Foreword
The compilation of mortality tables using death
flows by sex and age and the population rate
resulting from the census figures classified in
the same manner, is traditionally performed by
the National Statistics Institute.
At present, users can now access mortality
tables for the population in Spain calculated
using the deaths occurred in 1998 and 1999
and of the population forecast for 1998.
As the methodology used does not differ from
the previous one, the biometric functions
obtained are comparable.
Carmen Alcaide Guindo
INE President
Index
Foreword
3
Historical background
7
Methodology employed
9
1
Introduction
11
2
Obtaining death probability series
11
3
Obtaining derivative series
12
4
Obtaining prospective series
13
5
Synthesis of the smoothing procedure
employed
14
Base information used
15
Results obtained
17
1
Evolution of mortality during the 1980s
19
2
Mortality tables for 1998
20
3
Spanish mortality in the European Union
21
Charts and graphs
23
Complete mortality tables 19981999
35
Glossary of symbols
37
6
Complete mortality tables 1998-199938
Historical background
the same (therefore, they do not refer to the
studies corresponding to abbreviated tables,
or those related to smaller population spheres,
like Autonomous Communities and provinces).
In 1945, the National Statistics Institute
published mortality tables regarding the
Spanish population, by sex, calculated using
the deaths by age in 1930 and 1931 and the
population in the 1930 Census. By doing so,
the INE filled the gap that had existed in
Spanish statistical research until said year.
Moving on, the calculation of the forecast
values for the biometric functions of the
Spanish population is a relatively recent
project, which was implemented to obtain
figures for future survivors considering the
population forecasts calculated using the 1970
Population Census, and the last forecasts,
compiled using the 1991 Population Census.
Six years later, with the results from the 1940
Census, tables were created for said year, and
the figures from the Censuses of 1900, 1910
and 1920 were also used (after processing
them appropriately) as the denominator for
deaths by sex and age of the Vital Statistics
for the corresponding years, so as to establish
the biometric functions that were published
alongside those from 1930 and 1940. This
provided series for the 1900-1940 period,
which allowed the INE to analyse the evolution
of general mortality, by sex, in the Spanish
population.
Finally, the functions of the mortality tables for
the Spanish population 1998-1999, analysed
in this publication, have been calculated taking
forecast population figures, and not observed
data (like census information), as the
denominators.1. The advantage of this
procedure is that it continuously reflects
modifications regarding the intensity of the
mortality rate, each time new data on deaths is
provided. Nevertheless, the tables obtained
should be revised to ensure that the
populations used to calculate the data are
corrected, either in terms of the number of
persons by sex and age resulting from a
subsequent comprehensive population count,
or as a consequence of the errors in the
hypotheses devised regarding demographic
components
when
establishing
the
corresponding forecasts.
The INE used the data from the 1950 Census,
to compile the tables for said year, following a
process identical to the procedure used as the
base for the first five tables, consequently,
completing the information provided in the
abbreviated tables referred to said year, which
had been disseminated two years before.
The population rates obtained in the 1960 and
1970 Censuses and the figures concerning
deaths occurred during those decades,
allowed the calculation of new mortality tables
for the Spanish population.
The following page includes the evolution of
life expectancy at birth, for the total population
and by sex, throughout the century.
Using the aforementioned tables for 1970, the
National Statistics Institute has published
mortality tables every five years, using the
populations by sex and age from the municipal
recounts, as well as the census figures. The
methodology used enables the comparison
between the results for 1975, 1980, 1985 and
1990, always considering the changes in the
concepts used which, in any case, are
indicated in the publications (as occurs with
the concept live birth and still birth which
appears in the year 1975).
This has resulted in the dissemination of
comparable figures since –although the
methodology varies as regards the smoothing
procedures, which adapt to each situation– the
definitions for the basic biometric functions
calculated for the whole of the population are
1
Forecast population figures were already used to calculated
the tables for 1994-1995 and 1996-1997.
Methodology employed
1
Introduction
Mortality tables are compiled to measure the
incidence of this phenomenon on the
population under study, regardless of the
structure by age.
The type of table used is created after
performing a transversal analysis of the
mortality, examining how said phenomenon
affects the population classified by age or age
groups, at a certain moment in time.
Given the evolution usually experimented by
mortality, that does not present any brusque
modifications, these tables appear as an
acceptable description of the phenomenon for
short periods of time, close to the moment
they refer to.
