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Probability function
large deviations theory, a rate function is a function used to quantify the probabilities of rare events. Such functions are used to formulate large
Rate_function
Theory about lossy data compression
transforms, quantization, and bit-rate allocation procedures that capitalize on the general shape of rate–distortion functions. Rate–distortion theory was created
Rate–distortion_theory
Topics referred to by the same term
another Rate (mathematics), a specific kind of ratio, in which two measurements are related to each other (often with respect to time) Rate function, a function
Rate
Branch of probability theory
as before. Function I ( ⋅ ) {\displaystyle I(\cdot )} is called the "rate function" or "Cramér function" or sometimes the "entropy function". The above-mentioned
Large_deviations_theory
Ways of assessing the function of the kidneys
glomerular filtration rate (GFR) is regarded as the best overall measure of the kidney's ability to carry out these numerous functions. An estimate of the
Assessment_of_kidney_function
Fundamental result in the theory of large deviations
deviations, a subdiscipline of probability theory. It determines the rate function of a series of iid random variables. A weak version of this result was
Cramér's theorem (large deviations)
Cramér's_theorem_(large_deviations)
Minimum sampling rate to avoid aliasing
In signal processing, the Nyquist rate is a value equal to twice the highest frequency (bandwidth) of a given function or signal. It is named after Harry
Nyquist_rate
Concept in probability theory and statistics
theory and statistics, the moment generating function of a real-valued random variable is a generating function that provides an alternative specification
Moment_generating_function
Sufficiency theorem for reconstructing signals from samples
continuous function to a discrete sequence and interpolates back to a continuous function, the fidelity of the result depends on the density (or sample rate) of
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
Frequency with which an engineered system or component fails
but different to instantaneous failure rate f ( t ) {\displaystyle f(t)} is the hazard rate (or hazard function), h ( t ) {\displaystyle h(t)} . In the
Failure_rate
S-shaped curve
carrying capacity, the supremum of the values of the function; k {\displaystyle k} is the logistic growth rate, the steepness of the curve; and x 0 {\displaystyle
Logistic_function
of a family of random variables Zε as ε becomes small in terms of a rate function for the variables. Let X be a regular topological space; let (Zε)ε>0
Varadhan's_lemma
Limiting the data rate on network controllers
In computer networks, rate limiting is used to control the rate of requests sent or received by a network interface controller. It can be used to prevent
Rate_limiting
Tuning parameter (hyperparameter) in optimization
gradient of the loss function, the learning rate determines how big a step is taken in that direction. Too high a learning rate will make the learning
Learning_rate
Growth of quantities at rate proportional to the current amount
growth occurs when a quantity grows as an exponential function of time. The quantity grows at a rate directly proportional to its present size. For example
Exponential_growth
Ratio between two related quantities in different units
{\displaystyle f} of a rate is a function f ( a ) {\displaystyle f(a)} where a {\displaystyle a} happens to be the denominator of the rate δ f / δ a {\displaystyle
Rate_(mathematics)
Firearm actions
measurements for the rate of fire: cyclic, sustained, and rapid. Cyclic is the maximum given rate of fire given only mechanical function, not taking into
Rate_of_fire
Artificial neural network node function
activation function is usually an abstraction representing the rate of action potential firing in the cell. In its simplest form, this function is binary—that
Activation_function
Describes approximate behavior of a function
real or complex valued function by a simpler function. Often, big O notation characterizes functions according to their growth rates as the variable becomes
Big_O_notation
Renal function test
A major measure of kidney function is the glomerular filtration rate (GFR). The glomerular filtration rate is the flow rate of filtered fluid through
Glomerular_filtration_rate
Asymmetric sigmoid function
single function. It is based on the assumption that the mortality rate increases exponentially as a person ages. The resulting Gompertz function is for
Gompertz_function
Rate of energy expenditure by an endotherm at rest
body needs to function. Basal metabolic rate is the amount of energy per unit of time that a person needs to keep the body functioning at rest. Some of
Basal_metabolic_rate
Compounding sum paid for the use of money
interest rate n {\displaystyle n} = number of payment periods In spreadsheets, the PMT() function is used. The syntax is: PMT(interest_rate, number_payments
Compound_interest
Continuous probability distribution
failure rates, useful for reliability and survival analysis. The failure rate function can also show an increasing shape. Its probability density function is
Chen_distribution
Mathematical relation consisting of a multi-variable function equal to zero
line Isosurface Marginal rate of substitution Implicit function theorem Logarithmic differentiation Polygonizer Related rates Folium of Descartes Chiang
Implicit_function
