Demography () is the statistical study of human populations: their size, composition (e.g., ethnic group, age), and how they change through the interplay of fertility (births), mortality (deaths), and migration.

Formal demography limits its object of study to the measurement of population processes, while the broader field of social demography (or population studies) also analyses the relationships among economic, social, institutional, cultural, and biological processes that influence a population. Educational institutions usually treat demography as a field of sociology, although independent demography departments do exist.Andrew Hinde Demographic Methods Ch. 1

Demographic analysis (usually abbreviated to DA) examines and measures the dimensions and dynamics of populations, including whole societies or groups defined by criteria such as education, nationality, religion, and ethnicity. The methods of DA have primarily been developed to study human populations, but have also been used in a variety of areas where researchers want to know how other non-human populations of social actors can change across time through processes of birth, death, and migration.

Demographic analysis is used in a wide variety of contexts. In the labor force, DA is used to estimate sizes and flows of populations of workers; in population ecology the focus is on the birth, death, emigration and immigration of individuals in a population of living organisms; in the social sciences this could involve the movement of firms and institutional forms; in business planning DA is often used to describe the population in a business's geographic area.

In the context of human biological populations, demographic analysis uses administrative records to develop an independent estimate of the population. For example, patient demographics such as date of birth, gender, date of death, postal code, ethnicity, blood type, emergency contact information, family doctor, insurance provider data, allergies, major diagnoses, and major medical history form the core of the data for any medical institution, allowing the identification and categorization of a patient for the purpose of statistical analysis.

Demographic analysis estimates are often considered a reliable standard for judging the accuracy of census information. For example, the U.S. Census Bureau expanded its DA categories for the 2010 U.S. Census to include comparative analysis between independent housing estimates, and differences between census address lists at different key times.

History Demographic thought traces back to antiquity, and was present in many civilizations and cultures like Ancient Greece, Ancient Rome, China and India. Made up of the prefix demo- and the suffix -graphy, the term demography refers to the overall study of population.

Demography is discussed in the works of Greek thinkers such as Herodotus, Thucydides, Hippocrates, Epicurus, Protagoras, Polus, Plato and Aristotle, and Romans such as Cicero, Seneca, Pliny the Elder, Marcus Aurelius, Epictetus, Cato, and Columella.

In the Middle Ages, Christian thinkers devoted much time to refuting the Classical ideas on demography. Important contributors to the field were William of Conches,Peter Biller,The measure of multitude: Population in medieval thought. Bartholomew of Lucca, William of Auvergne, William of Pagula, and Muslim sociologists like Ibn Khaldun.See, e.g., Andrey Korotayev, Artemy Malkov, & Daria Khaltourina (2006). Introduction to Social Macrodynamics: Compact Macromodels of the World System Growth . Moscow: URSS, .

One of the earliest demographic studies in the modern period was Natural and Political Observations Made upon the Bills of Mortality (1662) by John Graunt, which contains a primitive form of life table. Among the study's findings were that one-third of the children in London died before their sixteenth birthday. Mathematicians, such as Edmond Halley, developed the life table as the basis for life insurance mathematics. Richard Price was credited with the first textbook on life contingencies published in 1771,"Our Yesterdays: the History of the Actuarial Profession in North America, 1809-1979," by E.J. (Jack) Moorhead, FSA, (1/23/10 – 2/21/04), published by the Society of Actuaries as part of the profession's centennial celebration in 1989. followed later by Augustus De Morgan, On the Application of Probabilities to Life Contingencies (1838).The History of Insurance, Vol 3, Edited by David Jenkins and Takau Yoneyama (1 85196 527 0): 8 Volume Set: (2000) Availability: Japan: Kinokuniya).

In 1755, Benjamin Franklin published his essay Observations Concerning the Increase of Mankind, Peopling of Countries, etc., projecting exponential growth in British colonies. His work influenced Thomas Robert Malthus, who, writing at the end of the 18th century, feared that, if unchecked, population growth would tend to outstrip growth in food production, leading to ever-increasing famine and poverty (see Malthusian catastrophe). Malthus is seen as the intellectual father of ideas of overpopulation and the limits to growth. Later, more sophisticated and realistic models were presented by Benjamin Gompertz and Verhulst.

In 1855, Belgian scholar Achille Guillard defined demography as the natural and social history of the human species or the mathematical knowledge of populations, of their general changes, and of their physical, civil, intellectual, and moral condition.