To calculate the functions of a complete
mortality table, it is necessary to have
information on the deceased and the
population classified both by ages and
referred to the same time period.
Since the figures for deaths classified by ages
are quite small (except for the oldest age
groups), not only in provinces and
Autonomous Communities but also on a
national level, recount errors and possible
disruptions, which could exceptionally affect
mortality in a certain year, have a notable
bearing on this information. Consequently, it is
necessary to eliminate these anomalies since
if they were to remain in the data, they would
present
an
incorrect
image of
the
phenomenon under study. This elimination is
performed during the initial stage. To calculate
the mortality table for a certain moment in time
and for each age group, it is necessary to
consider average deaths corresponding to a
specific number of years (generally from two
to four), focusing on that particular moment.
In a second stage, it is necessary to eliminate
the disruptions, both in terms of the number of
deaths and the population, caused by errors
when stating the age, and produce an
increase of the values observed for certain
ages to the detriment of the contiguous ones,
distorting the series of death probabilities on
the mortality table. This problem is usually
avoided applying a smoothing procedure to
the original data.
2
Obtaining death probability series
Death probability at age x, qX, is defined as
the probability a person from a specific
generation, exactly x years old, has of dying
before reaching age x+1. Therefore, it is
necessary to consider possible death cases, in
other words, persons who could die, as well as
real events, that is, persons of that age and
generation who have actually died. Possible
cases are persons who are x years old,
calculated as the sum of the inhabitants who
are that age at the end of the year and half of
the persons deceased aged x during the year
in question, since it is supposed that deaths
are distributed uniformly throughout the year in
question. Accepting the hypothesis that the
deaths of persons from a certain generation
aged x occur half in one year and half in the
following, the death probability would be
expressed by:
1 / 2 (Dzx +
z+ 1
Dx )
qx =
z
z
Px + 1 / 2 (Dx)
where:
Dzx represents deaths occurred in year z aged
x.
Dzx1 represents deaths occurred in year z+1
aged x.
Pxz population on December 31st of year z
aged x.
The previous expression has been used to
calculate all qx corresponding to all ages
ranging from two to ninety years old, both
inclusive.
Since the deaths of babies under one year old
mainly occur during the first weeks of life, it is
not possible to apply this hypothesis uniformly
throughout the year. Therefore, for this age,
the death probability has been calculated
using:
z
q0 =
z+ 1
D0, g(z) + D0, g(z)
z
z
P0 + D0, g(z)
where:
Dz0 ,g(z) deaths occurred in year z, 0 years old,
from the generation born that year.
D
z1
0 ,g(z)
deaths occurred in year z+1, 0 years
old, from the generation born the previous
year.
3
Obtaining derivative series
The death probability series can provide the
mortality
tables
functions
described
hereunder.
P0z population on December 31st of year z
PROBABILITY OF LIFE OR SURVIVAL AT AGE x,
aged 0.
Consequently, for babies aged one year old,
q1, has been calculated using:
z
q1 =
z+ 1
D1, g(z-1) + D1, g(z-1)
z
z
P1 + D1, g(z-1)
px
The probability of survival between two exact
ages. Therefore, for each age x,
px = 1 - qx
where:
D1z,g(z1) deaths in year z, aged 1, from
generation z-1.
D1z,g1(z1) deaths in year z+1, aged 1, from
SURVIVORS AGED x YEARS OLD, lx
Number of persons aged x among the initial l 0
on the mortality table. Therefore, for each age
x,
generation z-1.
lx = lx-1px-1
P1z population on December 31st of year z
Surveys usually work with l0 = 100,000
aged 1.
The low number of deaths registered for
persons who are over ninety years old and the
greater repercussion of errors when stating
the age, lead to distortions in the death
probability series for the aforementioned ages.
Therefore, the latter have been estimated
adjusting a third grade parabola, by least
squares, based on the qx calculated using the
previous expression, for
X = 90, 91, 92, 93 and 94.
The following conditions were established in
order to perform said adjustment: a) The cubic
parabola passes through point q90, which
implies the continuity of the qx adjusted and
those calculated for ages under 90 years old,
b) value q110 = 1, truncating the parabola as
from this point, which means that, a priori,
there are no survivors over one hundred and
ten years old, and c) the cubic parabola has a
tangent parallel to the x axis at point x = 110,
which implies an accelerated increase of
mortality as from the point of inflection of the
cubic parabola, given high mortalities for ages
around one hundred and ten years old.