Mathematical function, denoted exp(x) or e^x
In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative everywhere equal to its value. It is denoted
Exponential_function
Measurement of a signal at discrete time intervals
period. Then the sampled function is given by the sequence: s(nT), for integer values of n. The sampling frequency or sampling rate, fs, is the average number
Sampling_(signal_processing)
In the case of a positive rate of return, as in the case of interest, the accumulation function is an increasing function. The logarithmic or continuously
Accumulation_function
Instantaneous rate of change of the function
calculus, the directional derivative measures the instantaneous rate at which a function changes along a specified vector through a given point. If the
Directional_derivative
Distribution function associated with the empirical measure of a sample
exist to quantify the rate of convergence of the empirical distribution function to the underlying cumulative distribution function. A simple empirical
Empirical distribution function
Empirical_distribution_function
Kullback–Leibler divergence expressed in terms of the large deviations rate function. If P and Q are probability distributions on the real line, such that
Kullback's_inequality
Theorem in the large deviations theory of stochastic processes
processes (Xε)ε>0 satisfies the large deviations principle with good rate function I : C0 → R ∪ {+∞} given by I ( ω ) = 1 2 ∫ 0 T | ω ˙ t − b ( ω t ) |
Freidlin–Wentzell_theorem
Theorem
is +∞. Then: J : Y → [0, +∞] is a rate function on Y, J is a good rate function on Y if I is a good rate function on X, and (νε)ε>0 satisfies the large
Contraction principle (large deviations theory)
Contraction_principle_(large_deviations_theory)
Rate of change in the linear deformation of a material with respect to time
viscous stress is a linear function of the rate of strain, defined by two coefficients, one relating to the expansion rate (the bulk viscosity coefficient)
Strain_rate
Branch of statistics
{d}{dt}}F(t).} The function f is sometimes called the event density; it is the rate of death or failure events per unit time. The survival function can be expressed
Survival_analysis
Instantaneous rate of change (mathematics)
quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input
Derivative
Mathematical theorem
language of large deviations theory, Sanov's theorem identifies the rate function for large deviations of the empirical measure of a sequence of i.i.d
Sanov's_theorem
Geometric progression ratio that provides a constant rate of return over the time period
value of the investment). The RRI function (Return Rate on Investment) returns the equivalent constant interest rate per period, effectively matching the
Compound_annual_growth_rate
Derivative of a function with multiple variables
by fx, f'x, ∂xf, Dxf, D𝐞1f, D1f, ∂∂xf, or ∂f∂x. It is the rate of change of the function in the x-direction. Sometimes, for z=f(x,y,…), the partial derivative
Partial_derivative
Continuous probability distribution
'_{4}-4\mu '_{3}\mu +6\mu '_{2}\mu ^{2}-3\mu ^{4}}{\sigma ^{4}}}} The hazard rate function of the UGo distribution is given by: h ( x ∣ α , β ) = α β x − ( β +
Unit_Gompertz_distribution
Speed of the heartbeat, measured in beats per minute
the precise regulation of heart function, via cardiac reflexes. Increased physical activity results in increased rates of firing by various proprioreceptors
Heart_rate
Topics referred to by the same term
differential privacy, in information privacy Large deviation principle, the rate function in mathematics Damansara–Puchong Expressway or Lebuhraya Damansara–Puchong
LDP
Memory card format
Sampling as an option Variable Frame rate function Five P2 slots AJ-HPX2700 One of the new P2 Varicam range Variable Frame Rate of 1 frame/s to 60 frame/s 10
P2_(storage_media)
Discrete probability distribution
fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event. It can also be used for
Poisson_distribution
Nonparametric estimate of cumulative hazard
Nelson–Aalen estimator is a non-parametric estimator of the cumulative hazard rate function in case of censored data or incomplete data. It is used in survival
Nelson–Aalen_estimator
absolutely continuous functions whose derivative is in L 2 {\displaystyle L^{2}} (the so-called Cameron-Martin space). Define the rate function I ( ω ) = 1 2
Schilder's_theorem
Mortgage repaid through continuous or near-continuous amortisation
interest rate given the remaining parameters has not been possible using analytic methods. Implementations such as the Excel "rate" function employ a
Continuous-repayment_mortgage
Method of calculating an investment's rate of return
the NPV is a function of the rate of return. The internal rate of return is a rate for which this function is zero, i.e. the internal rate of return is
Internal_rate_of_return
Frequency swept signal
exponential chirp has an exponentially increasing frequency rate. The corresponding time-domain function for the phase of an exponential chirp is the integral
Chirp
Mathematical process of finding the derivative of a trigonometric function
differentiation of trigonometric functions is the mathematical process of finding the derivative of a trigonometric function, or its rate of change with respect
Differentiation of trigonometric functions
Differentiation_of_trigonometric_functions
Variation in the time intervals between heartbeats
Forte G, Favieri F, Casagrande M (2019-07-09). "Heart Rate Variability and Cognitive Function: A Systematic Review". Frontiers in Neuroscience. 13 710
