New Modified Burr III Distribution, Properties and Applications

Jamal, Farrukh; Abuzaid, Ali; Tahir, M. H.; Nasir, Muhammad Arslan; Khan, Sadaf; Khan, Wali Ullah

doi:10.3390/mca26040082

Cited by 5 publications

(5 citation statements)

References 32 publications

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“…There were 63 earthquakes recorded altogether, and so 62 recorded waiting times. The data are: 840, 157, 145, 44,33,121,150,280,434,736,584,887,263,1901,695,294,562,721,40,1336,335,1354,454,139,780,203,436,30,246,1617,638,937,735,76,710,36,667,384,129,46,402,194,40,556,99,9,209,599,38,365,92,82,220,759,304,83,319,375,832,460,567,328.…”

Section: Meteorology Datamentioning

confidence: 99%

“…The survival times, in weeks, of 33 patients who succumbed to Acute Myelogenous Leukemia are the subject of D2. This data was recently studied by the authors in [46] The data are: 65, 156, 100, 134, 16, 108, 121, 4,39, 143, 56, 26, 22, 1, 1, 5, 65, 56, 65, 17, 7, 16, 22, 3, 4, 2, 8, 4, 3, 30, 4,43. Cancer data 2. D3 signifies the number of patients suffering from blood cancer.…”

Section: Cancer Datamentioning

confidence: 99%

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A new extended gumbel distribution: Properties and application

et al. 2022

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A robust generalisation of the Gumbel distribution is proposed in this article. This family of distributions is based on the T-X paradigm. From a list of special distributions that have evolved as a result of this family, three separate models are also mentioned in this article. A linear combination of generalised exponential distributions can be used to characterise the density of a new family, which is critical in assessing some of the family’s properties. The statistical features of this family are determined, including exact formulations for the quantile function, ordinary and incomplete moments, generating function, and order statistics. The model parameters are estimated using the maximum likelihood method. Further, one of the unique models has been systematically studied. Along with conventional skewness measures, MacGillivray skewness is also used to quantify the skewness measure. The new probability distribution also enables us to determine certain critical risk indicators, both numerically and graphically. We use a simulated assessment of the suggested distribution, as well as apply three real-world data sets in modelling the proposed model, in order to ensure its authenticity and superiority.

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Section: Meteorology Datamentioning

confidence: 99%

Section: Cancer Datamentioning

confidence: 99%

A new extended gumbel distribution: Properties and application

et al. 2022

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“…Here we select the modified Burr III distribution [6] with T(s) = (1 + s −λ e −cs ) −k in Equation (1), where the parameters λ, c, k > 0. Building upon this baseline distribution, we introduce the new modified Burr III Odds Ratio-G (MB-OR-G) model that synthesizes the Burr III distribution with an exponentiated odds ratio generator.…”

Section: Burr III Scaled Inverse Odds Ratio-g Distributionmentioning

confidence: 99%

“…It was first introduced by Burr in 1942 [5], and has undergone substantial enhancements to augment its modeling capabilities. Such advancements have expanded the distribution's utility, allowing it to encompass a broader spectrum of data configurations and demonstrating its significant practical value [6][7][8]. Recent progress in the field has spurred the development of innovative regression models and analytical tools predicated on the structural nuances of the Burr III distribution.…”

Section: Introductionmentioning

confidence: 99%

Enhanced Real-Life Data Modeling with the Modified Burr III Odds Ratio–G Distribution

Yang,

Huang,

Chen

et al. 2024

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In this study, we introduce the modified Burr III Odds Ratio–G distribution, a novel statistical model that integrates the odds ratio concept with the foundational Burr III distribution. The spotlight of our investigation is cast on a key subclass within this innovative framework, designated as the Burr III Scaled Inverse Odds Ratio–G (B-SIOR-G) distribution. By effectively integrating the odds ratio with the Burr III distribution, this model enhances both flexibility and predictive accuracy. We delve into a thorough exploration of this distribution family’s mathematical and statistical properties, spanning hazard rate functions, quantile functions, moments, and additional features. Through rigorous simulation, we affirm the robustness of the B-SIOR-G model. The flexibility and practicality of the B-SIOR-G model are demonstrated through its application to four datasets, highlighting its enhanced efficacy over several well-established distributions.

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“…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. Other extensions are mostly based on the generalized families of distributions that are complex in nature.…”

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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New Modified Burr III Distribution, Properties and Applications

Cited by 5 publications

References 32 publications

A new extended gumbel distribution: Properties and application

A new extended gumbel distribution: Properties and application

Enhanced Real-Life Data Modeling with the Modified Burr III Odds Ratio–G Distribution

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

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