THEORETICAL DEATHS AGED x YEARS OLD, dx
Deaths occurred between two exact ages x
and x+1, obtained from the mortality table.
L0  a0 l 0  a1l1 , where a0  a1  1
in which
z+ 1
D0, g(z)
z+ 1
z+ 1
D0, g(z) + D0, g(z+ 1)
Therefore, for each age x,
a0 =
d x  l x q x  l x  l x 1
where
Dz0,g1(z) represents the deaths of children under
LIFE EXPECTANCY AT AGE x, ex
Average number of years each person aged
exactly x is expected to live, for survivors that
reach said age, under the supposition that the
years lived by all persons are the same for all
of them.
Considering the hypothesis that all persons
who die at a certain age live, on average, half
the year in which they die, life expectancy is
calculated as
ex =
1
2
+
1
lx
For x = 99 and x = 100
L99 = e99 l99 - e100 l100
L100 = e100 l100
where L100 are survivors aged 100 years old
and older.

l
PROBABILITY OF SURVIVAL AT x YEARS OLD,
TX
i
i= x+ 1
with  representing the oldest age, for which
there are supposedly no survivors.
4
one year old occurred in year z+1 among
those born in generation g(z).
Obtaining prospective series
As well as the previous classical biometric
series or functions, it was considered of major
importance to include the two prospective
series specified hereunder.
The probability of survival for ages x and x+1
for persons aged x years old. This is easily
obtained from the former using
Tx =
and, for the population aged 99 years old and
older, the probability of reaching 100 years old
or over is
T99 =
SURVIVORS AGED x YEARS OLD, LX
Represents the number of survivors on the
mortality table who are x years old. The
estimate of this function has been performed
implementing
this
next
formula
(see
Introduction to the Mathematics of Population.
Keyfitz. Addison-Wesley):
Lx =
13
24
(lx + lx+ 1) -
1
24
for x = 1, 2, ..., 98.
For the remaining ages
(lx-1+ lx+ 2)
Lx+ 1
Lx
L100
L99 + L100
5
Synthesis
of
the
procedure employed
smoothing
Both population stocks obtained from
population censuses and register renewals,
and data on deaths obtained from the Vital
Statistics, sometimes, contain mistakes due to
flaws that appear when interviewees state
their age. This increases the values of some
ages to the detriment of those corresponding
to similar ages, which causes distortions in the
death probability series calculated. In order to
avoid this problem, it is necessary to
implement a smoothing procedure for the
original data before employing them.
The smoothing procedure employed for the
original data was the Variate Difference
Method. The National Statistics Institute had
used said method to compile the former
comprehensive mortality tables. A complete
explanation of the application, with vast
bibliography, can be found in the book by G.
Tintner, The Variate Difference Method, 1940,
in the Cowles Commission collection. The
following paragraphs explain the foundations
of the procedure briefly.
The basic hypothesis for the application of the
method is that the series observed is the
additive superimposition of two other series,
one of which expresses the correct value or
the value expected for each age x, and the
other the random distortion that alters the
observed value. In this case, the latter would
be the sum of all the causes and
circumstances that lead to persons stating an
incorrect age.
Therefore, the model is:
yx = ux + ex
where for each age x:
yx is the observed value.
ux is the expected or correct value.
ex is the error or random distortion.
In this application, values ux theoretically
follow a slow trend, without sharp zigzags, and
random errors are supposedly unrelated. This
hypothesis could be smoothed given the noncorrelation of the random errors.
A second essential hypothesis, that has
allowed the implementation of the Variate
Difference Method, consists in supposing that
the expected value ux is simply a grade n
polynomial, when n is an unknown value. The
Variate Difference Method determines the
exact value of n. Subsequently, after obtaining
n, a polynomial for said degree is adjusted to
the data observed yx. In this respect, it is
necessary to mention the existence of a close
relationship between the moving average
method and the variate difference method.
Specifically, M..G. Kendall (A Theorem in
Trend Analysis, Biometrika, vol. 48, 1961.
Advanced Theory of Statistics) has proven
that the moving average method calculations
result from the application of the variate
difference method based on a lineal
combination of some of the successive terms
of the observed values yx. More precisely, all
moving average formulae result in an
adjustment of 2K + 1 successive terms of a
grade p - 1 polynomial, with 2K - p + 1
numbers bi (with p - K < i < K), so that
 k

ûx = y x - p   bi y x+ i 
 i= p-k

where:
p difference of order p.
