ASYMPTOTIC CONFIDENCE ELLIPSE FOR LOG-NORMAL DISTRIBUTION WITH APPLICATIONS IN ACTUARIAL PRICING
DOI:
https://doi.org/10.55766/sujst6597Keywords:
Actuarial Pricing, Asymptotic Statistics, Confidence Ellipse, Log-normal DistributionAbstract
This study develops and validates asymptotic are particularly advantageousare particularly advantageous for the parameters of the log-normal distribution by leveraging the asymptotic properties of Maximum Likelihood Estimators (MLEs). Monte Carlo simulations across various parameter settings are used to evaluate the performance of these ellipses. The results indicate that they yield accurate parameter estimates with empirical coverage probabilities closely matching the nominal 95% level, ranging from 94.27% to 95.13%, even in small samples. A theoretical lower bound on the sample size required to attain a specified level of precision is also derived and confirmed via simulation. Furthermore, the methodology is applied to health insurance pricing to visualize parameter uncertainty and quantify its impact on premium estimates under a log-normal loss model. The framework allows the derivation of confidence intervals for premiums and estimation of the number of policyholders needed to meet target pricing accuracy.
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