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Shorthand method to record math formulas that deal with interest rates and life tables
Actuarial notation is a shorthand method to allow actuaries to record mathematical formulas that deal with interest rates and life tables. The core alphabet
Actuarial_notation
Reserve set aside for future insurance liabilities
the loss random variable, L {\displaystyle L} , can be written in actuarial notation as a function of K ( x ) {\displaystyle K(x)} L = v K ( x ) + 1 −
Actuarial_reserves
Statistics applied to risk in insurance and other financial products
this new world . Actuarial control cycle Actuarial exam Actuarial notation Actuarial present value Black swan theory Category:Actuarial associations Data
Actuarial_science
Expected present value of life-contingent cash flows
and are commonly expressed using standard actuarial notation for life-contingent contracts. An actuarial present value is defined as the expected value
Actuarial_present_value
Organization of India
may be found here: Category:Actuarial associations Actuary Actuarial present value Actuarial science Actuarial notation Catastrophe modeling Risk theory
Institute of Actuaries of India
Institute_of_Actuaries_of_India
Series of payments made at equal intervals
_{\text{perpetuity}}={\frac {R}{i}}} provided i {\displaystyle i} is positive. In actuarial notation the present value factors for level perpetuities are a ∞ ¯ | i = 1
Annuity
Survival model in actuarial science
{\displaystyle S(x)=1-{\frac {x}{\omega }},\qquad 0\leq x<\omega .} In actuarial notation (x) denotes a status or life that has survived to age x, and T(x)
De_Moivre's_law
Measure of average lifespan in a given population
between investment of the animal in reproduction and its life span. In actuarial notation, the probability of surviving from age x {\displaystyle x} to age
Life_expectancy
Overview of and topical guide to actuarial science
An applied science – A subdiscipline of statistics – Actuarial science Actuary Actuarial notation Mathematical finance Insurance, especially: Life insurance
Outline_of_actuarial_science
Fourth letter in the Greek alphabet
automata. Deflection in engineering mechanics. The force of interest in actuarial science. The chemical shift of nuclear magnetic resonance in chemistry
Delta_(letter)
Sum paid for the use of money
by the administrative costs component of the total interest rate. Actuarial notation Credit card interest Credit rating agency DIRTI 5 Discount Fisher
Interest
Function in actuarial science
( x ) = μ ( x ) S ( x ) . {\displaystyle f(x)=\mu (x)\,S(x).} In actuarial notation, the probability that a life aged x {\displaystyle x} survives for
Force_of_mortality
Last letter of the Greek alphabet
number of prime divisors of n (counting multiplicity). In notation related to Big O notation to describe the asymptotic behavior of functions. Chaitin's
Omega
Situations involving imperfect or unknown information
and risk are fairly consistent among fields such as probability theory, actuarial science, and information theory. Some also create new terms without substantially
Uncertainty
version of the Schuette–Nesbitt formula has practical applications in actuarial science, where it is used to calculate the net single premium for life
Schuette–Nesbitt_formula
Branch of mathematics
paradoxes. Calculus is used in every branch of the physical sciences, actuarial science, computer science, statistics, engineering, economics, business
Calculus
Theory in actuarial science and applied probability
In actuarial science and applied probability, ruin theory (sometimes risk theory or collective risk theory) uses mathematical models to describe an insurer's
Ruin_theory
theorem in actuarial science that describes the allocation of the variance or risk of the loss random variable over the lifetime of an actuarial reserve
Hattendorff's_theorem
Probability modelling tool
article on stochastic reserving from the Australian Actuarial Journal, 2006 (pdf) Stochastic Modelling For Dummies, Actuarial Society of South Africa
Stochastic modelling (insurance)
Stochastic_modelling_(insurance)
Better to receive money now than later
different dates long predate the modern terminology. Historical accounts of actuarial practice describe the use of compound interest in business transactions
Time_value_of_money
Public university in Sydney, New South Wales, Australia