ûx the estimated value of ux.
bi coefficients of the Sheppard smoothing
formula.
If the expected value ux follows a grade n
polynomial, it is a case of determining the
latter. For this, an iterative process is
implemented to calculate the successive finite
differences. There will evidently be a point in
the process when the expected value u x will
disappear, on cancelling the grade n
polynomial. That is to say, the corresponding
difference will be constant, thus cancelling
subsequent differences. Nevertheless, since
calculations are performed with the observed
values yx, it is necessary to know the moment
at which the expected value has supposedly
been cancelled in this process of successive
finite differences, with only a residue
remaining from the existence of random errors
ex. This question can be answered using the
following consideration: if there is a time series
that only contains a random element, the
variations of the successive series of finite
differences are equal, after correcting them by
multiplying a binomial coefficient given that the
series, which is random, is not ordered in time.
Consequently, the variation of the first and
second differences is the same as in the
original series.
problem to be resolved. Nevertheless, the
number of values included in each average
should be taken respecting the length of the
main cycle that is to be cancelled. In this case,
moving averages have been taken considering
each series of five consecutive observed
values yx.
The aforementioned provides a criterion to
determine when the expected value ux has
disappeared. If a certain difference k is
calculated with variation equal to that of
difference k + 1, and equal to that of K+2, etc.,
it is possible to say that the expected value u x
has been cancelled, taking K-th difference.
Nevertheless, the equation between two
variations is never reached, since there is
always a random variation residue. Yet since
the table uses a probability method it is proven
that the only necessary element is that the
difference between the variation of two
successive series of finite differences is
smaller than three time the standard error of
the lowest difference.
To apply this aspect to the compilation of the
mortality tables, the series of the expected
values always disappears in the first or second
differences. This implies a constant application
of moving averages when smoothing original
series.
6
The deaths used to calculate each table
(males, females and total) have been obtained
as an average of the figures registered by age
in the Vital Statistics for 1998 and 1999.
The irregularities in these original death
figures, caused by the possible errors
regarding the classification by age, have been
cancelled using the smoothing procedure
explained in the previous section.
After determining the degree of the polynomial
to be adjusted, it is merely a case of applying
the corresponding weighted average to the
coefficients of Sheppard's smoothing formula.
The moving average type is determined as
follows: if the non-random element or
expected value ux is more or less cancelled in
the first or second difference, the table uses n
= 1 or a moving average that is equivalent to
adjusting a straight line to a certain number
(not determined by the method) of consecutive
observed values yx. If the expected value is
cancelled in the third or fourth finite
differences, we will obtain n = 2, and select a
moving average equivalent to adjusting a
second grade parabola to a certain number of
consecutive observed values. If the nonrandom element is cancelled in the fifth or
sixth differences, n = 3, we use a weighted
average equivalent to adjusting a third grade
(cubic) polynomial to a selected number of
consecutive observed values, etc. If the nonrandom element is cancelled in the k-th finite
difference, n = k/2, when k is even, or n = (k
+1)/2, when k is uneven.
As aforementioned, moving averages are
implemented on a specific number of
consecutive observed values, which have
been centred appropriately. Nevertheless, this
number is undetermined. The criterion is open
to the experience and specific nature of the
Base information used
The simple populations by sex and age on
December 31st 1998 correspond to the
revision of the population forecasts calculated
using the results from the 1991 Population
Census1, except for the population aged 100
years old and over.
As regards the group aged 100 years old and
older, of each sex, the figure used is obtained
by lineal interpolation between populations
aged 100 years old and older from the 1991
Population Census of 1991 and the 1996
Registry Renewal.
The figures used appear, alongside the
biometric functions of the mortality tables
calculated for 1998, in the first two columns.
1
Forecasts for the Spanish population calculated using the
1991 Population Census. Assessment and revision. INE 2001
Results obtained
1
and 7 represent the evolution, from 1980,
1985 and 1990, of the number of survivors, for
each sex, at the different ages, for an initial
cohort of 100,000 persons in each group.
Evolution of mortality during the
1980s
The secular evolution of mortality in Spain has
been characterised by the decrease of death
rates and probabilities corresponding to each
age.