Newell (1988, pp. 4-5) claims that the first major developments in the 20th century, in what was to become formal demography, were made in three papers by Alfred J. Lotka (1907, 1911 (with F.R. Sharpe), and 1922), which developed a Stable Population Model. This model was similar to Leonhard Euler's earlier, overlooked modeling, which showed how a population with constant fertility and mortality might grow geometrically using a difference equation. Under this geometric growth model, Euler also examined relationships among various demographic indices, showing how they could be used to produce estimates when data were missing. Lotka and Sharpe showed that a closed population, assuming constant both age-specific mortality and fertility, developed along a path leading to a fixed age structure - the Stable Population.Newell, Colin. (1988) Methods and models in demography. Belhaven Press.Inaba, Hisashi (2017) Chapter 1 The Stable Population Model in Age-structured population dynamics in demography and epidemiology. Springer Singapore.Lotka, A. J. (1907). Relation between birth rates and death rates. Science, 26(653), 21-22.Sharpe, F. R., & Lotka, A. J. (1911). L. A problem in age-distribution. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 21(124), 435-438.Lotka, A. J. (1922). The stability of the normal age distribution. Proceedings of the National Academy of Sciences, 8(11), 339-345.

Methods

Direct methods + Types of data arising from direct methods Data type Examples Population Total population, sex ratio, birth rate, death rate Geography Place of residence, place of birth, duration of residence Migration Foreign-born status, nation of birth, citizenship, arrival date, migrant flows Social features Sex, age, marital status, religion, language, ethnicity Education Literacy, school attendance, highest educational attainment Economic Occupation, industry, employment status, workforce size, personal income Buildings Building type (residential vs. non-residential), period of construction Health Health status, disability level, live-born children, household deaths Sensor data Satellite imaging, surveillance footage, climate logs, road sensors Administrative Electronic medical records, hospital visits, insurance claims, bank records Direct methods calculate measures from empirical records of demographic events and population counts collected through administrative registers, civil registration systems, censuses, surveys, or big data .

A register continuously updates administrative data and attributes for its target population of persons or objects (such as dwellings, buildings or businesses). Registers serve administrative functions of government or private institutions such as "monitoring of taxes, the allocation of pensions, the provision of services, the production of goods, or the administering of bank accounts." Civil registration systems record the occurrence and characteristics of vital events, such as births, deaths, and infant mortality.

A census periodically records information from people within a specific geographic area, attempting to represent each person within this region. The typical interval between censuses is 5 to 10 years. A national census measures total female, and male populations. A census may fail to count a person or count one person multiple times. Demographers may identify and correct these errors by comparing the census's observed male-to-female ratio at each age to the expected ratio at each age.

Surveys record data from a sample rather than the whole population. Although this method can provide more timely or distinct data than a census or register, sampled data may be less comprehensive and less precise for local data. The United Kingdom conducted four consecutive prospective cohort surveys: the 1946 National Survey of Health and Development, the 1958 National Child Development Study, the 1970 British Cohort Study, and the 2000 Millennium Cohort Study. These surveys sampled cohorts to identify generational changes over decades in health, education, development, economic status, and lifestyle choices.

The World Wide Web and electronic device sensors generate big data: high-volume, high-velocity, and highly varied information. Big data originates from multiple sources: administrative records, sensor recordings, mobile phone communications, and social media. Statisticians use specialized methods to process big data, evaluate quality, and fix bias, missing data, or missing identifiers.

Researchers commonly combine these methods. For instance, France's rolling census continuously surveys its population over an extended time to generate nationwide data.

Indirect methods When complete, accurate information is unavailable, demographers use indirect methods; they apply mathematical models to incomplete or proxy data to estimate the desired demographic measurement. This commonly occurs for developing nations and in historical demography.

Demographers use these models to describe a broad range of demographic measures; examples include: Survivorship: Parametric models describe survivorship, the probability of surviving from birth to each age. The Gompertz model applies to older adults, the Gompertz–Makeham model applies to all adults, and the Siler model applies to persons of all ages. In the Brass method relational logit system, a linear function relates logit transformed survivorship of a study population to logit transformed survivorship of a standard population. The Lee-Carter model predicts age-specific mortality rates from prior age-specific rates. Maternal mortality ratio: The sisterhood method surveys adults about whether their sisters of reproductive age died during pregnancy, childbirth, or the postpartum period. It then applies a model to this survey data to estimate maternal mortality ratios. Age-specific fertility rate: The Coale–Trussell model estimates age-specific marital fertility using empirical data of natural age-specific fertility and age-specific fertility control. Statistical probability distributions may also describe age-specific fertility. These include the inverse Gaussian (Hadwiger model), gamma distribution, and beta distribution. Spline methods generate smooth distributions from incomplete data. The Brass relational Gompertz model relates incomplete fertility data in a study population to a standard data set. The Page model of marital fertility estimates fertility rates from a woman's age and duration of marriage.