graduates. Upon successful completion of the GLP, students receive a formal notation on their academic transcript and a certificate. Macquarie's GLP was the
Macquarie_University
Probability distribution
is used to describe social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena; the principle originally
Pareto_distribution
Statistical programming language
ISBN 978-0-471-74406-1. Charpentier, Arthur (2014-08-26). Computational Actuarial Science with R. CRC Press. p. 4. ISBN 978-1-4987-5982-3. Chambers, John
S_(programming_language)
Type of random mathematical object
including experiments on radioactive decay, telephone call arrivals and actuarial science. This point process is used as a mathematical model for seemingly
Poisson_point_process
Statistical experimental design approach
from a full-factorial table. Fractional designs are expressed using the notation lk − p, where l is the number of levels of each factor, k is the number
Fractional_factorial_design
Characterization of how many integers are prime
This article uses technical mathematical notation for logarithms. All instances of log ( x ) {\displaystyle \log(x)} without a subscript base should
Prime_number_theorem
New Zealand mathematician (1895–1967)
concept of generalized least squares, along with now standard vector/matrix notation for the linear regression model. Another influential paper co-authored
Alexander_Aitken
Experimental design in statistics
letter μ. (The term cell is borrowed from its use in tables of data.) This notation is illustrated here for the 2 × 3 experiment. A contrast in cell means
Factorial_experiment
English actuary (1776–1851)
and Assurances (1815). Milne's new "Carlisle table" marked an epoch in actuarial science. Considering the narrow base of data from which he had to work
Joshua_Milne
Difference between two successive prime numbers
This article uses technical mathematical notation for logarithms. All instances of log ( x ) {\displaystyle \log(x)} without a subscript base should
Prime_gap
Variable capable of taking on a limited number of possible values
Process / quality control Reliability System identification Social statistics Actuarial science Census Crime statistics Demography Econometrics Jurimetrics National
Categorical_variable
Statistical test based on the gradient of the likelihood function
lead to bias in small samples. Note that some texts use an alternative notation, in which the statistic S ∗ ( θ ) = S ( θ ) {\displaystyle S^{*}(\theta
Score_test
Number of values in the final calculation of a statistic that are free to vary
Z_{n}} . The restriction to three groups and equal sample sizes simplifies notation, but the ideas are easily generalized. The observations can be decomposed
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Branch of statistics
(2012). "A handbook of parametric survival models for actuarial use". Scandinavian Actuarial Journal. 2012 (4): 233–257. doi:10.1080/03461238.2010.506688
Survival_analysis
Statistical model used in time series analysis
Jenkins. ARMA models can be estimated by using the Box–Jenkins method. The notation AR(p) refers to the autoregressive model of order p. The AR(p) model is
Autoregressive moving-average model
Autoregressive_moving-average_model
English mathematician, philosopher, and engineer (1791–1871)
electromagnetic theory, staying close to Ampère's force law. Babbage purchased the actuarial tables of George Barrett, who died in 1821 leaving unpublished work, and
Charles_Babbage
Sequence of data points over time
and irregular fluctuations. Time series are widely used in statistics, actuarial science, signal processing, pattern recognition, econometrics, mathematical
Time_series
Non-parametric statistic used to estimate the survival function
/ n ( s ) {\displaystyle {\hat {q}}(s)=1-d(s)/n(s)} where, using the actuarial science terminology, d ( s ) = | { 1 ≤ k ≤ n : c k > s , τ ~ k = s } |
Kaplan–Meier_estimator
Differential equations involving stochastic processes
ISBN 978-981-4678-93-3. Teugels, J.; Sund, B., eds. (2004). Encyclopedia of Actuarial Science. Chichester: Wiley. pp. 523–527. Gardiner, C. W. (2004). Handbook
Stochastic differential equation
Stochastic_differential_equation
Estimatation in number theory
This article uses technical mathematical notation for logarithms. All instances of log ( x ) {\displaystyle \log(x)} without a subscript base should
