A New Modified Kumaraswamy Distribution: Actuarial Measures and Applications

Alanzi, Ayed R. A.; Rafique, M. Qaisar; Tahir, M. H.; Sami, Waqas; Jamal, Farrukh

doi:10.1155/2022/4288286

Cited by 6 publications

(3 citation statements)

References 32 publications

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“…Numerical approaches were applied in this paper's risk analysis and evaluation procedure (see Section 4), as well as in the issue of distributional validation under the NRR and its updated equivalent version (see Section 7). For more details, see Alanzi et al [14], Zhou and Gao [15], Hamed et al [16], and Yousof et al [17].…”

Section: Risk Indicatorsmentioning

confidence: 99%

Distributional Censored and Uncensored Validation Testing under a Modified Test Statistic with Risk Analysis and Assessment

Tashkandy

Emam

Cordeiro

et al. 2023

Journal of Mathematics

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This paper introduces and studies a unique probability distribution. The maximum likelihood estimation, the ordinary least squares, the weighted least squares, and the Anderson–Darling estimation methods all take into account a number of financial risk indicators, including the value-at-risk, tail-value-at-risk, tail variance, tail mean-variance, and mean excess loss function. These four approaches were used in a simulation study and an application to insurance claims data for the actuarial evaluation. The well-known Nikulin–Rao–Robson statistic is taken into consideration for distributional validation under the whole set of data. Three complete actual datasets and a simulation study are used to evaluate the Nikulin–Rao–Robson test statistic. An updated version of the Nikulin–Rao–Robson statistic is taken into consideration for censored distributional validation. Three censored actual datasets and a thorough simulation analysis are used to evaluate the novel Nikulin–Rao–Robson test statistic.

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Section: Risk Indicatorsmentioning

confidence: 99%

Distributional Censored and Uncensored Validation Testing under a Modified Test Statistic with Risk Analysis and Assessment

Tashkandy

Emam

Cordeiro

et al. 2023

Journal of Mathematics

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“…This has necessitated the development of new distributions for risk modelling and assessment. Some of the distributions that have been developed and used to model financial and insurance data include: unit half-logistic geometric (UHLG) distribution (see [1]), unit exponentiated Fréchet distribution (see [2]), new modified Kumaraswamy distribution (see [3]), new beta power transformed Weibull distribution (see [4]), unit Weibull distribution (see [5]), WT-XW distribution (see [6]), extended exponential geometric distribution (see [7]), Weibull loss distribution (see [8]), unit Gompertz distribution (see [9]) and log-Lindley distribution (see [10]).…”

Section: Introductionmentioning

confidence: 99%

Generalized Unit Half-Logistic Geometric Distribution: Properties and Regression with Applications to Insurance

Nasiru¹,

Chesneau

Abubakari³

et al. 2023

Analytics

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The use of distributions to model and quantify risk is essential in risk assessment and management. In this study, the generalized unit half-logistic geometric (GUHLG) distribution is developed to model bounded insurance data on the unit interval. The corresponding probability density function plots indicate that the related distribution can handle data that exhibit left-skewed, right-skewed, symmetric, reversed-J, and bathtub shapes. The hazard rate function also suggests that the distribution can be applied to analyze data with bathtubs, N-shapes, and increasing failure rates. Subsequently, the inferential aspects of the proposed model are investigated. In particular, Monte Carlo simulation exercises are carried out to examine the performance of the estimation method by using an algorithm to generate random observations from the quantile function. The results of the simulation suggest that the considered estimation method is efficient. The univariate application of the distribution and the multivariate application of the associated regression using risk survey data reveal that the model provides a better fit than the other existing distributions and regression models. Under the multivariate application, we estimate the parameters of the regression model using both maximum likelihood and Bayesian estimations. The estimates of the parameters for the two methods are very close. Diagnostic plots of the Bayesian method using the trace, ergodic, and autocorrelation plots reveal that the chains converge to a stationary distribution.

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“…Zografos and Balakrishnan (2009) proposed the gamma generated family. Bourguignon et al [3] [7], Kumaraswamy Laplace by Aryal [7], Kumaraswamy exponential-Weibull by Cordeiro et al [5], Kumaraswamyexponentiated inverse Rayleigh by Haq [8]; Olalekan et al [9]; Ayed et al [10].…”

Section: Introductionmentioning

confidence: 99%

A New Life-Time Model with Bathtub and Inverted Bathtub Failure Rate Function

Manu,

Usman,

Audu

et al. 2023

AJPAS

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In this paper, a three parameter model called Zubair- Kumaraswamy (Z-Kum) distribution is proposed. The extension was done using Zubair G-Family [1] of continuous probability distribution to extend the well knownKumaraswamy distribution to make it more flexible in modeling and predicting real world phenomenon. Some basic structural properties of the new distributions like cdf, pdf, quantile functions, moments, moment generating functions, characteristics functions and order statistics was obtained. Survival function, hazard function, reversed hazard rate function and a cumulative hazard rate function was also obtained. Behavior of the hazard rate plot exhibit increase, decrease, Bathtub and inverted Bathtub shape. Maximum likelihood estimate was used to estimate the Z-Kum distribution parameters. Monte Carlo simulation was carried out to evaluate the performance of MLE method adopted. Result of the simulation studies indicates that MLE is good for the estimation of our distribution parameters. To compare the proposed model with the other fitted existing models, analytical measure of goodness of fit of some information criterion was considered using three real life data sets. From the results obtained, it is evident that our proposed model gives better fit than the other competing models and therefore, our proposed model provide greater flexibility in modeling real world phenomenon.

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A New Modified Kumaraswamy Distribution: Actuarial Measures and Applications

Cited by 6 publications

References 32 publications

Distributional Censored and Uncensored Validation Testing under a Modified Test Statistic with Risk Analysis and Assessment

Distributional Censored and Uncensored Validation Testing under a Modified Test Statistic with Risk Analysis and Assessment

Generalized Unit Half-Logistic Geometric Distribution: Properties and Regression with Applications to Insurance

A New Life-Time Model with Bathtub and Inverted Bathtub Failure Rate Function

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