Mixture modeling of data with multiple partial right-censoring levels

Michael, Semhar; Miljkovic, Tatjana; Melnykov, Volodymyr

doi:10.1007/s11634-020-00391-x

Cited by 5 publications

(6 citation statements)

References 30 publications

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“…As a member of log-location-scale family, the lognormal distribution has diverse applications in actuarial science, business, and economics (see, e.g., Serfling, 2002, and the references therein) which closely approximates certain types of homogeneous actuarial loss data (Hewitt et al, 1979;Punzo et al, 2018). Further, it has been established that, even for the heterogeneous actuarial losses, lognormal distribution is able to capture the nature of the data set either on the head or on the tail or on both head and tail parts of different composite models, see, for example, Cooray and Ananda (2005), Brazauskas and Kleefeld (2016), Miljkovic and Grün (2016), Punzo et al (2018), Blostein and Miljkovic (2019), and Michael et al (2020). More comprehensive investigation of 256 different composite models have been analyzed by Grün and Miljkovic (2019).…”

Section: Introductionmentioning

confidence: 69%

“…This section is to observe the performance of the estimation methods developed in the previous sections. For the illustration purpose only, we consider the 1500 US indemnity losses which is widely studied in actuarial literature, see, for example, Frees and Valdez (1998), Punzo et al (2018), Michael et al (2020).…”

Section: Numerical Examplesmentioning

confidence: 99%

“…We consider this example purely for illustrative purpose and a preliminary diagnostics, see Figure 1, shows that the lognormal distribution provides a satisfactory, thought not perfect, fit to the indemnity data. Moreover, the complete ground-up data (though the data set contains some right-censored observations) set is identified to fit LN(w 0 = 0, θ, σ ), see, for example, Punzo et al (2018) and Michael et al (2020), distribution. The Kolmogorov-Smirnov (KS) test statistics (see, e.g., Klugman et al, 2019, Section 15.4.1, p. 360) is computed to be 0.0266 and with the significance level of 5% the corresponding critical value is 0.0351.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…As seen in Tables 1 and 2, the dynamic MTM estimators sacrifice little asymptotic efficiency with respect to MLE but are more robust as well as computationally more efficient than MLE if properly implemented, see, for example, (4.18) and Note 4.1, and these properties are highly desirable in practice. Finally, the developed estimators are implemented on a real-life data set to analyze the 1500 US indemnity losses which is widely studied in the actuarial literature (see, e.g., Frees and Valdez, 1998;Michael et al, 2020), and it is found that most of the fitted models are plausible for this data set.…”

Section: Summary and Future Directionmentioning

confidence: 99%

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Robust Estimation of Loss Models for Lognormal Insurance Payment Severity Data

Poudyal¹

2021

ASTIN Bull.

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Abstarct The primary objective of this scholarly work is to develop two estimation procedures – maximum likelihood estimator (MLE) and method of trimmed moments (MTM) – for the mean and variance of lognormal insurance payment severity data sets affected by different loss control mechanism, for example, truncation (due to deductibles), censoring (due to policy limits), and scaling (due to coinsurance proportions), in insurance and financial industries. Maximum likelihood estimating equations for both payment-per-payment and payment-per-loss data sets are derived which can be solved readily by any existing iterative numerical methods. The asymptotic distributions of those estimators are established via Fisher information matrices. Further, with a goal of balancing efficiency and robustness and to remove point masses at certain data points, we develop a dynamic MTM estimation procedures for lognormal claim severity models for the above-mentioned transformed data scenarios. The asymptotic distributional properties and the comparison with the corresponding MLEs of those MTM estimators are established along with extensive simulation studies. Purely for illustrative purpose, numerical examples for 1500 US indemnity losses are provided which illustrate the practical performance of the established results in this paper.

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Section: Introductionmentioning

confidence: 69%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Summary and Future Directionmentioning

confidence: 99%

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Robust Estimation of Loss Models for Lognormal Insurance Payment Severity Data

Poudyal¹

2021

ASTIN Bull.

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“…The important conclusion that can be drawn from these observations is that MLE-based model estimates are usually flawed, resulting in biased risk predictions and/or unreliable assessment of their variability. One of the most popular proposals to deal with such a problem that emerged in the literature is to fit spliced (or mixtures of) loss distributions; see Cooray and Ananda (2005), Scollnik (2007), Brazauskas and Kleefeld (2016), Blostein and Miljkovic (2019), Michael et al (2020), Gui et al…”

Section: Introductionmentioning

confidence: 99%

Method of Winsorized Moments for Robust Fitting of Truncated and Censored Lognormal Distributions

Poudyal¹,

Zhao²,

Brazauskas³

2022

Preprint

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When constructing parametric models to predict the cost of future claims, several important details have to be taken into account: (i) models should be designed to accommodate deductibles, policy limits, and coinsurance factors, (ii) parameters should be estimated robustly to control the influence of outliers on model predictions, and (iii) all point predictions should be augmented with estimates of their uncertainty. The methodology proposed in this paper provides a framework for addressing all these aspects simultaneously. Using payment-per-payment and payment-per-loss variables, we construct the adaptive version of method of winsorized moments (MWM) estimators for the parameters of truncated and censored lognormal distribution. Further, the asymptotic distributional properties of this approach are derived and compared with those of the maximum likelihood estimator (MLE) and method of trimmed moments (MTM) estimators. The latter being a primary competitor to MWM. Moreover, the theoretical results are validated with extensive simulation studies and risk measure sensitivity analysis. Finally, practical performance of these methods is illustrated using the well-studied data set of 1500 U.S. indemnity losses. With this real data set, it is also demonstrated that the composite models do not provide much improvement in the quality of predictive models compared to a stand-alone fitted distribution specially for truncated and censored sample data.

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Loss modeling with the size-biased lognormal mixture and the entropy regularized EM algorithm

Bae,

Miljkovic

2024

Insurance: Mathematics and Economics

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Mixture modeling of data with multiple partial right-censoring levels

Cited by 5 publications

References 30 publications

Robust Estimation of Loss Models for Lognormal Insurance Payment Severity Data

Robust Estimation of Loss Models for Lognormal Insurance Payment Severity Data

Method of Winsorized Moments for Robust Fitting of Truncated and Censored Lognormal Distributions

Loss modeling with the size-biased lognormal mixture and the entropy regularized EM algorithm

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