Heart_rate_variability
Study of rates of change
that studies the rates at which quantities change. The primary objects of study in differential calculus are the derivative of a function, related notions
Differential_calculus
Probability distribution
right of the edge. Let Φ ( w ) {\displaystyle \Phi (w)} denote the rate function governing the large deviations of the largest eigenvalue λ max {\displaystyle
Tracy–Widom_distribution
Continuous probability distribution
'_{4}-4\mu '_{3}\mu +6\mu '_{2}\mu ^{2}-3\mu ^{4}}{\sigma ^{4}}}} The hazard rate function of the UW distribution is given by: h ( x ; α , β ) = f ( x ; α , β
Unit_Weibull_distribution
Mathematical result in large deviations theory
principle with good rate function Ij : Yj → R ∪ {+∞}. Then the family (με)ε>0 satisfies the large deviation principle on X with good rate function I : X → R ∪ {+∞}
Dawson–Gärtner_theorem
Relation between chemical reaction rate and concentrations of the reactants
In chemistry, the rate equation (also known as the rate law or empirical differential rate equation) is an empirical differential mathematical expression
Rate_equation
Multivariate derivative (mathematics)
differentiable function f of several variables is the vector field (or vector-valued function) whose value at a point p gives the direction and the rate of fastest
Gradient
Aircraft vertical velocity during flight
In aeronautics, the rate of climb (RoC) is an aircraft's vertical speed, that is the positive or negative rate of altitude change with respect to time
Rate_of_climb
Maximum frequency of non-aliased component upon sampling
converts a continuous function or signal into a discrete sequence. It is named after Harry Nyquist. For a given sampling rate (samples per second), the
Nyquist_frequency
Probability of survival beyond any specified time
certain time. The survival function is also known as the survivor function or reliability function. The term reliability function is common in engineering
Survival_function
Rate of change of angle
called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument
Angular_frequency
Mathematical functions
As the figures indicate, hyperbolastic functions can fit a sigmoidal curve indicating that the slowest rate occurs at the early and late stages. In addition
Hyperbolastic_functions
Mathematical concept
which is the rate function in Sanov's theorem. Convex conjugate – Generalization of the Legendre transformation Integral of inverse functions – Mathematical
Young's inequality for products
Young's_inequality_for_products
Family of lifetime distributions with decreasing failure rate
p}}\right)^{2}.} The survival function (also known as the reliability function) and hazard function (also known as the failure rate function) of the EL distribution
Exponential-logarithmic distribution
Exponential-logarithmic_distribution
Exponentially decreasing bounds on tail distributions of random variables
distribution function of X {\displaystyle X} (folded at the mean, not the median). The logarithm of the two-sided Chernoff bound is known as the rate function (or
Chernoff_bound
real exchange rate. E = E(A*,σ) Where A* and σ are variable functions related to the total foreign absorption and the real exchange rate. For an explanation
Export_function
Ecological concept; intake rate of a consumer as a function of food density
A functional response in ecology is the intake rate of a consumer as a function of food density (the amount of food available in a given ecotope). It is
Functional_response
Mathematical operation
of a function f is the derivative of the derivative of f. Informally, the second derivative can be phrased as "the rate of change of the rate of change";
Second_derivative
Theorem in mathematics
differentiable functions, roughly stating that the average rate of change of such a function over an interval is equal to the instantaneous rate of change
Mean_value_theorem
Mathematical model of the interactions between neuronal populations
recovery of excitation u; ϵ>0 and β>0 determine the rate of change of recovery. The connection function ω(x,y) is positive, continuous, symmetric, and has
Wilson–Cowan_model
Function increasing at a decreasing rate of increase
asymptotic growth, occurs when the growth rate of a mathematical function is constantly increasing at a decreasing rate. Asymptotically, bounded growth approaches
Bounded_growth
Economic formula of productivity
econometrics, the Cobb–Douglas production function is a particular functional form of the production function, widely used to represent the relationship
Cobb–Douglas production function
Cobb–Douglas_production_function
Concept in consumer economics
consumer utility function is defined by U ( x , y ) {\displaystyle U(x,y)} , where U is consumer utility, x and y are goods. Then the marginal rate of substitution
Marginal_rate_of_substitution
Change of voltage or current per unit of time
amplifier as a function of time t. The slew rate can be measured using a function generator (usually square wave) and an oscilloscope. The slew rate is the same
Slew_rate
Software development toolkit
service encoding: literal int ns__get_rate(char* hotel, int guests, float *rate); The last parameter of the function is always the service return value,
GSOAP
Mathematical transformation
deviations theory, the rate function is defined as the Legendre transformation of the logarithm of the moment generating function of a random variable.