It is important to note that, opposed to the
trajectory observed during the previous period,
the survival curve for males corresponding to
1990 decreases rapidly for ages around 20
years old, reaching values under those
registered previously and does not increase
again until the section corresponding to
persons over 60 years old. As regards
females, the curve for said year coincides
almost completely with that of 1985, without
the favourable evolution of the previous
quinquennium.
The decrease noticed in Spanish mortality
during the 1970s continued, albeit less
intensely, during the first five years of the
1980s. Nevertheless, in following years, this
favourable evolution has been accompanied
by changing trends that have appeared among
certain young persons (mainly males between
18 and 35 years old); an unfortunate novelty
compared to previous years.
Graphs 8 and 9 represent the series of
theoretical deaths in the mortality tables for
males and females for 1980, 1985 and 1990.
The upper part of graphs 1 and 2 presents the
evolution of mortality quotients by sex and
age, between 1980, 1985 and 1990.
The evolution of the mortality calendar in the
1980s results in a deceleration of the rhythm
of increase of life expectancy, more marked
for males than for females.
In the early ages, under 15 years old, the
trend is still favourable as regards general
mortality. With reference to infant mortality
specifically, the risk of death of children under
1 year old was 7.8 per thousand in 1990, 8.5
for boys and 7.1 for girls.
Life expectancy at birth for Spain’s population
in 1990 reached 76.9 years old, 73.4 years for
males and 80.5 for females (i.e. women live
about seven years longer). Consequently,
male excess mortality continues on the rise.
On considering the subsequent ages up to 40
years old, the recent mortality trend is
unfavourable, with a significant increase
between the ages of 18 and 35 years old. The
graphs corresponding to males and females
show that this situation is more frequent
among the former, whilst the rates for females
show a very slight decrease. On examining
the origin of the increase of deaths of young
persons, the three main causes of death are
traffic accidents, AIDS and drug addiction.
The evolution of the difference between life
expectancy for females and males at each
age, between years 1980 and 1990, is
represented in graph 10, showing the upward
trend of the corresponding line.
In brief, chart 1 presents life expectancy by
age, in years 1980, 1985 and 1990, for each
sex and every five years for ages.
For people over 40 years old, the increase as
regards mortality in 1985 and 1990 is very
similar to that of the previous quinquennium.
Even when the previous graphs show that the
evolution of mortality is more favourable for
females than for males, graph 5 represents
the quotients between the respective mortality
risks by age, for 1980, 1990, 1994 and 1998.
All values represented are higher than one.
For persons over fifty years old, there is an
upward trend of the corresponding curve over
time.
The quotients of mortality by age provide the
distribution of survivors on the table. Graphs 6
2
Mortality tables for 1998
Mortality quotients obtained for 1998 have
been represented, alongside those for 1990
and 1994, in the second part of graphs 1 and
2, respectively, for males and females.
The results in the mortality tables compiled for
1998 suppose a continuation of the tendency
this phenomenon has experienced between
both quinquennia of the previous decade, with
new reductions of the mortality rates by age,
except for persons in the interval between 18
and 40 years old, which present a peculiar
trajectory that will be commented in the
following paragraphs.
The general comment in the previous
paragraph is applicable to young persons, up
to 15 years old, with very similar mortality
quotients for 1990 and 1998.
Thus, in the aforementioned interval, 18 to 40
years old, death probabilities up to 25 years
old reach their maximum values in 1990, as
from when there is a favourable evolution until
1995. On the contrary, between 25 and 40
years old, the trajectory of the risk of death is
unfavourable, reaching maximum values in
1995, as appears in the first part of graphs 3
and 4, which present, respectively, the
quotients for males and females, from 15 to 44
years old, between 1990 and 1996.
As regards infant mortality specifically, the risk
of death for children under 1 year old is still
evolving favourably: in 1998 the rate was 5.1
per thousand for boys and 4.3 per thousand
for girls.
The values for death probability obtained for
the following years, in other words, 1996, 1997
and 1998, show a decreasing tendency.
Consequently, this means an improvement of
mortality in all young persons under study.
Comparing the levels obtained in 1998 with
those from 1985 shows that, for persons under
29 years old, current risks of mortality are
inferior. As of said age, although the risks are
higher, they tend towards those for said year,
as appears in the second part of graphs 3 and
4.