Cramér's_conjecture
Function that measures dissimilarity between two probability distributions
a commonly used statistical divergence, does not satisfy condition 3. Notation for divergences varies significantly between fields, though there are some
Divergence_(statistics)
Academic fields of study or professions
Scheduling Stochastic processes Systems analysis Statistics (outline) Actuarial science Demography Econometrics Mathematical statistics Data visualization
Outline of academic disciplines
Outline_of_academic_disciplines
Statistical measure of association
overestimate the strength of association. A bias correction, using the above notation, is given by V ~ = φ ~ 2 min ( k ~ − 1 , r ~ − 1 ) {\displaystyle {\tilde
Cramér's_V
Middle quantile of a data set or probability distribution
Huygens, but as an example of a statistic that was inappropriate for actuarial practice. The earliest recommendation of the median dates to 1757, when
Median
Statistical hypothesis test
that had to be estimated from the sample, and suggested that, with the notation of mi being the true expected numbers and m′i being the estimated expected
Chi-squared_test
Compound probability distribution
probability distribution. Mixed Poisson distributions can be found in actuarial mathematics as a general approach for the distribution of the number of
Mixed_Poisson_distribution
Frequency with which an engineered system or component fails
( t ) {\displaystyle F(t)} need be defined. Confusion can occur as the notation λ ( t ) {\displaystyle \lambda (t)} for "failure rate" often refers to
Failure_rate
Model selection principle
Process / quality control Reliability System identification Social statistics Actuarial science Census Crime statistics Demography Econometrics Jurimetrics National
Minimum_description_length
Person who has turned 100 years old
of supercentenarians in low-mortality countries" (PDF). North American Actuarial Journal. 6 (3): 54–63. doi:10.1080/10920277.2002.10596057. S2CID 129046321
Centenarian
Equations with an unknown function under an integral sign
which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: f ( x 1
Integral_equation
Concept in financial mathematics
while in the latter it is associated with the right tail. The common notation for a risk measure associated with a random variable X {\displaystyle X}
Risk_measure
Statistical test
(1993). "The Method of Maximum Likelihood : Fundamental Concepts and Notation". Estimation and Inference in Econometrics. New York: Oxford University
Wald_test
German polymath (1646–1716)
these geometrical associations. Leibniz was also one of the pioneers in actuarial science, calculating the purchase price of life annuities and the liquidation
Gottfried_Wilhelm_Leibniz
Statistical test
{\displaystyle h-p-q} . The Box–Pierce test uses the test statistic, in the notation outlined above, given by Q BP = n ∑ k = 1 h ρ ^ k 2 , {\displaystyle Q_{\text{BP}}=n\sum
Ljung–Box_test
Statistical model to calculate the value of multiple quantities as they change over time
concise matrix notation: Y = B Z + U {\displaystyle Y=BZ+U\,} A VAR(1) in two variables can be written in matrix form (more compact notation) as [ y 1 ,
Vector_autoregression
Hungarian mathematician (1866–1942)
of time from 1891 to 1940. However, Hlawka (2007) cites two papers on actuarial mathematics which do not appear in these two bibliographical lists and
Alfred_Tauber
Branch of statistics
Statistics Outline Statisticians Glossary Notation Journals Lists of topics List of articles Category Mathematics portal v t e
Mathematical_statistics
Discrete (i.e., incremental) version of infinitesimal calculus
discretization of infinitesimal calculus in every branch of the physical sciences, actuarial science, computer science, statistics, engineering, economics, business
Discrete_calculus
Measure of variation in statistics
discussion on Bessel's correction further down below. or, by using summation notation, σ = 1 N ∑ i = 1 N ( x i − μ ) 2 , where μ ≡ 1 N ∑ i = 1 N
Standard_deviation
Glossary of experimental design Glossary of probability and statistics Notation in probability and statistics List of actuaries List of statisticians List
Lists_of_statistics_topics
Representation of a type of random process
classical autoregressive model in this sense because they are not linear. The notation A R ( p ) {\displaystyle AR(p)} indicates an autoregressive model of order
