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## Life expectancy

Life expectancy is the expected (in the statistical sense) number of years of life remaining at a given age.[1] It is denoted by ex, which means the average number of subsequent years of life for someone now aged x, according to a particular mortality experience. (In technical literature, this symbol means the average number of complete years of life remaining, excluding fractions of a year. The corresponding statistic including fractions of a year, the normal meaning of life expectancy, has a symbol with a small circle over the e.) The life expectancy of a group of individuals is heavily dependent on the criteria used to select the group. Life expectancy is usually calculated separately for males and females. Females live longer than males in countries with modern obstetric care.

The term that is known as life expectancy is most often used in the context of human populations, but is also used in plant or animal ecology[2]; it is calculated by the analysis of life tables (also known as actuarial tables). The term life expectancy may also be used in the context of manufactured objects[3] although the related term shelf life is used for consumer products and the terms "mean time to breakdown" (MTTB) and "mean time before failures" (MTBF) are used in engineering literature.

## Interpretation of life expectancy

In countries with high infant mortality rates, the life expectancy at birth is highly sensitive to the rate of death in the first few years of life. Because of this sensitivity to infant mortality, simple life expectancy at age zero can be subject to gross misinterpretation, leading one to believe that a population with a low overall life expectancy will necessarily have a small proportion of older people. For example, in a hypothetical stationary population in which half the population dies before the age of five, but everybody else dies exactly at 70 years old, the life expectancy at age zero will be about 35 years, while about 25% of the population will be between the ages of 50 and 70. Another measure such as life expectancy at age 5 (e5) can be used to exclude the effect of infant mortality to provide a simple measure of overall mortality rates other than in early childhood'in the hypothetical population above, life expectancy at age 5 would be 70 years. Aggregate population measures such as the proportion of the population in various age classes should also be used alongside individual-based measures like formal life expectancy when analyzing population structure and dynamics.

One example of this common misinterpretation can be seen in the In Search of... episode "The Man Who Would Not Die" (About Count of St. Germain) where it is stated "Evidence recently discovered in the British Museum indicates that St. Germain may have well been the long lost third son of R�¡kóczi born in Transylvania in 1694. If he died in Germany in 1784, he lived 90 years. The average life expectancy in the 18th century was 35 years. Fifty was a ripe old age. Ninety... was forever." This ignores the fact that life expectancy changes depending on age and the one often presented is the "at birth" number. For example, a Roman Life Expectancy table at the University of Texas shows that at birth the life expectancy was 25 but if one lived to the age of 5 one's life expectancy jumped to 48. Similar papers such as Plymouth Plantation; "Dead at Forty" and Life Expectancy by Age, 1850'2004 show dramatic increases in life expectancy after childhood.

## Human life expectancy patterns

Humans live on average 39.5 years in Swaziland[4] and 81 years in Japan (2008 est.), although Japan's recorded life expectancy may have been very slightly increased by counting many infant deaths as stillborn.[5] The oldest confirmed recorded age for any human is 122 years (see Jeanne Calment). This is referred to as the "maximum life span", which is the upper boundary of life, the maximum number of years any human is known to have lived.[6]

### Life expectancy variation over time

The following information is derived from Encyclopaedia Britannica, 1961 and other sources, and unless otherwise stated represents estimates of the life expectancies of the population as a whole. In many instances life expectancy varied considerably according to class and gender.

Sometimes, mainly in the past, life expectancy increased during the years of childhood, as the individual survived the high mortality rates then associated with childhood. The life expectancies at birth listed below take account of infant mortality but not pre-natal mortality (miscarriage or abortion).

Humans by Era Average Lifespan at Birth
(years)
Comment
Upper Paleolithic 33 At age 15: 39 (to age 54)[7][8]
Neolithic[9] 20
Bronze Age and Iron Age[10] 35+
Classical Greece[11] 28
Classical Rome[11] 28
Pre-Columbian North America[12] 25-30
Medieval Islamic Caliphate[13] 35+
Medieval Britain[14][15] 30
Early Modern Britain[10] 40+
Early 20th Century[16][17] 30-45
Current world average[18] 67.2 2010 est.

