(6 citation statements)

References 19 publications

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“…The application of Modified Burr III distribution in reliability analysis was done by [ 50 ]. [ 51 ] originated the McDonald modified Burr–III. [ 52 ] developed Cubic rank transmuted modified Burr III-Pareto.…”

Section: The Hcmb−iii Distributionmentioning

confidence: 99%

Half circular modified burr−III distribution, application with different estimation methods

2022

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The data related to many medical, environmental and ecological variables are often measured in terms of angles wherein its range is defined in [0,π). This type of data is referred to as axial or half circular data. Modeling based on half circular data has not received its due share of attention in statistical literature. In this paper, we introduce a new half circular distribution based on inverse stereographic projection technique on modified Burr−III distribution, called the half circular modified Burr−III (hcMB−III) distribution. The basic properties of the proposed distribution are derived. It is common observation that while estimating the parameters of a model, one usually adopts maximum likelihood estimation method as the starting point. In this paper, we consider seven frequentist methods of estimation, besides using maximum likelihood method for estimating the parameters of the hcMB−III distribution. Monte Carlo simulations are performed for investigating the performances of the considered methods in terms of their biases and mean square errors using small, medium and large sample sizes. Finally, one data set related to posterior corneal curvature of the eyes of 23 patients, is analyzed to check potentiality of the newly proposed model.

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Section: The Hcmb−iii Distributionmentioning

confidence: 99%

Half circular modified burr−III distribution, application with different estimation methods

2022

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“…This section presents two applications of the new distribution using real data sets. We shall compare the fit of the new distribution with the Poisson Burr X Fr [19], Abd El-Bar and Ragab [27], Hamedani et al [28], Ahsanul Haq et al [29], Basheer [30], Korkmaz et al [31], Mukhtar [32], Alizadeh et al [33,34], Yousof et al [35][36][37] and Korkmaz et al [38]. In order to compare the distributions, we consider the following criteria: the −2 (α,β,λ) (Maximized…”

Section: Real Data Modellingmentioning

confidence: 99%

A new three parameter Fréchet model with mathematical properties and applications

Al-Babtain

Elbatal

Yousof

2020

Journal of Taibah University for Science

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A new three-parameter extension of the Fréchet model is proposed and studied. Some of its statistical properties are derived. A simple type Copula-based construction via Morgenstern family and via Clayton copula is used to derive many bivariate and multivariate extensions of the new model. We assessed the performance of the maximum likelihood estimators using a simulation study. The importance of the new model is shown via two applications to real data sets.

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“…For example, Ali and Ahmad [18] introduced transmuted modified Burr III distribution. Haq et al [19] introduced generalized odd Burr III-G family of distributions, and Mukhtar et al [20] introduced McDonald modified Burr-III distribution. Also, Jamal et al [21] proposed the New modified Burr III (NMBIII) distribution which has monotonic decreasing, increasing, unimodal, bathtub and approximately constant hazard rate shapes.…”

Section: Introductionmentioning

confidence: 99%

Actuarial Measures, Estimation and Applications of Sine Burr III Loss Distribution

John¹,

Mwaniki²,

Aduda³

2023

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The usefulness of heavy-tailed distributions for modeling insurance loss data is arguably an important subject for actuaries. Appropriate use of trigonometric functions allows a good understanding of the mathematical properties, limits over parameterization, and gives better applicability in modeling different datasets. Thus, the proposed method ensures that no additional parameter(s) is/are introduced in the bit to make a distribution from the F-Loss family of distributions flexible. The purpose of this paper is to improve the flexibility of the F-Loss family of distributions without introducing any additional parameter(s) and to develop heavy-tailed distributions with fewer parameters that give a better parametric fit to a given dataset than other existing distributions. In this paper, a new heavy-tailed distribution known as sine Burr III Loss distribution is proposed using the sine F-Loss generator. This distribution is flexible and able to model varying shapes of the hazard rate compared with the traditional Burr III distribution. The densities exhibit different kinds of decreasing and right-skewed shapes. The hazard rate functions show different kinds of decreasing, increasingconstant-decreasing, and upside-down bathtub shapes. The statistical properties and actuarial measures are studied. The skewness is always positive, and the kurtosis is increasing. The numerical values of the actuarial measures show that increasing confidence levels are associated with increasing VaR, TVaR, and TV. The maximum likelihood estimators are studied, and simulations are carried out to ascertain the behavior of the estimators. It is observed that the estimators are consistent. The usefulness of the proposed distribution is demonstrated with two insurance loss datasets and compared with other known classical heavy-tailed distributions. The results show that, the proposed distribution provides the best parametric fit for the two insurance loss datasets. Insurance practitioners can employ the proposed models in modeling insurance loss since they are flexible.

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Mc-Donald modified Burr-III distribution: properties and applications

Cited by 6 publications

References 19 publications

Half circular modified burr−III distribution, application with different estimation methods

Half circular modified burr−III distribution, application with different estimation methods

A new three parameter Fréchet model with mathematical properties and applications

Actuarial Measures, Estimation and Applications of Sine Burr III Loss Distribution

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