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ّ1A)Frequency relativities for each value of the age variable
DrivAgeVehBodyexp
ّ1A)Frequency relativities for each value of the age variable
DrivAgeVehBodyexposInc_lossCountFrequencyRatingVariableinc_lossTotalClaimsTotalExposFrequencyFrequencyRelativities
old peopleBus6.40109514462.349999410.156223268old people1061412.1846485171.0088980.1253140370.78091582
old peopleConvertible6.23956194453010.160267661older work. people2145303.02211857616.5420940.1555824130.969538376
old peopleCoupe40.761122526881.73998730.073599543oldest people683568.51413903099.6659820.1258200080.784068868
old peopleHardtop101.22929534158.81991130.128421323working people2132107.07411897409.4565370.1604706091
old peopleHatchback1329.253936244194.4161530.115102161young people1984840.7510005891.8713210.1697253631.057672584
old peopleMinibus34.0041067820653.9399530.088224638youngest people1307372.8985252612.2737850.200974341.252405919
old peopleMotorized caravan17.360711841088.7530.172803974
old peoplePanel van68.8049281339061.0098980.116270741
old peopleRoadster2.21492128720010.451483313Frequency relativities for each value of the vehicle type variable
old peopleSedan1961.344285385001.17952410.122874909RatingVariableinc_lossTotalClaimsTotalExposFrequencyFrequencyRelativities
old peopleStation wagon1145.831622235662.1351720.150109315Bus13363.119991025.848049280.386876392.528641418
old peopleTruck147.104722830758.65993130.088372418Convertible6888.809998332.596851470.0920334290.601534612
old peopleUtility310.4585962759.18352360.115957494Coupe187723.250675319.12662560.2350164291.53607791
older work. peopleBus4.5859000684790.83999610.218059701Hardtop294811.8686136783.29911020.1736246071.134818208
older work. peopleConvertible9.0403832996125.80999810.110614779Hatchback2589136.19213308810.3134840.1509594410.98667767
older work. peopleCoupe96.0930869354877.07997240.249757821Minibus116104.879745316.84052020.1420272890.928296721
older work. peopleHardtop167.060917257971.48718280.167603533Motorized caravan10673.949991559.279945240.2530366711.653859017
older work. peopleHatchback2159.537303634523.13743160.146327641Panel van133113.412568409.16084870.1661938091.086250182
older work. peopleMinibus89.056810411029.15999130.145974238Roadster1369.458179311.668720050.2570976071.680401476
older work. peopleMotorized caravan15.049965784474.79999940.265781335Sedan2681622.477159810444.599590.1529977271
older work. peoplePanel van112.670773423677.15993180.15975749Station wagon2363091.21112487638.3901440.1633852131.067893071
older work. peopleRoadster4.167008898000Truck319496.8485130843.96440790.1540349321.006779215
older work. peopleSedan2624.80219796301.45024560.173727377Utility597208.96482762105.7303220.1310709150.856685372
older work. peopleStation wagon1685.667351416571.24752460.145936267
older work. peopleTruck205.442847421712.38997190.0924831421B)cross-tabulation of variables to obtain empirical frequencies
older work. peopleUtility443.3675565113248.4598590.133072434Column Labels
oldest peopleBus1.204654346490.909999910.830113636old peopleolder work. peopleoldest peopleworking peopleyoung peopleyoungest peopleTotal Claim CountTotal exposuresTotal Empirical Frequency
oldest peopleConvertible0.125941136000Row LabelsClaim CountexposuresEmpirical FrequencyClaim CountexposuresEmpirical FrequencyClaim CountexposuresEmpirical FrequencyClaim CountexposuresEmpirical FrequencyClaim CountexposuresEmpirical FrequencyClaim CountexposuresEmpirical Frequency
oldest peopleCoupe8.9117043124720.86999520.224423963Bus16.401095140.15622326814.5859000680.21805970111.2046543460.83011363635.21834360.57489506823.1704312120.63082901625.2676249140.3796777551025.848049280.38687639
oldest peopleHardtop45.4154688610052.8954470.154132505Convertible16.2395619440.16026766119.0403832990.11061477900.125941136005.448323066015.6043805610.17843185106.1382614650332.596851470.092033429
oldest peopleHatchback952.4900753203356.99991080.113387008Coupe340.761122520.0735995432496.093086930.24975782128.9117043120.2244239632283.731690620.2627440081864.835044490.277627634624.793976730.24199425875319.12662560.235016429
oldest peopleMinibus7.414099931000Hardtop13101.2292950.12842132328167.06091720.167603533745.415468860.15413250534192.09308690.1769975234204.84873370.165976132072.651608490.275286403136783.29911020.173624607
oldest peopleMotorized caravan11.455167691633.41999810.087296845Hatchback1531329.2539360.1151021613162159.5373030.146327641108952.49007530.1133870082891758.5626280.1643387592651645.8973310.161006398199964.57221080.20630907413308810.3134840.150959441
oldest peoplePanel van20.380561261068.17999820.098132724Minibus334.004106780.0882246381389.05681040.14597423807.414099931019127.63039010.148867366850.401095140.1587267128.3340177960.23998028945316.84052020.142027289
oldest peopleRoadster0.292950034000Motorized caravan317.360711840.172803974415.049965780.265781335111.455167690.08729684545.5386721420.7221947616.3353867220.15784356123.5400410680.5649651971559.279945240.253036671
oldest peopleSedan1479.652293290130.471870.126381043Panel van868.804928130.11627074118112.67077340.15975749220.380561260.0981327241593.861738540.1598095271155.277207390.1989970281458.165639970.24069192868409.16084870.166193809
oldest peopleStation wagon449.3990418128521.239640.142412409Roadster12.2149212870.45148331304.167008898000.292950034001.037645448023.1074606430.64361233500.8487337440311.668720050.257097607
oldest peopleTruck31.7152635227387.1499460.189183356Sedan2411961.3442850.1228749094562624.802190.1737273771871479.6522930.1263810433512221.5852160.157995292431521.1964410.159742682120636.0191650.18867356159810444.599590.152997727