While different sample attributes and sizes, methodologies, and theoretical assumptions produce sometimes notable variations, in general, interpretations of the available data indicate that the occurance of older age became more common late in human evolution.[8][19] This increased longevity is attributed by some writers to cultural adaptations rather than phylogenetic change,[20] although some research indicates that during the Neolithic Revolution there was a selection effect of extrinsic mortality risk upon genotypic expressions favouring increased longevity in subsequent populations.[9] Nevertheless, all researchers acknowledge the effect of cultural adaptations upon life expectancy.[19]

The average life expectancy in Colonial America was under 25 years in the Virginia colony,[21] and in New England about 40% of children failed to reach adulthood.[22] During the Industrial Revolution, the life expectancy of children increased dramatically.[23] The percentage of children born in London who died before the age of five decreased from 74.5% in 1730-1749 to 31.8% in 1810-1829.[24][25]

Public health measures are credited with much of the recent increase in life expectancy. During the 20th century, the average lifespan in the United States increased by more than 30 years, of which 25 years can be attributed to advances in public health.[26]

In order to assess the quality of these additional years of life, 'healthy life expectancies' have been calculated for the last 30 years. Since 2001, the World Health Organization publishes statistics called Healthy life expectancy (HALE), defined as the average number of years that a person can expect to live in "full health", excluding the years lived in less than full health due to disease and/or injury. Since 2004, Eurostat publishes annual statistics called Healthy Life Years (HLY) based on reported activity limitations. The United States of America uses similar indicators in the framework of their nationwide health promotion and disease prevention plan "Healthy People 2010". An increasing number of countries are using health expectancy indicators to monitor the health of their population.

### Regional variations

CIA World Factbook 2008 Estimates for Life Expectancy at birth (years).
 over 80      77.5-80      75-77.5      72.5-75      70-72.5      67.5-70      65-67.5 60-65      55-60      50-55      45-50      40-45      under 40      not available

There are great variations in life expectancy between different parts of the world, mostly caused by differences in public health, medical care and diet. Much of the excess mortality (higher death rates) in poorer nations is due to war, starvation, and diseases (AIDS, Malaria, etc.). Over the past 200 years, countries with Black or African populations have generally not had the same improvements in mortality rates that have been enjoyed by populations of European origin. Even in countries with a majority of White people, such as USA, Britain, Ireland and France, Black people tend to have shorter life expectancies than their White counterparts (although often the statistics are not analysed by sexuality). For example, in the U.S. White Americans are expected to live until age 78, but black people only until age 71.[6]. Climate may also have an effect, and the way data is collected may also influence the figures. According to the CIA World Factbook, Macau Special Administrative Region of the People's Republic of China has the world's longest life expectancy of 84.4 years.

There are also significant differences in life expectancy between men and women in most countries, with women typically outliving men by around five years. Economic circumstances also affect life expectancy. For example, in the United Kingdom, life expectancy in the wealthiest areas is several years longer than in the poorest areas. This may reflect factors such as diet and lifestyle as well as access to medical care. It may also reflect a selective effect: people with chronic life-threatening illnesses are less likely to become wealthy or to reside in affluent areas.[27] In Glasgow the disparity is among the highest in the world with life expectancy for males in the heavily deprived Calton standing at 54 ' 28 years less than in the affluent area of Lenzie, which is only eight kilometres away.[28][29]

Life expectancy is also likely to be affected by exposure to high levels of highway air pollution or industrial air pollution.[citation needed] This is one way that occupation can have a major effect on life expectancy. Well-educated professionals working in offices have a high life expectancy, while coal miners (and in prior generations, asbestos cutters) do not. Other factors affecting an individual's life expectancy are genetic disorders, obesity, access to health care, diet, exercise, tobacco smoking, drug use and excessive alcohol use.

### Gender differences

Female vs. male life expectancy at birth in 2005.

Women tend to have a lower mortality rate at every age. In the womb, male fetuses have a higher mortality rate (babies are conceived in a ratio of about 124 males to 100 females, but the ratio of those surviving to birth is only 105 males to 100 females). Among the smallest premature babies (those under 2 pounds or 900 g) females again have a higher survival rate. At the other extreme, about 90% of individuals aged 110 are female.

In the past, mortality rates for females in child-bearing age groups were higher than for males at the same age. This is no longer the case, and female human life expectancy is considerably higher than those of men. The reasons for this are not entirely certain. Traditional arguments tend to favor socio-environmental factors: historically, men have generally consumed more tobacco, alcohol and drugs than females in most societies, and are more likely to die from many associated diseases such as lung cancer, tuberculosis and cirrhosis of the liver.[30] Men are also more likely to die from injuries, whether unintentional (such as car accidents) or intentional (suicide, violence, war).[30] Men are also more likely to die from most of the leading causes of death (some already stated above) than women. Some of these in the United States include: cancer of the respiratory system, motor vehicle accidents, suicide, cirrhosis of the liver, emphysema, and coronary heart disease [6]. These far outweigh the female mortality rate from breast cancer and cervical cancer etc.[citation needed]

Some argue that shorter male life expectancy is merely another manifestation of the general rule, seen in all mammal species, that larger individuals tend on average to have shorter lives.[31][32] This biological difference occurs because women have more resistance to infections and degenerative diseases [6].

