1.2 Emulsiones agua/aceite
1.3.5 Masa molecular de los polímeros
1.3.5.1 Definición de masa molecular
A summary of the results obtained from an analysis of mortality data for Germany is given in Table 2.8.1. From the table it can be seen that the present value of annuity rates derived on the basis of the Richttafeln 2005 G mortality tables assumed for pension liability calculations are higher than annuity rates derived on the basis of the 2006 German population mortality experience, which is consistent with lighter mortality experience for pensioners. For example, assuming a discount rate of 3% per annum, the difference between the present value of the annuity rate assumed for pension liability calculations and the annuity rate derived from the population mortality at age 65 is 9.1% for males and 9.8% for females, when expressed as a percentage of the population value. When a reversionary widow’s pension of 60% of
member’s pension is included, the percentage difference between male annuity rates at age 65 is 8.2% assuming a discount rate of 3%.
Figure 2.8.1 and Table 2.8.2 show comparisons of the observed probabilities of death (qx rates) based on the most recent (2006) population experience and the Richttafeln 2005 G mortality tables. It can be seen that for both males and females, the Richttafeln 2005 G mortality tables generally exhibit lighter mortality than the observed population except for ages below 55 years. For example, the probability from the Richttafeln 2005 G mortality tables that a 65-year male will die before his 66th birthday is 91% of the probability derived from the German male population experience. The corresponding proportion for a 65-year old female is 85%. The same trends are depicted in Figure 2.8.2 which shows the ratios of probabilities of death from the Richttafeln 2005 G mortality tables to probabilities of death derived from the male and female population mortality experiences respectively.
Figure 2.8.3 shows age-related ratios of female probabilities of death to male probabilities of death based on pension-related tables and population mortality experience. Similar trends are exhibited from both experiences with the difference between male and female mortality rates being generally decreasing as age increases.
Table 2.8.3 and Figure 2.8.4 show comparisons of expected future lifetime (ex) values for an individual aged x based on the Richttafeln 2005 G mortality tables with corresponding expected future lifetime values for the population. Expressed as a percentage of the expected future lifetime value derived from the population mortality experience, the differences tend to increase with age for both males and females, with the proportional differences at age 65 being 12.1% for males and 13.8% for females (Tables 2.8.1 and 2.8.3). Based on the Richttafeln 2005 G mortality tables, the life expectancy at age 65 is about 2 years longer for males and 2.8 years longer for females compared to the observed male and female population respectively.
Figures 2.8.5, 2.8.6, 2.8.7 and 2.8.8 and the associated tables show conditional survival probabilities for an individual aged x (kpx), where x = 50, 60, 65 or 70 and 0≤k≤100-x. Considering age 65 (Figure 2.8.7 and the associated table), it is noted that
whereas a 65-year old male would be expected to live to nearly age 84 on the basis of the Richttafeln 2005 G tables and to about age 82 on the basis of the population mortality experience, 25% of the males alive at age 65 would be expected to live to at least age 90 on the basis of the Richttafeln 2005 Gtables and to about age 89 on the basis of the male population mortality experience. For females, whereas a 65-year old female would be expected to live to at least age 88 on the basis of the Richttafeln 2005 G tables and to at least age 85 on the basis of the female population mortality experience, 25% of the females alive at age 65 would be expected to live to at least age 94 on the basis of the Richttafeln 2005 Gtables and to nearly age 92 on the basis of the female population experience.
Table 2.8.1
Germany: Summary Statistics age x = 50
male female
population Richttafeln
2005G difference percentage
difference population Richttafeln
2005G difference percentage difference
2005G difference percentage
difference population Richttafeln
2005G difference percentage difference
2005G difference percentage
difference population Richttafeln
2005G difference percentage difference
2005G difference percentage
difference population Richttafeln
2005G difference percentage difference
ex 13.38 15.43 2.05 15.3 16.08 18.84 2.76 17.1
ax : 3% 10.05 11.30 1.25 12.5 11.83 13.39 1.57 13.2
ax : 6% 8.10 8.91 0.81 10.0 9.33 10.27 0.94 10.1
Table 2.8.2
Germany: One-year probabilities of death (initial rates of mortality, qx rates)
