Kommutationszahlen i=0.035 (3.5 Prozent) für Männer Version 1.0 Der Berechnung liegt die Sterbetafel 2002/04 des Statistischen Bundesamtes zugrunde (Näheres dazu in der Lehrveranstaltung) x qx lx dx Dx Nx Cx Mx [1,] 0 4.562303e-03 100000.0000 456.230287 100000.00000 2.700243e+06 440.802209 8687.42298 [2,] 1 4.039899e-04 99543.7697 40.214674 96177.55528 2.600243e+06 37.540828 8246.62078 [3,] 2 2.013310e-04 99503.5550 20.033152 92887.63335 2.504066e+06 18.068756 8209.07995 [4,] 3 1.824246e-04 99483.5219 18.148242 89728.43690 2.411178e+06 15.815145 8191.01119 [5,] 4 1.341036e-04 99465.3736 13.338661 86678.32679 2.321450e+06 11.230795 8175.19605 [6,] 5 1.369391e-04 99452.0350 13.618869 83735.94485 2.234771e+06 11.078959 8163.96525 [7,] 6 1.165507e-04 99438.4161 11.589615 80893.21558 2.151035e+06 9.109333 8152.88629 [8,] 7 1.234775e-04 99426.8265 12.276980 78148.58688 2.070142e+06 9.323280 8143.77696 [9,] 8 1.189030e-04 99414.5495 11.820687 75496.55776 1.991994e+06 8.673205 8134.45368 [10,] 9 9.358174e-05 99402.7288 9.302281 72934.86086 1.916497e+06 6.594562 8125.78047 [11,] 10 9.396649e-05 99393.4266 9.339651 70461.87004 1.843562e+06 6.397154 8119.18591 [12,] 11 1.444701e-04 99384.0869 14.358030 68072.70433 1.773100e+06 9.501904 8112.78876 [13,] 12 1.305913e-04 99369.7289 12.976822 65761.22692 1.705028e+06 8.297434 8103.28685 [14,] 13 1.296605e-04 99356.7520 12.882649 63529.11988 1.639266e+06 7.958666 8094.98942 [15,] 14 1.844895e-04 99343.8694 18.327905 61372.83349 1.575737e+06 10.939755 8087.03075 [16,] 15 2.358877e-04 99325.5415 23.429672 59286.48391 1.514364e+06 13.512030 8076.09100 [17,] 16 3.830151e-04 99302.1118 38.034210 57268.11493 1.455078e+06 21.192806 8062.57897 [18,] 17 5.068579e-04 99264.0776 50.312778 55310.31921 1.397810e+06 27.086444 8041.38616 [19,] 18 7.585036e-04 99213.7648 75.253999 53412.83549 1.342500e+06 39.143796 8014.29972 [20,] 19 8.054065e-04 99138.5108 79.846805 51567.46055 1.289087e+06 40.128280 7975.15592 [21,] 20 7.602630e-04 99058.6640 75.310632 49783.50510 1.237519e+06 36.568652 7935.02764 [22,] 21 7.840896e-04 98983.3534 77.611822 48063.43628 1.187736e+06 36.411635 7898.45899 [23,] 22 7.539615e-04 98905.7416 74.571119 46401.69105 1.139672e+06 33.802017 7862.04736 [24,] 23 7.412106e-04 98831.1705 73.254711 44798.74972 1.093271e+06 32.082423 7828.24534 [25,] 24 7.255807e-04 98757.9157 71.656835 43251.73373 1.048472e+06 30.321374 7796.16292 [26,] 25 7.314628e-04 98686.2589 72.185324 41758.79334 1.005220e+06 29.512080 7765.84154 [27,] 26 7.151687e-04 98614.0736 70.525703 40317.14815 9.634614e+05 27.858516 7736.32946 [28,] 27 7.151451e-04 98543.5479 70.472934 38925.90781 9.231442e+05 26.896301 7708.47095 [29,] 28 7.350368e-04 98473.0749 72.381332 37582.67647 8.842183e+05 26.690482 7681.57465 [30,] 29 7.033449e-04 98400.6936 69.209629 36285.07422 8.466356e+05 24.657897 7654.88416 [31,] 30 7.305606e-04 98331.4840 71.837108 35033.38483 8.103505e+05 24.728513 7630.22627 [32,] 31 7.896775e-04 98259.6469 77.593431 33823.95248 7.753172e+05 25.806777 7605.49775 [33,] 32 8.192545e-04 98182.0534 80.436091 