LEADER 03632nam 2200625Ia 450 001 9910830084103321 005 20230213211631.0 010 $a1-282-30796-7 010 $a9786612307966 010 $a0-470-31663-2 010 $a0-470-31730-2 035 $a(CKB)1000000000687538 035 $a(EBL)468960 035 $a(OCoLC)264615496 035 $a(SSID)ssj0000339951 035 $a(PQKBManifestationID)11256702 035 $a(PQKBTitleCode)TC0000339951 035 $a(PQKBWorkID)10383524 035 $a(PQKB)10232439 035 $a(MiAaPQ)EBC468960 035 $a(EXLCZ)991000000000687538 100 $a19830912d1984 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLoss distributions$b[electronic resource] /$fRobert V. Hogg, Stuart A. Klugman, with the assistance of Charles C. Hewitt and Gary Patrik 210 $aNew York $cWiley$dc1984 215 $a1 online resource (254 p.) 225 1 $aWiley series in probability and mathematical statistics 300 $aDescription based upon print version of record. 311 $a0-471-87929-0 320 $aIncludes bibliography and index. 327 $aLOSS DISTRIBUTIONS; Contents; 1. Introduction; 1.1. Basic Terminology; 1.2. Coverage Limitations; 1.3. Evaluation of Coverage Limitations; 1.4. Data Collection and Modeling; 2. Models for Random Variables; 2.1. Models; 2.2. The Poisson Process and Related Models; 2.3. Models for Joint Random Variables; 2.4. Normal Models; 2.5. Linear Functions of Random Variables; 2.6. Functions of Random Variables; 2.7. The Mixture of Models; 3. Statistical Inference; 3.1. Model-Free Estimation of Distributions; 3.2. Estimating Distributions by Simulation; 3.3. Point Estimation; 3.4. Interval Estimation 327 $a3.5. Tests of Statistical Hypotheses3.6. Testing the Fit of Models; 3.7. Applications and Associated Algorithms; 4. Modeling Loss Distributions; 4.1. Introduction; 4.2. Ungrouped Data, Truncation from Below; 4.3. Grouped Data, Mixture of Models; 4.4. Truncated and Shifted Data, Mixture of Models; 4.5. Clustering, Truncation from Above, Combining Samples; 4.6. A Bivariate Model; 4.7. A Review of the Modeling Process; 5. Applications of Distributional Models; 5.1. Introduction; 5.2. Inflation, Percentile Estimation; 5.3. Deductibles, Leveraging 327 $a5.4. Other Deductibles, Comparisons of Distributions5.5. Limits, Comparisons of Distributions; 5.6. Limits, Layers, Allocated Loss Adjustment Expenses; References; Appendix Characteristics of Selected Distributions; Index 330 $aDevoted to the problem of fitting parametric probability distributions to data, this treatment uniquely unifies loss modeling in one book. Data sets used are related to the insurance industry, but can be applied to other distributions. Emphasis is on the distribution of single losses related to claims made against various types of insurance policies. Includes five sets of insurance data as examples. 410 0$aWiley series in probability and mathematical statistics. 606 $aInsurance$xMathematical models 606 $aInsurance$xStatistical methods 615 0$aInsurance$xMathematical models. 615 0$aInsurance$xStatistical methods. 676 $a368 676 $a368.0101519532 676 $a368.015 700 $aHogg$b Robert V$022385 701 $aKlugman$b Stuart A.$f1949-$0103763 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830084103321 996 $aLoss distributions$969174 997 $aUNINA