On the robustness of an epsilon skew extension for Burr III distribution on the real line

Çankaya, Mehmet Niyazi; Yalçınkaya, Abdullah; Altındağ, Ömer; Arslan, Olçay

doi:10.1007/s00180-018-0859-y

Cited by 8 publications

(1 citation statement)

References 48 publications

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“…Shao et al [11] studied low-flow frequency analysis in hydrology with threeparameter-modified Burr III distribution with supreme interest in the lower tails of a distribution. C ¸ankaya et al [12] extended the BIII model by adding a skew parameter with an epsilon skew extension approach. Modi and Gill [13] introduced the unit-modified BIII model.…”

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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Section: Introductionmentioning

confidence: 99%

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

John¹,

Mwaniki²,

Aduda³

2023

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Maximum $$\log _q$$ likelihood estimation for parameters of Weibull distribution and properties: Monte Carlo simulation

Çankaya

Vila

2023

Soft Comput

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The maximum log q likelihood estimation method is a generalization of the known maximum log likelihood method to overcome the problem for modeling non-identical observations (inliers and outliers). The parameter q is a tuning constant to manage the modeling capability. Weibull is a flexible and popular distribution for problems in engineering.In this study, this method is used to estimate the parameters of Weibull distribution when non-identical observations exist. Since the main idea is based on modeling capability of objective function ρ(x; θ) = log q f (x; θ) , we observe that the finiteness of score functions cannot play a role in the robust estimation for inliers. The properties of Weibull distribution are examined. In the numerical experiment, the parameters of Weibull distribution are estimated by log q and its special form, log, likelihood methods if the different designs of contamination into underlying Weibull distribution are applied. The optimization is performed via genetic algorithm. The modeling competence of ρ(x; θ) and insensitiveness to non-identical observations are observed by Monte Carlo simulation. The value of q can be chosen by use of the mean squared error in simulation and the p-value of Kolmogorov-Smirnov test statistic used for evaluation of fitting competence. Thus, we can overcome the problem about determining of the value of q for real data sets.

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A general class of trimodal distributions: properties and inference

Vila

Victor

Çankaya

et al. 2023

Journal of Applied Statistics

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On the robustness of an epsilon skew extension for Burr III distribution on the real line

Cited by 8 publications

References 48 publications

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

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

Maximum $$\log _q$$ likelihood estimation for parameters of Weibull distribution and properties: Monte Carlo simulation

A general class of trimodal distributions: properties and inference

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