32654.34055 7.414932e+05 25.847552 7579.69098 [34,] 33 8.772070e-04 98101.6174 86.055428 31524.23993 7.088389e+05 26.718150 7553.84342 [35,] 34 9.550883e-04 98015.5619 93.613516 30431.48468 6.773146e+05 28.081889 7527.12528 [36,] 35 1.046494e-03 97921.9484 102.474745 29374.31877 6.468831e+05 29.700534 7499.04339 [37,] 36 1.128842e-03 97819.4737 110.422740 28351.28379 6.175088e+05 30.921858 7469.34285 [38,] 37 1.208142e-03 97709.0509 118.046456 27361.62286 5.891575e+05 31.938878 7438.42100 [39,] 38 1.377961e-03 97591.0045 134.476581 26404.41172 5.617959e+05 35.153860 7406.48212 [40,] 39 1.541276e-03 97456.5279 150.207400 25476.35504 5.353915e+05 37.938254 7371.32826 [41,] 40 1.722189e-03 97306.3205 167.579865 24576.89754 5.099152e+05 40.894744 7333.39000 [42,] 41 1.899684e-03 97138.7406 184.532902 23704.89998 4.853383e+05 43.509002 7292.49526 [43,] 42 2.205543e-03 96954.2077 213.836715 22859.77600 4.616334e+05 48.713264 7248.98626 [44,] 43 2.475530e-03 96740.3710 239.483658 22038.02683 4.387736e+05 52.710907 7200.27299 [45,] 44 2.682843e-03 96500.8874 258.896774 21240.06864 4.167356e+05 55.056791 7147.56209 [46,] 45 3.077060e-03 96241.9906 296.142409 20466.74866 3.954955e+05 60.847749 7092.50529 [47,] 46 3.394265e-03 95945.8482 325.665634 19713.78864 3.750287e+05 64.651036 7031.65755 [48,] 47 3.748007e-03 95620.1825 358.385119 18982.48774 3.553149e+05 68.740578 6967.00651 [49,] 48 4.082474e-03 95261.7974 388.903814 18271.82729 3.363325e+05 72.071749 6898.26593 [50,] 49 4.488338e-03 94872.8936 425.821629 17581.86766 3.180606e+05 76.244800 6826.19418 [51,] 50 4.955330e-03 94447.0720 468.016375 16911.06695 3.004788e+05 80.966098 6749.94938 [52,] 51 5.180798e-03 93979.0556 486.886530 16258.22902 2.835677e+05 81.382227 6668.98328 [53,] 52 5.864856e-03 93492.1691 548.318072 15627.05161 2.673095e+05 88.551112 6587.60106 [54,] 53 6.285602e-03 92943.8510 584.208071 15010.04948 2.516824e+05 91.156714 6499.04995 [55,] 54 6.790051e-03 92359.6429 627.126691 14411.30655 2.366724e+05 94.544451 6407.89323 [56,] 55 7.485403e-03 91732.5162 686.654895 13829.42323 2.222611e+05 100.018176 6313.34878 [57,] 56 7.831339e-03 91045.8613 713.011014 13261.74340 2.084316e+05 100.345130 6213.33060 [58,] 57 8.652800e-03 90332.8503 781.632104 12712.93352 1.951699e+05 106.282583 6112.98547 [59,] 58 9.530044e-03 89551.2182 853.427018 12176.74497 1.824570e+05 112.120687 6006.70289 [60,] 59 1.051117e-02 88697.7912 932.317403 11652.85030 1.702802e+05 118.343062 5894.58220 [61,] 60 1.125835e-02 87765.4738 988.094023 11140.44950 1.586274e+05 121.181671 5776.23914 [62,] 61 1.201121e-02 86777.3798 1042.301763 10642.53765 1.474869e+05 123.507060 5655.05747 [63,] 62 1.346978e-02 85735.0780 1154.832986 10159.13801 1.368444e+05 132.213908 5531.55041 [64,] 63 1.445092e-02 84580.2450 1222.262568 9683.37837 1.266852e+05 135.201691 5399.33650 [65,] 64 1.578176e-02 83357.9825 1315.535840 9220.71944 1.170019e+05 140.598261 5264.13481 [66,] 65 1.751311e-02 82042.4466 1436.818612 8768.30941 1.077811e+05 148.367527 5123.53655 [67,] 66 1.913461e-02 80605.6280 1542.356877 