The Measures of Accuracy of Claim Frequency Credibility Predictor
Abstract
:1. Introduction
 The procedure in premium prediction taking into account some completely new risk factors (for which realizations of the response variable are not observed);
 Use of two accuracy measures applicable for any prediction problem based on the quantiles of absolute prediction errors;
 The parametric bootstrap estimators of the accuracy measures of the considered credibility predictor.
2. The Background of Bühlmann–Straub Model
3. Credibility Predictor of Claim Frequency
4. Bootstrap Estimators of Prediction Accuracy Measures for Claim Frequency
Algorithm 1 The parametric bootstrap algorithm 

5. The Case Study Based on Longitudinal Portfolio
 The type of the engine—benzine (BEN), diesel (DIE), hybrid (HYBRID);
 The power range—0–60, 61–80, 81–100, 101–120, 121–140, 141–160, 160+;
 The type of payment—cash, transfer.
6. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
GLMM  Generalized Linear Mixed Model 
LMM  Linear Mixed Model 
MSE  Mean Squared Error 
QAPE  Quantile of Absolute Prediction Errors 
QMAPE  Quantile of Mixture of Absolute Prediction Errors 
RMSE  Root Mean Squared Error 
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Number of Claims  0  1  2  3  4  5  6  7 

number of policies  41  23  11  5  2  1  1  1 
fraction of policies  0.482  0.271  0.128  0.059  0.024  0.012  0.012  0.012 
Statistic  Value 

${min}_{i=1,\dots ,K}{\widehat{N}}_{i,T+1}{max}_{i=1,\dots ,K}{\widehat{N}}_{i,T+1}$  0.26–3.73 
${min}_{i=1,\dots ,K}\widehat{RMSE}({\widehat{N}}_{i,T+1}){max}_{i=1,\dots ,K}\widehat{RMSE}({\widehat{N}}_{i,T+1})$  1.06–1.50 
${\widehat{QMAPE}}_{0.5}\left({({\widehat{N}}_{i,T+1})}_{i=1}^{K}\right)$  0.60 
${\widehat{QMAPE}}_{0.75}\left({({\widehat{N}}_{i,T+1})}_{i=1}^{K}\right)$  1.01 
${\widehat{QMAPE}}_{0.9}\left({({\widehat{N}}_{i,T+1})}_{i=1}^{K}\right)$  1.66 
${\widehat{QMAPE}}_{0.95}\left({({\widehat{N}}_{i,T+1})}_{i=1}^{K}\right)$  2.27 
${\widehat{QMAPE}}_{0.99}\left({({\widehat{N}}_{i,T+1})}_{i=1}^{K}\right)$  3.92 
Statistic  Value 

${\widehat{N}}_{i,T+1}$  0.65 
$\widehat{RMSE}({\widehat{N}}_{i,T+1})$  1.50 
${\widehat{QAPE}}_{0.5}({\widehat{N}}_{i,T+1})$  0.89 
${\widehat{QAPE}}_{0.75}({\widehat{N}}_{i,T+1})$  1.18 
${\widehat{QAPE}}_{0.9}({\widehat{N}}_{i,T+1})$  1.86 
${\widehat{QAPE}}_{0.95}({\widehat{N}}_{i,T+1})$  2.92 
${\widehat{QAPE}}_{0.99}({\widehat{N}}_{i,T+1})$  5.69 
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WolnyDominiak, A.; Żądło, T. The Measures of Accuracy of Claim Frequency Credibility Predictor. Sustainability 2021, 13, 11959. https://doi.org/10.3390/su132111959
WolnyDominiak A, Żądło T. The Measures of Accuracy of Claim Frequency Credibility Predictor. Sustainability. 2021; 13(21):11959. https://doi.org/10.3390/su132111959
Chicago/Turabian StyleWolnyDominiak, Alicja, and Tomasz Żądło. 2021. "The Measures of Accuracy of Claim Frequency Credibility Predictor" Sustainability 13, no. 21: 11959. https://doi.org/10.3390/su132111959