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{"sheet":"Describe","index":0,"n_rows":19,"n_cols":2,"rows_kept":19,"cut":false,"hidden":false,"merged":[]}
["This workbook gives some examples of graduating data, mostly using the Whittaker-Henderson method, in 64-bit Excel."]
[]
["Worksheet","Description"]
["Underlying","The hypothetical data used for the 1-dimensional example.  Note that this data is not from a real experience study."]
["LeastSquares","Applying weighted least squares graduation to the ratios of the raw rates to the 1983 IAM basic table."]
["WH","Applying Whittaker-Henderson graduation to the raw mortality rates"]
["WHL","Applying Lowrie's variation of Whittaker-Henderson"]
["h","An example of some tests that might be done to find an appropriate value for \"h\""]
["2-dim","A hypothetical construction of a select lapse table.  Note that this data is not from a real experience study."]
[]
["To run the Whittaker-Henderson examples, you will need to obtain a copy of WHGrad64.dll and put it into a directory in your path,"]
["such as c:\\Windows.  The file is available at http://www.howardfamily.ca/~bob/graduation."]
[]
["I encourage you to use this sample as a model for your own graduations.  You can see the VBA code by Alt-F11.  You can use"]
["the VBA procedures in your own workbooks by dragging the module \"Grad\" from this workbook to yours in the VBA Project window."]
[]
["R.C.W. (Bob) Howard, FSA, FCIA"]
["bob@howardfamily.ca"]
["2007 01 22"]

{"sheet":"Underlying","index":1,"n_rows":34,"n_cols":8,"rows_kept":34,"cut":false,"hidden":false,"merged":[]}
["Simulated experience by policies"]
["Age","Exposure","Deaths","Raw q","\"Real\" q","Basic 83","Raw/Basic","Real/Basic"]
[67,915,14,1.5300546448087432E-2,8.4210618622448975E-3,1.0011999999999998E-2,{"$f":"D3/F3","v":1.528220779872896},{"$f":"E3/F3","v":0.84109686998051325}]
[68,1016,8,7.874015748031496E-3,9.4075892857142848E-3,1.0931E-2,{"$f":"D4/F4","v":0.72033809788962544},{"$f":"E4/F4","v":0.86063391141837753}]
[69,1202,7,5.8236272878535774E-3,1.0512500000000001E-2,1.1916E-2,0.48872333734924284,0.88221718697549523]
[70,1398,18,1.2875536480686695E-2,1.1750000000000002E-2,1.3026999999999999E-2,0.98837310821268876,0.901972825669763]
[71,1504,17,1.1303191489361703E-2,1.3136000000000004E-2,1.4326E-2,0.78899842868642345,0.91693424542789359]
[72,1694,30,1.770956316410862E-2,1.4688320000000005E-2,1.5872000000000001E-2,1.1157738888677307,0.92542338709677441]
[73,1829,45,2.4603608529250958E-2,1.6426918400000004E-2,1.7716999999999997E-2,1.3887005999464335,0.92718397019811516]
[74,2095,40,1.9093078758949882E-2,1.8374148608000004E-2,1.9882999999999998E-2,0.96027152637679847,0.92411349434190049]
[75,2246,48,2.1371326803205699E-2,2.0555046440960009E-2,2.2383E-2,0.95480171573094308,0.91833295094312684]
[76,2458,57,2.3189585028478437E-2,2.2997652013875214E-2,2.5228E-2,0.91920029445371954,0.91159235824778873]
[77,2771,87,3.1396607722843736E-2,2.5733370255540244E-2,2.8433E-2,1.1042312708065887,0.90505294044034201]
[78,3021,78,2.5819265143992055E-2,2.8797374686205069E-2,3.2016999999999997E-2,0.80642362319992689,0.89944013137411605]
[79,3192,90,2.819548872180451E-2,3.2229059648549677E-2,3.6028999999999999E-2,0.78257761030848794,0.89453106243719438]
[80,3387,128,3.7791555949217598E-2,3.6072546806375644E-2,4.0524999999999999E-2,0.93254919060376551,0.8901307046607192]
[81,3804,157,4.1272344900105153E-2,4.0377252423140719E-2,4.5560999999999997E-2,0.90587004016823935,0.88622401666207329]
[82,3740,163,4.3582887700534756E-2,4.5198522713917624E-2,5.1194000000000003E-2,0.85132804040580445,0.88288711008941712]
[83,3702,194,5.2404105888708807E-2,5.0598345439587744E-2,5.7482999999999999E-2,0.91164528449643911,0.88023146738318714]
[84,3631,224,6.1690994216469293E-2,5.6646146892338281E-2,6.4511999999999986E-2,0.95627161173842545,0.87807147340554148]
[85,3350,245,7.3134328358208961E-2,6.3419684519418887E-2,7.2367999999999988E-2,1.0105893261967855,0.87634983030371016]
[86,2700,170,6.2962962962962957E-2,7.1006046661749131E-2,8.1137000000000001E-2,0.77600802301000726,0.87513768886881604]
[87,2380,182,7.6470588235294124E-2,7.9502772261159038E-2,9.0907000000000002E-2,0.84119581809205146,0.87455060953676877]
[88,2069,204,9.8598356694055103E-2,8.9019104932498122E-2,0.10172099999999999,0.96930188155892205,0.87513006097559132]
[89,1888,207,0.10963983050847458,9.9677397524397887E-2,0.11345399999999999,0.96638135727673413,0.87857102900204398]
[90,1707,195,0.11423550087873462,0.11161468522732565,0.12593599999999999,0.90709170434772124,0.88628100961858136]
[91,1268,162,0.12776025236593061,0.12498444745460474,0.13899700000000001,0.91915834417959097,0.89918809366104835]
[92,849,106,0.1248527679623086,0.1399585811491573,0.15246899999999999,0.8188731346195528,0.91794778708561942]
[93,607,79,0.13014827018121911,0.1567296108870562,0.166187,0.78314350810363687,0.94309188376380937]
[94,396,62,0.15656565656565657,0.17551316419350305,0.180008,0.8697705466737955,0.97502979975058357]
[95,249,42,0.16867469879518071,0.19655074389672345,0.193795,0.87037693849263764,1.0142198916211638]
[96,182,35,0.19230769230769232,0.22011283316433025,0.20741100000000001,0.92718174208548398,1.0612399205651111]
[97,108,32,0.29629629629629628,0.24650237314404988,0.220718,1.3424201755013017,1.1168204366841394]
["Total",{"$f":"SUM(Exposure)","v":61358},{"$f":"SUM(Deaths)","v":3126}]