8323.42901 9.901283e+04 153.879738 4975.16902 [68,] 67 2.142009e-02 79063.2711 1693.542028 7888.08065 9.068940e+04 163.249625 4821.28928 [69,] 68 2.363984e-02 77369.7291 1829.007752 7458.08434 8.280132e+04 170.345792 4658.03966 [70,] 69 2.575185e-02 75540.7214 1945.313451 7035.53280 7.534324e+04 175.051205 4487.69387 [71,] 70 2.851814e-02 73595.4079 2098.803781 6622.56503 6.830770e+04 182.476525 4312.64266 [72,] 71 3.149067e-02 71496.6041 2251.476264 6216.13703 6.168514e+04 189.130769 4130.16614 [73,] 72 3.520509e-02 69245.1279 2437.781053 5816.79872 5.546900e+04 197.855972 3941.03537 [74,] 73 3.878444e-02 66807.3468 2591.085867 5422.23941 4.965220e+04 203.187001 3743.17940 [75,] 74 4.245583e-02 64216.2609 2726.354845 5035.69166 4.422996e+04 206.564719 3539.99239 [76,] 75 4.623541e-02 61489.9061 2843.010777 4658.83785 3.919427e+04 208.119092 3333.42768 [77,] 76 4.988595e-02 58646.8953 2925.656039 4293.17352 3.453543e+04 206.926605 3125.30858 [78,] 77 5.473617e-02 55721.2393 3049.967036 3941.06713 3.024226e+04 208.424065 2918.38198 [79,] 78 6.070293e-02 52671.2722 3197.300456 3599.37027 2.630119e+04 211.103686 2709.95791 [80,] 79 6.659321e-02 49473.9718 3294.630588 3266.54875 2.270182e+04 210.173880 2498.85423 [81,] 80 7.431867e-02 46179.3412 3431.987128 2945.91186 1.943527e+04 211.532605 2288.68035 [82,] 81 8.210466e-02 42747.3541 3509.756932 2634.75905 1.648936e+04 209.010622 2077.14774 [83,] 82 9.386364e-02 39237.5971 3682.983719 2336.65030 1.385460e+04 211.909666 1868.13712 [84,] 83 1.018952e-01 35554.6134 3622.844307 2045.72347 1.151795e+04 201.400381 1656.22746 [85,] 84 1.102649e-01 31931.7691 3520.953616 1775.14404 9.472230e+03 189.117001 1454.82708 [86,] 85 1.162056e-01 28410.8155 3301.496719 1525.99801 7.697086e+03 171.332909 1265.71007 [87,] 86 1.324653e-01 25109.3188 3326.113376 1303.06130 6.171088e+03 166.773336 1094.37717 [88,] 87 1.501733e-01 21783.2054 3271.255211 1092.22309 4.868027e+03 158.476053 927.60383 [89,] 88 1.655011e-01 18511.9502 3063.749015 896.81196 3.775804e+03 143.404260 769.12778 [90,] 89 1.797967e-01 15448.2012 2777.535962 723.08072 2.878992e+03 125.611155 625.72352 [91,] 90 1.940125e-01 12670.6652 2458.266835 573.01756 2.155911e+03 107.413085 500.11236 [92,] 91 2.127017e-01 10212.3984 2172.194200 446.22707 1.582893e+03 91.703618 392.69928 [93,] 92 2.299152e-01 8040.2042 1848.565462 339.43365 1.136666e+03 75.401902 300.99566 [94,] 93 2.476620e-01 6191.6387 1533.433590 252.55332 7.972327e+02 60.432713 225.59376 [95,] 94 2.658873e-01 4658.2051 1238.557512 183.58015 5.446794e+02 47.160994 165.16104 [96,] 95 2.845360e-01 3419.6476 973.012982 130.21114 3.610992e+02 35.796870 118.00005 [97,] 96 3.035530e-01 2446.6346 742.683357 90.01099 2.308881e+02 26.399139 82.20318 [98,] 97 3.228832e-01 1703.9513 550.177172 60.56800 1.408771e+02 18.895061 55.80404 [99,] 98 3.424717e-01 1153.7741 395.134979 39.62475 8.030911e+01 13.111454 36.90898 [100,] 99 3.622646e-01 758.6391 274.828064 25.17333 4.068436e+01 8.811018 23.79753 [101,] 100 1.000000e+00 483.8111 483.811057 15.51104 1.551104e+01 14.986508 14.98651