索赔次数数据分布的拟合

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1、ABSTRACTWil．htlledavelopmentofthesocietyinChina，theinsuranceindustrygrowsfasterandt'astmEspeciallyafterenteringWTO，thecompetitionbetweentheinsurancecompaniesbec01nesnloreintensive．ttowcananinsmantecorot)anykeeptheadvantageplaceintheIUarht?Thekeysattlementistodesignthereason

2、ableinsurancepolicyandequitableIn—ei[1innlAsweallknow，claimfrequencyandclaimamonntaretwoimpoitantfactorsincaculatingpremium．PoissouandNegativeBinomiaJdistributionsareusuallyusedtofitclaimfrequency—thenunlbelofclaimsinaunitoftime．Especiallywhentheclaimfrequencydataarefr0111P

3、oissondistribution，itcanbeprovedthatthedish‘ibutionoftotalclaimamountisCompomulPoisson，whichisoftenusedbytheinsurancecompany．Poisson，NegativeBinomialandBinomialdistributiontotallyconstituteaclassofdiscretelion—negativeinteger—valueddistributionscalled(a，b，0)family．Adismeten

4、ou—negativeinteger—valuedrandomvariableNwithprobabilityfunctionn=PIN=k1isanumberoftile(a，b，0)familyinthereareconstantsaandbsuchthatforallk=1，2，⋯，tileprobabili—Yfunctionsatisfiestherelationship老=o+ibGivenadat．asetofclaimfrequency，itmightbepossibletomakeaninitialchoicebclween

5、thethreedistributionsjustmentionedbytwosimplemethods．Oneistocomparethesamplemeanandthesamplevariance．Theotheristolookataplotofknk／na——laSafunctionof☆，wheremisthenumberot‘obsm。vationsatintegervaluek．Iftiledatasetresultsillanapproximatelystraightlinetbrtheplot，thenaslopeofa=0

6、suggestsaPoissonmodel．aPositiveslopea>0suggestsaNegativeBinomialmodel，an

7、LSEandGLSE)basedontheideaoflatl．elmethod．Additionally，wegivethepowerofthemtocomparethethreetestingstatisticsabuve．InchallI，el3and4，weintroduceze7+D—Tr仳ncnted(n，b，0)andZero—Modified(a，b，0)Bothtechniquesallowmoremodellingflexibilityinsituationswhere岛mightbeabadlitwithduetosot

8、nespecialcircumstanceswithregardtotheinsuranceprocess．Wealsogivethetwotestingstati