Autoregressive_model
Fundamental theorem in probability theory and statistics
implication, however, does not hold. In the same setting and with the same notation as above, the Lyapunov condition can be replaced with the following weaker
Central_limit_theorem
manipulations of probability distributions rather than to statistical analysis. Actuarial science is the discipline that applies mathematical and statistical methods
List of fields of application of statistics
List_of_fields_of_application_of_statistics
Probability distribution
Halliwell, Leigh (2015). The Lognormal Random Multivariate (PDF). Casualty Actuarial Society E-Forum, Spring 2015. Arlington, VA. Archived (PDF) from the original
Log-normal_distribution
Measure of covariance of components of a random vector
matrix, since the diagonal terms are in fact variances. By comparison, the notation for the cross-covariance matrix between two vectors is cov ( X , Y )
Covariance_matrix
Statistical measure of the magnitude of a phenomenon
cleanup to meet Wikipedia's quality standards. The specific problem is: Math notation uses different symbols to represent the same quantities in similar formulas
Effect_size
Generalization of the one-dimensional normal distribution to higher dimensions
=(X_{1},\ldots ,X_{k})^{\mathrm {T} }} can be written in the following notation: X ∼ N ( μ , Σ ) , {\displaystyle \mathbf {X} \ \sim \ {\mathcal {N}}({\boldsymbol
Multivariate normal distribution
Multivariate_normal_distribution
Concept in statistics
Process / quality control Reliability System identification Social statistics Actuarial science Census Crime statistics Demography Econometrics Jurimetrics National
Vector generalized linear model
Vector_generalized_linear_model
Statistical property
an estimator for the true "standard error", it is common to see other notations here such as: σ ^ x ¯ := σ x n or s x ¯ := s n . {\displaystyle {\widehat
Standard_error
Accidental sampling Accuracy and precision Accuracy paradox Acquiescence bias Actuarial science Adapted process Adaptive estimator Additive Markov chain Additive
List_of_statistics_articles
Set of statistical processes for estimating the relationships among variables
{\beta }}_{k}=\sum _{i=1}^{n}x_{ij}y_{i},\ j=1,\dots ,p.\,} In matrix notation, the normal equations are written as ( X ⊤ X ) β ^ = X ⊤ Y , {\displaystyle
Regression_analysis
Study of collection and analysis of data
extensively that they have specialized terminology. These disciplines include: Actuarial science (assesses risk in the insurance and finance industries) Applied
Statistics
Bias in causal inference
required to distinguish causal effects from spurious associations. Several notation systems and formal frameworks, such as causal directed acyclic graphs (DAGs)
Confounding
Bound on probability of a random variable being far from its mean
the Tchebycheff Lemma]. Skandinavisk Aktuarietidskrift (Scandinavian Actuarial Journal) (in German). 1940 (3–4): 121–125. doi:10.1080/03461238.1940.10404804
Chebyshev's_inequality
Statistical measure of how far values spread from their average
Process / quality control Reliability System identification Social statistics Actuarial science Census Crime statistics Demography Econometrics Jurimetrics National
Variance
Statistical modeling method
β. Often these n equations are stacked together and written in matrix notation as y = X β + ε , {\displaystyle \mathbf {y} =\mathbf {X} {\boldsymbol {\beta
Linear_regression
Mathematical sequence
matrix Lah, Ivo (1954). "A new kind of numbers and its application in the actuarial mathematics". Boletim do Instituto dos Actuários Portugueses. 9: 7–15
Lah_number
Collection of random variables
large deviations and applications to statistical mechanics". Scandinavian Actuarial Journal. 1995 (1): 98. doi:10.1080/03461238.1995.10413952. ISSN 0346-1238
Stochastic_process
Collection of statistical models
intercept term. Let that vector be X k {\displaystyle X_{k}} . With this notation in place, we now have the exact connection with linear regression. We simply
Analysis_of_variance
Cryptologic device
University of Göttingen Rejewski completed the first year of a two-year actuarial statistics course, then returned to Poznań. In September 1932 he, Różycki
Cyclometer
Method of estimating the parameters of a statistical model, given observations