### Influence of disabilities

The main disabilities influencing life expectancy are physical disabilities, including congenital conditions and the results of accidents.

In the Western world, people with a serious mental illness die on average 25 years earlier than the rest of the population[citation needed], even though there is no objective test for mental illness[citation needed]. Mental illnesses include schizophrenia, bipolar disorder and major depression. Three out of five mentally ill die from mostly preventable physical diseases, such as Heart/Cardiovascular disease, Diabetes, Dyslipidaemia, Respiratory ailments, Pneumonia, Influenza.[citation needed]

Stress also decreases life expectancy. The side effects of stress are: pain of any kind, heart disease, digestive problems, sleep problems, depression, obesity, autoimmune diseases, skin conditions, et[citation needed]

### Centenarians

The number of centenarians is increasing at 7% per year, which means doubling the centanarian population every decade, pushing it into the millions in the next few years.[33] Japan has the highest ratio of centenarians. In Okinawa, there are 34.7 centenarians for every 100,000 inhabitants [6].

In the United States, the number of centenarians grew from 15,000 in 1980 to 77,000 in 2000.[citation needed]

## Evolution and aging rate

Various species of plants and animals, including humans, have different lifespans. There is a well-developed evolutionary theory of aging, and general consensus in the academic community of evolutionary theorists; however the theory doesn't work well in practice, and there are many unexplained exceptions. Evolutionary theory states that organisms that, by virtue of their defenses or lifestyle, live for long periods whilst avoiding accidents, disease, predation, etc., are likely to have genes that code for slow aging - which often translates to good cellular repair. This is theorized to be true because if predation or accidental deaths prevent most individuals from living to an old age, then there will be less natural selection to increase intrinsic life span.[34] The finding was supported in a classic study of opossums by Austad [35], however the opposite relationship was found in an equally-prominent study of guppies by Reznick.[36][37]

One prominent and very popular theory attributes aging to a tight budget for food energy.[38] The theory has difficulty with the caloric restriction effect observed in many animals, where tighter the calorific intake, lesser the rate of aging.

In theory, reproduction is costly and takes energy away from the repair processes that extend life spans. However, in actuality females of many species invest much more energy in reproduction than do their male counterparts, and live longer nevertheless. In a broad survey of zoo animals, no relationship was found between the fertility of the animal and its life span.[39]

One area in which theory seems to be well validated: Better-defended animals such as small birds and bats, that can fly away from danger, and naked mole rats that live underground, survive for decades, whereas mice, which cannot, die of old age in a year or two. Tortoises and turtles are very well defended and can live for over 100 years.

## Calculating life expectancies

The starting point for calculating life expectancies is the age-specific death rates of the population members. A very simple model of age-specific mortality uses the Gompertz function, although these days more sophisticated methods are used.[40]

In cases where the amount of data is relatively small, the most common methods are to fit the data to a mathematical formula, such as an extension of the Gompertz function, or to look at an established mortality table previously derived for a larger population and make a simple adjustment to it (e.g. multiply by a constant factor) to fit the data.

With a large amount of data, one looks at the mortality rates actually experienced at each age, and applies smoothing (e.g. by cubic splines) to iron out any apparently random statistical fluctuations from one year of age to the next.

While the data required is easily identified in the case of humans, the computation of life expectancy of industrial products and wild animals involves more indirect techniques. The life expectancy and demography of wild animals are often estimated by capturing, marking and recapturing them.[41] The life of a product, more often termed shelf life is also computed using similar methods. In the case of long-lived components such as those used in critical applications, such as in aircraft methods such as accelerated aging are used to model the life expectancy of a component.[3]

The age-specific death rates are calculated separately for separate groups of data which are believed to have different mortality rates (e.g. males and females, and perhaps smokers and non-smokers if data is available separately for those groups) and are then used to calculate a life table, from which one can calculate the probability of surviving to each age. In actuarial notation the probability of surviving from age x to age x+n is denoted $\,_np_x\!$ and the probability of dying during age x (i.e. between ages x and x+1) is denoted $q_x\!$. For example, if 10% of a group of people alive at their 90th birthday die before their 91st birthday, then the age-specific death probability at age 90 would be 10%.

The life expectancy at age x, denoted $\,e_x\!$, is then calculated by adding up the probabilities to survive to every age. This is the expected number of complete years lived (one may think of it as the number of birthdays they celebrate).

