Empirical implementation of credibi

Empirical implementation of credibility
We have discussed the limited-fluctuation credibility method, the Buhlmann and Buhlmann-Straub credibility methods, as well as the Byesian method for future loss prediction. The implementation of these methods requires the knowledge or assumptions of some unknown parameters of the model. Foe the limited-fluctuation credibility method, Poisson distribution is usually assumed for claim frequency. In addition, we need to know the coefficient of variation of claim severity if predictions of claim severity or aggregate loss/pure premium are required. For the Buhlmann and Buhlmann-Straub methods, the key quantities required are the expected value of the process variance, 0, and the variance of the hypothetical means, 0. These quantities depend on the assumptions of the prior distribution of the risk parameters and the conditional distribution of the random loss variable. For the Bayesian method, the predicted loss can be obtained relatively easily if the prior distribution is conjugate to the likelihood. Yet the posterior mean, which is the Bayesian predictor of the future loss, depends on the hyperparameters of the posterior distribution. Thus, for the empirical implementation of the Bayesian method, the hyperparameters have to be estimated.
In this chapter, we discuss the estimation of the required parameters for the implementation of the credibility estimates. We introduce the empirical Bayes method, which may be nonparametric, semiparametric, or parametric, depending on the assumptions concerning the prior distribution and the likelihood. Our main focus is on the Buhlmann and Buhlmann-Straub credibility models, the nonparametic implementation of which is relatively straightforward.
Learning objectives
1. Empirical Bayes method
2. Nonparametric estimation
3. Semiparametric estimation
4. Parametric estimation

Hasil (Bahasa Indonesia) 1:

Empiris pelaksanaan kredibilitasKita telah membahas metode terbatas-fluktuasi kredibilitas, yang Buhlmann dan Buhlmann-Straub metode kredibilitas, serta metode Byesian untuk prediksi hilangnya masa depan. Pelaksanaan metode ini memerlukan pengetahuan atau asumsi beberapa parameter yang tidak diketahui model. Musuh metode kredibilitas terbatas-fluktuasi, distribusi Poisson biasanya diasumsikan untuk frekuensi klaim. Selain itu, kita perlu tahu koefisien variasi keparahan klaim jika prediksi keparahan klaim atau agregat kerugian/murni premium diperlukan. Bagi yang Buhlmann dan Buhlmann-Straub metode, jumlah kunci yang diperlukan adalah nilai yang diharapkan dan proses varians, 0, varians sarana hipotetis, 0. Jumlah ini bergantung pada asumsi-asumsi dari distribusi sebelumnya parameter risiko dan distribusi bersyarat variabel acak kerugian. Metode Bayesian, kerugian diperkirakan dapat diperoleh relatif mudah jika distribusi sebelumnya konjugat untuk kemungkinan. Namun berarti posterior, yaitu prediksi Bayesian hilangnya masa depan, tergantung pada hyperparameters distribusi posterior. Dengan demikian, untuk implementasi empiris metode Bayesian, hyperparameters harus dapat diperkirakan. In this chapter, we discuss the estimation of the required parameters for the implementation of the credibility estimates. We introduce the empirical Bayes method, which may be nonparametric, semiparametric, or parametric, depending on the assumptions concerning the prior distribution and the likelihood. Our main focus is on the Buhlmann and Buhlmann-Straub credibility models, the nonparametic implementation of which is relatively straightforward.Learning objectives1. Empirical Bayes method2. Nonparametric estimation3. Semiparametric estimation4. Parametric estimation