predicting probabilities is recommended in statistics text-books and actuarial textbooks, and is widely used in the scientific literature. However, maximum
Maximum_likelihood_estimation
Linear regression model with a single explanatory variable
regressions toward the mean. Generalizing the x ¯ {\displaystyle {\bar {x}}} notation, we can write a horizontal bar over an expression to indicate the average
Simple_linear_regression
Covariance and correlation
correlation Spectral density Wiener–Khinchin theorem Bracewell, R. "Pentagram Notation for Cross Correlation." The Fourier Transform and Its Applications. New
Cross-correlation
Distribution (mathematics) in the generalized function sense; but the notation treats it as if it were a continuous distribution. The Kent distribution
List of probability distributions
List_of_probability_distributions
Number measuring the chance an event occurs
risk assessment and modeling. The insurance industry and markets use actuarial science to determine pricing and make trading decisions. Governments apply
Probability
Statistical estimator for ratio of means
generate confidence intervals. The bias is of the order O(1/n) (see big O notation) so as the sample size (n) increases, the bias will asymptotically approach
Ratio_estimator
Numeric quantity representing the center of a collection of numbers
column we will use the mapping arrow to denote a function. Under this notation, the function f {\displaystyle f} is denoted by x ↦ f ( x ) {\displaystyle
Mean
Approximation method in statistics
y_{i}\qquad (j=1,\ldots ,m).} The normal equations are written in matrix notation as ( J T J ) Δ β = J T Δ y . {\displaystyle \left(\mathbf {J} ^{\mathsf
Least_squares
Statistic measuring inter-rater agreement for categorical items
[ i ≠ j ] {\displaystyle W_{i,j}:=[i\neq j]} using the Iverson bracket notation), this produces the same value as the unweighted kappa calculation given
Cohen's_kappa
Probabilistic model
graphical model with many repeated subunits can be represented with plate notation. A conditional random field is a discriminative model specified over an
Graphical_model
Statistical model for a binary dependent variable
{\displaystyle f(i)={\boldsymbol {\beta }}\cdot \mathbf {X} _{i},} using the notation for a dot product between two vectors. The above example of binary logistic
Logistic_regression
Probability distribution
gamma distributions and aggregate losses, Proceedings of the Casualty Actuarial Society, 1983. Kalbfleisch, J.D. and R.L. Prentice, The Statistical Analysis
Generalized_beta_distribution
Mathematicians of Welsh nationality
pressures. These models are still used today. Aside from minor differences in notation, Bryan's 1911 equations are the same as those used today to evaluate modern
List_of_Welsh_mathematicians
Statistical test that compares goodness of fit
brackets is called the likelihood ratio. Here, the sup {\displaystyle \sup } notation refers to the supremum. As all likelihoods are positive, and as the constrained
Likelihood-ratio_test
probability of some event A, assuming the occurrence of event B. In mathematical notation, conditional probability is written P(A|B), and is read "the probability
Glossary of probability and statistics
Glossary_of_probability_and_statistics
Statistical relationship
corr {\displaystyle \operatorname {corr} } is a widely used alternative notation for the correlation coefficient. The Pearson correlation is defined only
Correlation
Ways of computing statistical significance
Pearson in the Pearson's chi-squared test, where he defined P (original notation) as the probability that the statistic would be at or above a given level
One-_and_two-tailed_tests
Overview of and topical guide to statistics
List of graphical methods Lists of statistics topics Monte Carlo method Notation in probability and statistics Outline of probability Philosophy of statistics
Outline_of_statistics
Kth smallest value in a statistical sample
mathematics, survival analysis, epidemiology, sports, quality control, and actuarial risk. There is an extensive literature devoted to studies on applications
Order_statistic
Type of mathematical model
{\displaystyle {\mathcal {P}}=\{F_{\theta }:\theta \in \Theta \}} . In notation, we write that Θ ⊆ R k {\displaystyle \Theta \subseteq \mathbb {R} ^{k}}
Statistical_model
ACTUARIAL NOTATION
ACTUARIAL NOTATION
ACTUARIAL NOTATION
ACTUARIAL NOTATION
Girl/Female
Indian, Tamil
Little Princes
Male
African
night.
