# De Moivre Distribution

The de Moivre distribution is another name for the normal distribution [1], which also goes by many different names [2] including “the law of error”, the “frequency law”, the “Gaussian curve”,  and “Laplace-Gauss”.

The use of “de Moivre distribution” to describe the normal distribution is thought to originate with Freudenthal [3], who advocated the name because De Moivre was the first to define the distribution, in 1733 [4]. Although de Moivre’s contribution was not widely recognized at the time, Pierre-Simon Marquis de Laplace generalized de Moivre’s findings and included in his influential Theorie Analytique des Probabilites published in 1812 [5].

## De Moivre Distribution in Actuarial Science

In actuarial science, a de Moivre is another name for the uniform distribution. For example, the de Moivre distribution is often used in relation to the actuarial study of uniform (de Moivre) distribution of deaths [6, 7]. For example [8], let T represent the time from birth until death of a random member of the population and assume that T follows a de Moivre distribution:

The function F(t) allows us to calculate the probability a person will die by age t.

## References

[1]  Johnson, Kotz, and Balakrishnan, (1994), Continuous Univariate Distributions, Volumes I and II, 2nd. Ed., John Wiley and Sons.
[2] Stigler, S. M. (1999). Statistics on the table. The history of statistical concepts and methods. Cambridge, MA: Harvard University Press.
[3] Freudenthal, H. (1966b). Waarschijnlijkheid en Statistiek [Probability and Statistics]. Haarlem: De Erven F. Bohn.
[4] Daw, R. & Pearson, E. Studies in the History of Probability and Statistics. XXX. Abraham De Moivre’s 1733 Derivation of the Normal Curve: A Bibliographical Note. Biometrika Vol. 59, No. 3 (Dec., 1972), pp. 677-680 (4 pages)
[5] BIOSTATISTICS TOPIC 5: SAMPLING DISTRIBUTION II THE NORMAL DISTRIBUTION. Online: http://vietsciences.free.fr/khaocuu/nguyenvantuan/Topic05[1].Normal%20distribution.pdf
[6] Humphreys, N. ACTS 4301 formula summary. Lesson 1: Probability Review. Online: https://personal.utdallas.edu/~natalia.humphreys/MLC%20SP18/FORMULAE_MLC.pdf
[7] Randles, R. (n.d.). Chapter 4 – Insurance Benefits Section 4.4 – Valuation of Life Insurance Benefits. Online: http://users.stat.ufl.edu/~rrandles/sta4930/4930lectures/chapter4/chapter4R.pdf
[8] Hassett, M. & Stewart, J. (2006). Probability for Risk Management. ACTEX Publications.

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Stephanie Glen. "De Moivre Distribution" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/de-moivre-distribution/
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