{"sheet":"LeastSquares","index":2,"n_rows":34,"n_cols":6,"rows_kept":34,"cut":false,"hidden":false,"merged":[[1,2,1,5]]}
["Simulated experience - weighted least squares polynomial fit to data"]
[null,null,"Degree Polynomial"]
["Age","Raw/Basic",0,1,2,3]
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[69,0.48872333734924284,0.92625983816032775,0.97741287935030641,0.99879487325083394,0.99083554729777334]
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[77,1.1042312708065887,0.92625983816032775,0.94233296355226814,0.93503410370534212,0.94167494642943117]
[78,0.80642362319992689,0.92625983816032775,0.9379479740775134,0.92924847363368923,0.93458806963087737]
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[82,0.85132804040580445,0.92625983816032775,0.92040801617849421,0.91096032250604042,0.9090950038796648]
[83,0.91164528449643911,0.92625983816032775,0.91602302670373947,0.90760187701386907,0.90400619404347426]
[84,0.95627161173842545,0.92625983816032775,0.91163803722898462,0.90472886843759404,0.89965950534427375]
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[90,0.90709170434772124,0.92625983816032775,0.88532810038045595,0.89768499221376685,0.89555739492351338]
[91,0.91915834417959097,0.92625983816032775,0.8809431109057011,0.89821004204876609,0.89960229313206963]
[92,0.8188731346195528,0.92625983816032775,0.87655812143094636,0.89922052879966174,0.90530266646299506]
[93,0.78314350810363687,0.92625983816032775,0.87217313195619162,0.90071645246645371,0.91277268416446233]
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[96,0.92718174208548398,0.92625983816032775,0.85901816353192717,0.90811684496220746,0.94694229597383761]
[97,1.3424201755013017,0.92625983816032775,0.85463317405717243,0.91155451629258488,0.96263258363919535]

{"sheet":"WH","index":3,"n_rows":34,"n_cols":10,"rows_kept":34,"cut":false,"hidden":false,"merged":[[1,2,1,5],[1,6,1,9]]}
["Simulated experience - Graduated with Whittaker-Henderson method"]
["Order",4,"Graduated q",null,null,null,"Grad / Basic 83"]
["Age","Raw q",1,100,10000,1000000,{"$f":"C3","v":1},{"$f":"D3","v":100},{"$f":"E3","v":10000},{"$f":"F3","v":1000000}]
[{"$f":"Age","v":67},{"$f":"Raw","v":1.5300546448087432E-2},{"$f":"gradrange(Raw,Exposure,$B2,C3)","v":{"$error":"#VALUE!"}},{"$f":"gradrange(Raw,Exposure,$B2,D3)","v":0},{"$f":"gradrange(Raw,Exposure,$B2,E3)","v":0},{"$f":"gradrange(Raw,Exposure,$B2,F3)","v":0},{"$f":"C4:C34/Basic83","v":{"$error":"#VALUE!"}},{"$f":"D4:D34/Basic83","v":0},{"$f":"E4:E34/Basic83","v":0},{"$f":"F4:F34/Basic83","v":0}]
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[null,null,null,"Graduated q",null,null,"Grad / Basic 83"]
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["Testing to find an appropriate value of h"]
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