Boy/Male
Indian, Tamil
Lord Vishnu
Biblical
God is my father; God is the father
Boy/Male
Tamil
Girijanandan | கிரிஜாநஂதந
Lord Ganesh (Son of Girija)
Boy/Male
Hindu
Description, Narration of An event
Girl/Female
Hindu
Principled, Moral person, Virtuous
Boy/Male
Tamil
Himaneesh | ஹிமாஂநிஷÂ
Lord Shiva
Boy/Male
Hindu, Indian
Happy; Caring
Female
Bulgarian
, flowers.
ACTUARIAL NOTATION
ACTUARIAL NOTATION
ACTUARIAL NOTATION
ACTUARIAL NOTATION
ACTUARIAL NOTATION
n.
Literal or etymological signification.
n.
The practice of using symbols, or the system of notation developed thereby.
n.
The written and printed notation of a musical composition; the score.
n.
Any particular system of characters, symbols, or abbreviated expressions used in art or science, to express briefly technical facts, quantities, etc. Esp., the system of figures, letters, and signs used in arithmetic and algebra to express number, quantity, or operations.
n.
According to the French notation, which is followed also upon the Continent and in the United States, a unit with fifteen ciphers annexed; according to the English notation, the number produced by involving a million to the fourth power, or the number represented by a unit with twenty-four ciphers annexed. See the Note under Numeration.
a.
Representing sounds; as, phonetic characters; -- opposed to ideographic; as, a phonetic notation.
n.
A method of analysis developed by Newton, and based on the conception of all magnitudes as generated by motion, and involving in their changes the notion of velocity or rate of change. Its results are the same as those of the differential and integral calculus, from which it differs little except in notation and logical method.
a.
Of or pertaining to actuaries; as, the actuarial value of an annuity.
n.
According to the English notation, a million involved to the tenth power, or a unit with sixty ciphers annexed; according to the French and American notation, a thousand involved to the eleventh power, or a unit with thirty-three ciphers annexed. [See the Note under Numeration.]
n.
A table showing the notation, length, or duration of the several notes.
n.
The act or practice of recording anything by marks, figures, or characters.
a.
Alt. of Aquarian
a.
Of or pertaining to decimals; numbered or proceeding by tens; having a tenfold increase or decrease, each unit being ten times the unit next smaller; as, decimal notation; a decimal coinage.
n.
According to the French notation, which is used on the Continent and in America, the cube of a million, or a unit with eighteen ciphers annexed; according to the English notation, a number produced by involving a million to the fifth power, or a unit with thirty ciphers annexed. See the Note under Numeration.
pl.
of Actuary
n.
According to the French and American notation, a thousand octillions, or a unit with thirty ciphers annexed; according to the English notation, a million octillions, or a unit with fifty-four ciphers annexed. See the Note under Numeration.
n.
The act of specifying or determining by a mark or limit; notation of limits.
n.
Ornamental notes or short passages, either introduced by the performer, or indicated by the composer, in which case the notation signs are called grace notes, appeggiaturas, turns, etc.
n.
A method of notation for all spoken sounds, proposed by Mr. Sweet; -- so called because it is based on the common Roman-letter alphabet. It is like the palaeotype of Mr. Ellis in the general plan, but simpler.
n.
According to the French notation, which is used upon the Continent generally and in the United States, the number expressed by a unit with twelve ciphers annexed; a million millions; according to the English notation, the number produced by involving a million to the third power, or the number represented by a unit with eighteen ciphers annexed. See the Note under Numeration.