male female
age population Richttafeln
2005G ratio population Richttafeln
2005G ratio
50 0.004430 0.004472 1.01 0.002440 0.002530 1.04
55 0.007020 0.006504 0.93 0.003380 0.003444 1.02
60 0.010060 0.009589 0.95 0.004990 0.004555 0.91
65 0.015480 0.014042 0.91 0.007350 0.006271 0.85
70 0.024840 0.021136 0.85 0.012600 0.009800 0.78
75 0.041830 0.031252 0.75 0.023420 0.016266 0.69
80 0.067220 0.049674 0.74 0.045260 0.029677 0.66
85 0.113560 0.084178 0.74 0.086640 0.056697 0.65
90 0.183370 0.140359 0.77 0.156850 0.105217 0.67
95 0.286830 0.219536 0.77 0.263680 0.177710 0.67
age at death (in years)
mortality rate
50 60 70 80 90 100 110
0.00.10.20.30.40.5
Germany: population and pensioners' probabilities of death
male population female population male pensioners female pensioners
Figure 2.8.1
age at death (in years)
ratio of mortality rates
50 60 70 80 90 100 110
0.50.60.70.80.91.0
Germany:pensioners' probability of death divided by population probability of death
male mortality ratio female mortality ratio
Figure 2.8.2
age at death (in years)
ratio of mortality rates
50 60 70 80 90 100 110
0.50.60.70.80.91.0
Germany: female probability of death divided by male probability of death
ratio of population mortality ratio of pensioners' mortality
Figure 2.8.3
Table 2.8.3
Germany: Expected complete future lifetime in years
male female
age population Richttafeln
2005G difference percentage
difference population Richttafeln
2005G difference percentage difference
50 29.08 31.11 2.03 7.0 33.57 36.34 2.78 8.3
55 24.83 26.87 2.04 8.2 29.01 31.83 2.83 9.7
60 20.78 22.81 2.03 9.8 24.57 27.41 2.84 11.5
65 16.94 18.99 2.05 12.1 20.26 23.06 2.80 13.8
70 13.38 15.43 2.05 15.3 16.08 18.84 2.76 17.1
75 10.23 12.14 1.91 18.7 12.24 14.85 2.61 21.3
80 7.54 9.16 1.62 21.5 8.84 11.20 2.36 26.6
85 5.34 6.64 1.30 24.4 6.07 8.08 2.02 33.2
90 3.65 4.71 1.06 29.1 4.04 5.66 1.62 40.1
95 2.58 3.41 0.84 32.5 2.73 4.00 1.27 46.5
age (in years)
expected future lifetime (in years)
50 60 70 80 90 100
102030
Germany: population and pensioners' expected future lifetime
male population female population male pensioners female pensioners
Figure 2.8.4
age at death (in years)
probability
50 60 70 80 90 100
0.00.20.40.60.81.0
Germany: population and pensioners' probability of survival conditional on reaching age : 50
male population male pensioners female population female pensioners
Figure 2.8.5
Germany: Distribution of age at death given survival to age 50 Summary Statistics
male female
population Richttafeln
2005G difference population Richttafeln
2005G difference
Lower Quartile age 72.82 73.52 0.70 78.66 80.19 1.53
Median age 80.39 82.01 1.62 85.58 88.65 3.07
Upper Quartile age 87.81 89.07 1.27 90.29 95.00 4.71
Inter-quartile range 14.98 15.55 0.57 11.62 14.80 3.18
e50 29.08 31.11 2.03 33.57 36.34 2.78
age at death (in years)
probability
60 70 80 90 100
0.00.20.40.60.81.0
Germany: population and pensioners' probability of survival conditional on reaching age : 60
male population male pensioners female population female pensioners
Figure 2.8.6
Germany: Distribution of age at death given survival to age 60 Summary Statistics
male female
population Richttafeln
2005G difference population Richttafeln
2005G difference
Lower Quartile age 74.75 75.33 0.59 79.69 81.18 1.49
Median age 81.45 83.09 1.64 85.20 88.26 3.06
Upper Quartile age 87.26 90.63 3.36 90.09 94.79 4.70
Inter quartile range 12.52 15.29 2.78 10.40 13.61 3.20
e60 20.78 22.81 2.03 24.57 27.41 2.84
age at death (in years)
probability
70 80 90 100
0.00.20.40.60.81.0
Germany: population and pensioners' probability of survival conditional on reaching age : 65
male population male pensioners female population female pensioners
Figure 2.8.7
Germany: Distribution of age at death given survival to age 65 Summary Statistics
male female
population Richttafeln
2005G difference population Richttafeln
2005G difference
Lower Quartile age 75.23 77.70 2.47 80.92 82.50 1.58
Median age 82.69 84.35 1.67 86.89 89.98 3.09
Upper Quartile age 88.83 90.25 1.42 91.93 94.64 2.71
Inter quartile range 13.61 12.56 -1.05 11.01 12.14 1.13
e65 16.94 18.99 2.05 20.26 23.06 2.80
age at death (in years)
probability
70 75 80 85 90 95 100
0.00.20.40.60.81.0
Germany: population and pensioners' probability of survival conditional on reaching age : 70
male population male pensioners female population female pensioners
Figure 2.8.8
Germany: Distribution of age at death given survival to age 70 Summary Statistics
male female
population Richttafeln
2005G difference population Richttafeln
2005G difference
Lower Quartile age 77.27 79.65 2.37 81.94 83.59 1.65
Median age 83.64 85.35 1.72 86.47 89.58 3.11
Upper Quartile age 88.26 91.72 3.46 91.70 94.42 2.72
Inter quartile range 10.99 12.08 1.09 9.76 10.83 1.08
e70 13.38 15.43 2.05 16.08 18.84 2.76