Truncated, censored, and actuarial payment-type moments for robust fitting of a single-parameter Pareto distribution

Poudyal, Chudamani

doi:10.1016/j.cam.2020.113310

Cited by 14 publications

(5 citation statements)

References 17 publications

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“…, (12) this shows that, the estimator in ( 11) is consistent sufficient estimator of k, while the estimator…”

Section: Case 1: α Is Knownmentioning

confidence: 77%

“…Wu [10] has constructed an interval estimation for Pareto distribution using a doubly Type-II censored sample. Recently, Han [11] has investigated the expected Bayesian estimation and its expected mean square error of Pareto distribution parameter under different loss functions and Poudyal [12] has investigated the truncated, censored, and actuarial payment-type moments of the robust fitting of a single parameter Pareto distribution.…”

Section: Introductionmentioning

confidence: 99%

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The Combined-Unified Hybrid Censored Samples from Pareto Distribution: Estimation and Properties

Emam¹

2021

Applied Sciences

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In this paper, we use the combined-unified hybrid censoring samples to obtain the maximum likelihood estimates of the unknown parameters, survival, and hazard functions of Pareto distribution. Next, we discuss some efficiency criteria of the maximum likelihood estimators, including; the unbiasedness, consistency, and sufficiency. Additionally, we use MCMC to obtain the Bayesian estimates of the unknown parameters. In addition, we calculate the intervals estimation of the unknown parameters. Finally, we analyze a set of real data in view of the theoretical findings of the paper.

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“…, (12) this shows that, the estimator in ( 11) is consistent sufficient estimator of k, while the estimator…”

Section: Case 1: α Is Knownmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

The Combined-Unified Hybrid Censored Samples from Pareto Distribution: Estimation and Properties

Emam¹

2021

Applied Sciences

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“…We now define the Method of Truncated Moment (MTuM) estimator from grouped data. By using the empirical cdf, Equation (1), and pdf, Equation (3), the sample truncated moment for a grouped data as defined by Poudyal (2021b) is given by…”

Section: Mtum For Grouped Datamentioning

confidence: 99%

Robust Estimation of the Tail Index of a Single Parameter Pareto Distribution from Grouped Data

Poudyal

2024

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Numerous robust estimators exist as alternatives to the maximum likelihood estimator (MLE) when a completely observed ground-up loss severity sample dataset is available. However, the options for robust alternatives to a MLE become significantly limited when dealing with grouped loss severity data, with only a handful of methods, like least squares, minimum Hellinger distance, and optimal bounded influence function, available. This paper introduces a novel robust estimation technique, the Method of Truncated Moments (MTuM), pecifically designed to estimate the tail index of a Pareto distribution from grouped data. Inferential justification of the MTuM is established by employing the central limit theorem and validating it through a comprehensive simulation study.

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“…If a truncated (both singly and doubly) normal sample data set is available then the MLE procedures for such data have been developed by Cohen (1950) and the method of moments estimators can be found in Cohen (1951) and Shah and Jaiswal (1966). A novel robust estimation procedure called method of truncated moments (MTuM) for modeling different actuarial loss data scenarios is initially purposed by Poudyal (2018) and further developed by Poudyal (2021). But the goal and motivation of this research work is different.…”

Section: Introductionmentioning

confidence: 99%

Robust Estimation of Loss Models for Lognormal Insurance Payment Severity Data

Poudyal

2021

Preprint

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The primary objective of this scholarly work is to develop two estimation proceduresmaximum 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-perpayment 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 abovementioned 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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Truncated, censored, and actuarial payment-type moments for robust fitting of a single-parameter Pareto distribution

Cited by 14 publications

References 17 publications

The Combined-Unified Hybrid Censored Samples from Pareto Distribution: Estimation and Properties

The Combined-Unified Hybrid Censored Samples from Pareto Distribution: Estimation and Properties

Robust Estimation of the Tail Index of a Single Parameter Pareto Distribution from Grouped Data

Robust Estimation of Loss Models for Lognormal Insurance Payment Severity Data

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