$e_x =\sum_{t=1}^{\infty}\,_tp_x = \sum_{t=0}^{\infty}t \,_tp_x q_{x+t}$

Because age is rounded down to the last birthday, on average people live half a year beyond their final birthday, so half a year is added to the life expectancy to calculate the full life expectancy. (This is denoted by $\,e_x\!$ with a circle over the "e".)

Life expectancy is by definition an arithmetic mean. It can also be calculated by integrating the survival curve from ages 0 to positive infinity (the maximum lifespan, sometimes called 'omega'). For an extinct cohort (all people born in year 1850, for example), of course, it can simply be calculated by averaging the ages at death. For cohorts with some survivors it is estimated by using mortality experience in recent years.

It is important to note that this statistic is usually based on past mortality experience, and assumes that the same age-specific mortality rates will continue into the future. Thus such life expectancy figures are not generally appropriate for calculating how long any given individual of a particular age is expected to live. But they are a useful statistic to summarize the current health status of a population.

However for some purposes, such as pensions calculations, it is usual to adjust the life table used, thus assuming that age-specific death rates will continue to decrease over the years, as they have done in the past. This is often done by simply extrapolating past trends; however some models do exist to account for the evolution of mortality (e.g., the Lee-Carter model[42]).

As discussed above, on an individual basis, there are a number of factors that have been shown to correlate with a longer life. Factors that are associated with variations in life expectancy include family history, marital status, economic status, physique, exercise, diet, drug use including smoking and alcohol consumption, disposition, education, environment, sleep, climate, and health care.[6]

## Life expectancy forecasting

Forecasting life expectancy and mortality forms an important subdivision of demography. Future trends in life expectancy have huge implications for old-age support programs like U.S. Social Security and pension systems, because the cash flow in these systems depends on the number of recipients still living (along with the rate of return on the investments or the tax rate in PAYGO systems). With longer life expectancies, these systems see increased cash outflow; if these systems underestimate increases in life-expectancies, they won't be prepared for the large payments that will inevitably occur as humans live longer and longer.

Life expectancy forecasting usually is based on two different approaches:

• Forecasting the life expectancy directly, generally using ARIMA or other time series extrapolation procedures: This approach has the advantage of simplicity, but it cannot account for changes in mortality at specific ages, and the forecasted number cannot be used to derive other life table results. Analyses and forecasts using this approach can be done with any common statistical/ mathematical software package, like R, SAS, Matlab, or SPSS.
• Forecasting age specific death rates and computing the life expectancy from the results with life table methods: This approach is usually more complex than simply forecasting life expectancy because the analyst must deal with correlated age specific mortality rates, but it seems to be more robust than simple one dimensional time series approaches. This approach also yields a set of age specific rates that be used to derive other measures, like survival curves or life expectancies at different ages. The most important approach within this group is the Lee Carter method[43], which uses the singular value decomposition on a set of transformed age-specific mortality rates to reduce their dimensionality to a single time series, forecasts that time series, and then recovers a full set of age-specific mortality rates from that forecasted value. Software for this approach include Prof. Hyndeman's R libraries and UC Berkeley's LCFIT system.

## Policy uses of life expectancy

Life expectancy is one of the factors in measuring the Human Development Index (HDI) of each nation, along with adult literacy, education, and standard of living.[44]

Life expectancy is also used in describing the physical quality of life of an area.

## Life expectancy vs. life span

Life expectancy is often confused with life span to the point that they are nearly synonyms; when people hear 'life expectancy was 35 years' they often interpret this as meaning that people of that time or place had short life spans. [45] One such example can be seen in the In Search of... episode "The Man Who Would Not Die" (About Count of St. Germain) where it is stated "Evidence recently discovered in the British Museum indicates that St. Germain may have well been the long lost third son of R�¡kóczi born in Transylvania in 1694. If he died in Germany in 1784, he lived 90 years. The average life expectancy in the 18th century was 35 years. Fifty was a ripe old age. Ninety... was forever."

This ignores the fact that the life expectancy generally quoted is the at birth is an average that includes all the babies that die before their first year of life as well people that die from disease and war. In fact, there are examples of people living way past the life expectancy of their time such as Socrates, Saint Anthony, Michelangelo, and Ben Franklin.[46]

It can be argued that it is better to compare life expectancies of the period after adulthood to get a better handle on life span.[47] Even during childhood life expectancy can take a huge jump as seen in the Roman Life Expectancy table at the University of Texas where at birth the life expectancy was 25 but at the age of 5 it jumped to 48. Studies like Plymouth Plantation; "Dead at Forty" and Life Expectancy by Age, 1850'2004 similarly show a dramatic increase in life expectancy once adulthood was reached.

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