The Doctrine of Chances
Encyclopedia
The Doctrine of Chances was the first textbook on probability theory
, written by 18th-century French mathematician
Abraham de Moivre
and first published in 1718. De Moivre wrote in English because he resided in England at the time, having fled France to escape the persecution of Huguenots. The book's title came to be synonymous with probability theory, and accordingly the phrase was used in Thomas Bayes
' famous posthumous paper An Essay towards solving a Problem in the Doctrine of Chances
, wherein a version of Bayes' theorem
was first introduced.
Published in 1738 by Woodfall and running for 258 pages, the second edition of de Moivre's book introduced the concept of normal distributions as approximations to binomial distributions. In effect de Moivre proved a special case of the central limit theorem
. Sometimes his result is called the theorem of de Moivre–Laplace.
A third edition was published posthumously in 1756 by A. Millar, and ran for 348 pages; additional material in this edition included an application of probability theory to actuarial science
in the calculation of annuities
.
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
, written by 18th-century French mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
Abraham de Moivre
Abraham de Moivre
Abraham de Moivre was a French mathematician famous for de Moivre's formula, which links complex numbers and trigonometry, and for his work on the normal distribution and probability theory. He was a friend of Isaac Newton, Edmund Halley, and James Stirling...
and first published in 1718. De Moivre wrote in English because he resided in England at the time, having fled France to escape the persecution of Huguenots. The book's title came to be synonymous with probability theory, and accordingly the phrase was used in Thomas Bayes
Thomas Bayes
Thomas Bayes was an English mathematician and Presbyterian minister, known for having formulated a specific case of the theorem that bears his name: Bayes' theorem...
' famous posthumous paper An Essay towards solving a Problem in the Doctrine of Chances
An Essay towards solving a Problem in the Doctrine of Chances
An Essay towards solving a Problem in the Doctrine of Chances is a work on the mathematical theory of probability by the Reverend Thomas Bayes, published in 1763, two years after its author's death. It included a statement of a special case of what is now called Bayes' theorem. In 18th-century...
, wherein a version of Bayes' theorem
Bayes' theorem
In probability theory and applications, Bayes' theorem relates the conditional probabilities P and P. It is commonly used in science and engineering. The theorem is named for Thomas Bayes ....
was first introduced.
Editions
The full title of the first edition was The doctrine of chances: or, a method for calculating the probabilities of events in play; it was published in 1718, by W. Pearson, and ran for 175 pages.Published in 1738 by Woodfall and running for 258 pages, the second edition of de Moivre's book introduced the concept of normal distributions as approximations to binomial distributions. In effect de Moivre proved a special case of the central limit theorem
Central limit theorem
In probability theory, the central limit theorem states conditions under which the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed. The central limit theorem has a number of variants. In its common...
. Sometimes his result is called the theorem of de Moivre–Laplace.
A third edition was published posthumously in 1756 by A. Millar, and ran for 348 pages; additional material in this edition included an application of probability theory to actuarial science
Actuarial science
Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in the insurance and finance industries. Actuaries are professionals who are qualified in this field through education and experience...
in the calculation of annuities
Annuity (finance theory)
The term annuity is used in finance theory to refer to any terminating stream of fixed payments over a specified period of time. This usage is most commonly seen in discussions of finance, usually in connection with the valuation of the stream of payments, taking into account time value of money...
.