oldest peopleUtility91.2087611216206.37997120.131566308Station wagon1721145.8316220.1501093152461685.6673510.14593626764449.39904180.1424124093572251.9452430.158529613151647.7645450.1911680994457.78234090.20533775912487638.3901440.163385213
working peopleBus5.21834363103.52999930.574895068Truck13147.10472280.08837241819205.44284740.092483142631.715263520.18918335631163.46064340.18964809740173.67556470.23031449521122.56536620.171337146130843.96440790.154034932
working peopleConvertible5.448323066000Utility36310.458590.11595749459443.36755650.1330724341291.208761120.13156630864499.34291580.12816843560509.75770020.11770297945251.59479810.1788590242762105.7303220.131070915
working peopleCoupe83.7316906241234.83083220.262744008Grand Total6485171.0088980.12531403711857616.5420940.1555824133903099.6659820.12582000811897409.4565370.16047060910005891.8713210.1697253635252612.2737850.20097434493731800.818620.155247576
working peopleHardtop192.093086980514.1962340.17699752
working peopleHatchback1758.562628531199.69492890.164338759
working peopleMinibus127.630390159331.42985190.148867366combined rating classes by driver type frequency
working peopleMotorized caravan5.5386721421569.1340.72219476RatingVariableClaim Countsexposuresinc_lossfrequencyfrequency relativities
working peoplePanel van93.8617385445756.26267150.159809527younger people15258504.1451063292213.6480.1793243151
working peopleRoadster1.037645448000older people10388270.674881744980.6980.1255036640.69986975
working peopleSedan2221.585216585399.21093510.15799529working people11897409.4565372132107.0740.1604706090.894862519
working peopleStation wagon2251.945243552194.96933570.15852961older working people11857616.5420942145303.0220.1555824130.867603553
working peopleTruck163.460643494442.47984310.189648097lowrisk vehicle31129.393566132295.338150.2395791461.56040156
working peopleUtility499.3429158137361.3398640.128168435medium risk vehicle4542672.3915131051250.260.1698852871.106478892
young peopleBus3.1704312122992.53999320.630829016high risk vehicle458229842.997958550555.6930.1535368531
young peopleConvertible5.60438056123310.178431851
young peopleCoupe64.8350444963213.14989180.277627634
young peopleHardtop204.848733737921.44996340.16597613
young peopleHatchback1645.897331524767.55372650.161006398
young peopleMinibus50.401095149985.20997980.15872671
young peopleMotorized caravan6.335386722353.799999710.157843561
young peoplePanel van55.2772073910661.49998110.198997028
young peopleRoadster3.1074606431169.45817920.643612335combined rating classes by vehicle type risk and frequencies
young peopleSedan1521.196441397858.65572430.159742682RiskLevelclaim countsexposuresinc_lossfrequencyfrequency relativities
young peopleStation wagon1647.764545713646.90323150.19116809low31129.393566132295.338150.2395791461.56040156
young peopleTruck173.675564766873.39992400.230314495medium4542672.3915131051250.260.1698852871.106478892
young peopleUtility509.7577002155164.1299600.117702979high458229842.997958550555.6930.1535368531
youngest peopleBus5.2676249141522.94999720.379677755
youngest peopleConvertible6.138261465000
youngest peopleCoupe24.7939767316795.5799860.24199425833rd percentile of claim counts by vehicle type
youngest peopleHardtop72.6516084974193.01986200.27528640343.8
youngest peopleHatchback964.5722108451094.38981990.20630907467th percentile
youngest peopleMinibus8.33401779615105.1399420.239980289141.6
youngest peopleMotorized caravan3.5400410681554.04999820.564965197100th
youngest peoplePanel van58.1656399712889.29999140.2406919281598
youngest peopleRoadster0.848733744000
youngest peopleSedan636.019165226931.5111200.18867356
youngest peopleStation wagon457.7823409316494.7168940.205337759
youngest peopleTruck122.565366278322.76892210.171337146
youngest peopleUtility251.5947981112469.4718450.178859024
هI have this data and my part is to do this
Minimum Bias Method. Since we don’t know the relativities currently used in the rating plan,
the adjusted pure premium method cannot be applied directly. However, you could try using
the estimated relativities for territory to compute the adjusted relativities for rating class, and
vice versa.
a) Try this method. Does it improve the results (in the sense of moving the estimates closer
to the “true” values?)
b) Chapter 9 of the Werner & Modlin text describes a “minimum bias” method for
estimating relativities. Your answer to part a) is the first step in this minimum bias
method. You can compute additional steps using the relativities from the previous step
to compute the adjusted relativities in the current step. Do this and run additional
iterations until there is no difference in the result for the first 3 decimal places.
c) Check to see if the outer product of the relativities produced by this method produce a
result closer to the actual relativities that you produced in step 3
d) Prepare a rate table. You may convert pure premiums to rates using the “all variable”
method with a permissible loss ratio of .73.
5. Credibility Adjustment. Prepare an alternative rate table using credibility to compute the
classification pure premiums. Use the traditional method (“square root rule”) based on claim
counts with 1,082 claims as the standard for full credibility. The complement of credibility
should be the pure premium for the entire state (country). Covert these estimates to rates,
adjusted for any off-balance introduced by the credibility process. How do these rates compare
with the minimum bias rates? Comment on differences? Which do you think best meets
ratemaking objectives?
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