Legendre_transformation
Sum paid for the use of money
this demand is solely a function of the interest rate; and since the supply is given and equilibrium is assumed, the interest rate is determined by the money
Interest_(economics)
Equivalence relation on mathematical measures
0 {\displaystyle (\mu _{\varepsilon })_{\varepsilon >0}} with good rate function I {\displaystyle I} , and ( μ ε ) ε > 0 {\displaystyle (\mu _{\varepsilon
Exponentially equivalent measures
Exponentially_equivalent_measures
Cryptographic primitive
general), which is a "high-rate multi-block-length hash function based on block ciphers" and typically achieves (asymptotic) rates between 1 and 2 independent
One-way_compression_function
Probability distribution
{Gamma} (\alpha ,\beta )} The corresponding probability density function in the shape-rate parameterization is f ( x ; α , β ) = x α − 1 e − β x β α Γ (
Gamma_distribution
Rate of change of the second derivative
derivative is the rate at which the second derivative, or the rate of change of the rate of change, is changing. The third derivative of a function y = f ( x
Third_derivative
Economic model relating consumption and disposable income
In economics, the consumption function describes a relationship between consumption and disposable income. The concept is believed to have been introduced
Consumption_function
Vertical rate of change of temperature in atmosphere
The lapse rate is the rate at which an atmospheric variable, normally temperature in Earth's atmosphere, falls with altitude. Lapse rate arises from the
Lapse_rate
Probability distribution
distribution that has a constant failure rate. The quantile function (inverse cumulative distribution function) for Exp(λ) is F − 1 ( p ; λ ) = − ln
Exponential_distribution
function is the Taylor rule, developed by economist John Taylor in 1993. The rule provides a systematic formula for setting the nominal interest rate
Monetary policy reaction function
Monetary_policy_reaction_function
Mathematical formula
satisfies the large deviation principle with rate function I : X → [0, +∞]. Let F : X → R be a continuous function that is bounded from above. For each Borel
Tilted large deviation principle
Tilted_large_deviation_principle
Term in marketing on online shopping
seller, and poor website functioning or complicated processes. There are various reasons behind a high cart abandonment rate. To understand them, one
Abandonment_rate
Used to define marginal product and to distinguish allocative efficiency
production function gives the technological relation between quantities of physical inputs and quantities of output of goods. The production function is one
Production_function
Quickly growing function
Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not
Ackermann_function
Hyperbolic analogues of trigonometric functions
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just
Hyperbolic_functions
faced with, such as the wage rate, the unit cost of capital, the market-determined selling price of its output, etc. The function specifying the quantity of
Labor_demand
Resampling method
(filtering) and sample-rate reduction. When the process is performed on a sequence of samples of a signal or a continuous function, it produces an approximation
Downsampling (signal processing)
Downsampling_(signal_processing)
Generalized function whose value is zero everywhere except at zero
Dirac delta function (or δ {\displaystyle {\boldsymbol {\delta }}} distribution), also known as the unit impulse, is a generalized function on the real
Dirac_delta_function
Mathematical function with no sudden changes
In mathematics, a continuous function is a function such that a small variation of its argument induces at most a small variation of its value. This implies
Continuous_function
Mathematical statistics distance measure
more on the geometric interpretation. Relative entropy relates to "rate function" in the theory of large deviations. Arthur Hobson proved that relative
Kullback–Leibler_divergence
Problems that make use of the relations to rates of change
calculus, related rates problems involve finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are
Related_rates
Interest rates to maintain banks' balance
The federal funds rate is the interest rate at which depository institutions (banks and credit unions) lend reserve balances to other depository institutions
Federal_funds_rate
Distance from origin of tangent hyperplanes
In mathematics, the support function hA of a non-empty closed convex set A in R n {\displaystyle \mathbb {R} ^{n}} describes the (signed) distances of
Support_function
Medical condition
metabolic rate refers to a high or low basal metabolic rate (BMR). It has numerous causes, both physiological (part of the body's normal function) and pathological
Abnormal_basal_metabolic_rate
Optimality condition in optimal control theory
{\displaystyle C[\cdot ]} is the scalar cost rate function and D [ ⋅ ] {\displaystyle D[\cdot ]} is a function that gives the bequest value at the final
Hamilton–Jacobi–Bellman equation
Hamilton–Jacobi–Bellman_equation
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RATE FUNCTION
RATE FUNCTION
RATE FUNCTION
RATE FUNCTION
RATE FUNCTION
RATE FUNCTION
RATE FUNCTION
RATE FUNCTION
RATE FUNCTION
travel, tourism, insurance