Although the increase of mortality at young
persons during the period from 1985-1990
was due to three causes, traffic accidents,
AIDS and drug addiction, the subsequent
aforementioned evolution can be explained by
the different repercussion each cause has had
in society. Thus, mortality quotients for traffic
accidents presented a general reduction
during the 1990-1996 period, which was most
significant n persons between 15 and 30 years
old. Mortality due to AIDS increased death
probability between 25 and 40 years old
during the 1990-1995 period, showing a
gradual decrease afterwards. As regards the
third cause, drug addiction, this element is the
least relevant; risks of dying due to this cause
are very low and, after the increase observed
between 1985 and 1990, it is possible to say
that they have been stable since 1992.
Moving on to consider other age intervals, the
reductions noticed in the death probability in
persons over 42 years old, between 1990 and
1998, are, once again, decreasing, to the point
of being almost imperceptible. Nevertheless,
progress was observed in persons aged
between 50 and 60 years of age.
The different evolution of the mortality for
males and females means that the line for
quotients between the death probabilities for
males and females, at different ages, as
appears in graph 5, for 1998, experiences a
slight descent compared to 1990, until 47
years old, and starts to increase as of that
age.
The evolution of the survivors in the mortality
tables for 1980, 1985 and 1990, represented
for males and females, respectively, in graphs
6 and 7, is completed with the line
corresponding to the tables for 1998, which is
favourable if compared to years 1990 and
1994, both for the former and the latter.
The series of theoretical deaths in the
mortality tables for 1980, 1985, 1990, 1994
and 1998 have been represented in graphs 8
and 9, for males and females respectively.
As well as the comments in the previous
section regarding the evolution of the mortality
calendar, and the deceleration of the
increasing rhythm of life expectancy during the
1980s, it is necessary to add that the increase
of the same, registered between 1990 and
1996 up to 40 years of age approximately,
tends to recuperate it.
Chart 1 is completed with life expectancy in
1998, for each sex and different ages.
Life expectancy at birth of the population in
Spain in the year 1998 reaches 78.7 years old,
75.3 years old for males and 82.2 years old for
females (in other words, females live 6.9 years
longer). The improved mortality registered
between 1990 and 1998 in the group from 15
to 40 years old, has contributed to the evident
recuperation of life expectancy at birth,
positioned at 1.8 years for males and 1.7
years for females.
Graph 10 shows the evolution of the difference
between life expectancy for females and
males, at each age, during the 1980-1998
period.
3
Spanish mortality in the European
Union
This section assesses the situation of general
mortality in Spain comparing it to the other
countries in the European Union (EU). Life
expectancy at birth has been used as the
indicator.
The increase regarding the years people live
in said countries and the highest values
obtained are compared to the data for Spain.
Life expectancy at birth for males and females
corresponding to dates near years 1980,
1985, 1990 and 1998, in EU countries,
appears in Chart 2.
In 1980, life expectancy for males in Spain
appeared in the third place, with a difference
of just 0.2 and 0.3 years with Holland and
Sweden, respectively. Since this indicator
increased almost a full year over the five-year
period between 1980 and 1985, Spain was the
second country compared to the other EU
countries. Nevertheless, the slow growth
rhythm registered in the last quinquennium of
the 1980s made Spain dropping back to the
fifth place, behind Sweden, Greece, Holland
and Italy.
Between 1990 and 1998, the notable
recuperation observed as regards life
expectancy at birth for males is 0.7 years
above the EU average, this figure is 0.2 years
higher than Spain in Greece and Italy and 1.6
years higher in Sweden.
As regards females, the deceleration of the
rhythm of growth of life expectancy during the
1980s is not as pronounced as in the case of
the males. In 1980, Spanish female's life
expectancy was only below Sweden and
Holland in 0.2 and 0.7 years, respectively. In
1990, it was only below France and Holland,
both with 80.9 years life expectancy at birth,
i.e. 0.4 years higher than Spain.
The increase of life expectancy at birth for
females between 1990 and 1998, as occurs
with males, is important. As a consequence,
Spain is positioned 1.3 points above the EU
average, only below France, 0.1 years higher,
in the last year.
Glossary of symbols
Q(X)= Risk or probability of death between the
exact ages of X and X+1.
L(X)= Survivors aged
100,000 initial persons.
exactly X
among
D(X) = Theoretical deaths occurred between
two specific ages X and X+1.
E(X) = Life expectancy at a specific age X.
LL(X) = Survivors aged X years old.
T(X) = Probability of survival among persons
aged X and X+1.