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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
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)
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
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
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
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
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
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
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
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
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
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
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
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
Firearm actions
measurements for the rate of fire: cyclic, sustained, and rapid. Cyclic is the maximum rate of fire given only mechanical function, not taking into account
Rate_of_fire
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)
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
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
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
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
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
be a continuous function (or "signal") to be sampled, and let sampling be performed by measuring the value of the continuous function every T {\displaystyle
Sampling_(signal_processing)
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
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
Field of medical research
Gain-of-function research (GoF research or GoFR) is medical research that genetically alters an organism in a way that may enhance the biological functions of
Gain-of-function_research
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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)
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
Mathematical model of the interactions between neuronal populations
and β > 0 {\displaystyle \beta >0} determine the rate of change of recovery. The connection function ω ( x , y ) {\displaystyle \omega (x,y)} is positive
Wilson–Cowan_model
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
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
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
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
Sigmoid shape special function
mathematics, the error function (also called the Gauss error function), often denoted by e r f {\displaystyle \mathbf {erf} } , is the function erf ( z ) = 2
Error_function
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)
Responses/Unit of time = B/t Rate of reinforcement Herrnstein, R.J. (1961). Relative and absolute strength of responses as a function of frequency of reinforcement
Rate_of_response
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
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
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
Representation of the relationship between taxation and government revenue
tax rates of 0% and 100%, there must be a tax rate between 0% and 100% that maximizes government tax revenue. The shape of the curve is a function of taxable
Laffer_curve
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
Smooth approximation of one-hot arg max
The softmax function, also known as softargmax or normalized exponential function, converts a tuple of K real numbers into a probability distribution
Softmax_function
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
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
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
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
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
Historic category for Royal Navy ships
rating system of the Royal Navy used to categorise sailing warships, first-rate was the designation for the largest ships of the line. Originating in the
First-rate
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
Success rate of becoming pregnant
Pregnancy rate is the success rate for getting pregnant. It is the percentage of all attempts that leads to pregnancy, with attempts generally referring
Pregnancy_rate
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
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
Stochastic process generalizing Brownian motion
The information rate of the Wiener process with respect to the squared error distance, i.e. its quadratic rate-distortion function, is given by R ( D
Wiener_process
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
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
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
reinforcements/unit of time = SR+/t Rate of response Herrnstein, R.J. (1961). Relative and absolute strength of responses as a function of frequency of reinforcement
Rate_of_reinforcement
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
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
Function used in signal processing
processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside
Window_function
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
Diagnostic plot of binary classifier ability
these quantities). The ROC curve is thus the sensitivity as a function of false positive rate. Given that the probability distributions for both true positive
Receiver operating characteristic
Receiver_operating_characteristic
Curve for failure rates over time
products in use and associated failure rate data. In reliability engineering, the cumulative distribution function corresponding to a bathtub curve may
Bathtub_curve
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
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
Mathematical description of quantum state
In quantum mechanics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common
Wave_function
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
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
Characteristic of an optical system
The optical transfer function (OTF) of an optical system such as a camera, microscope, human eye, or projector is a scale-dependent description of their
Optical_transfer_function
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
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
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
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
Notion from the theory of entire functions
indicator function of an entire function indicates the rate of growth of the function in different directions. Let us consider an entire function f : C →
Indicator function (complex analysis)
Indicator_function_(complex_analysis)
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
Theorem bounding the growth rate of analytic functions
Nachbin) is a result used to establish bounds on the growth rates for analytic functions. In particular, Nachbin's theorem may be used to give the domain
Nachbin's_theorem
Signal (re-)construction algorithm
known as the sample rate, and f s / 2 {\displaystyle f_{s}/2} is the corresponding Nyquist frequency. When the sampled function has a bandlimit less
Whittaker–Shannon interpolation formula
Whittaker–Shannon_interpolation_formula
Summatory function of the Möbius function
In number theory, the Mertens function is defined for all positive integers n as M ( n ) = ∑ k = 1 n μ ( k ) , {\displaystyle M(n)=\sum _{k=1}^{n}\mu (k)
Mertens_function
RATE FUNCTION
RATE FUNCTION
Surname or Lastname
English
English : from the Old English personal name TÄta, possibly a short form of various compound names with the obscure first element tÄt, or else a nursery formation. This surname is common and widespread in Britain; the chief area of concentration is northeastern England, followed by northern Ireland.
Male
English
Variant spelling of English Ray, RAE means "wise protector."Â
Surname or Lastname
English (rare; mainly northeastern)
English (rare; mainly northeastern) : variant of Longwell.
Surname or Lastname
English
English : unexplained.Possibly from one of the many variants of Dutch kat ‘cat’. See also Kath, Catt.
Surname or Lastname
English (rare in England)
English (rare in England) : variant of Hug 1.
Surname or Lastname
English
English : of uncertain origin; Reaney suggests a nickname from Old French ras ‘clean shaven’, but he also cites documentary evidence of a personal name which probably also gave rise to the surname.Perhaps a variant of Dutch or German Rase.Slovenian (southwestern Slovenia) : nickname from raca ‘duck’, formed with the suffix -e, used mainly of young people, possibly denoting someone who walked like a duck.
Female
Hindi/Indian
(रति) Hindi myth name of the wife of Kama, RATI means "pleasure."
Male
Hebrew
Short form of Hebrew Nathan, NATE means "a giver" or "whom God gave."
Male
English
Medieval form of English Ralph, RAFE means "wise wolf."
Male
English
English surname transferred to unisex forename use, TATE means "cheerful."
Surname or Lastname
English
English : variant spelling of Raw.North German : variant of Rave.
Surname or Lastname
English and Scottish
English and Scottish : from the Middle English personal name Bat(t)e, a pet form of Bartholomew.
Female
English
English name, possibly derived from the vocabulary word ray, RAE means "sunbeam."
Surname or Lastname
English
English : variant spelling of Ray 1–4.
Female
English
Pet form of English Katherine, KATE means "pure."
Surname or Lastname
English and Scottish
English and Scottish : from the personal name Pat(t), Pate, a short form of Patrick.English and Scottish : nickname for a man with a bald head, from Middle English pate ‘head’, ‘skull’.French (Paté) : from Old French pat(t)é ‘with paws’, ‘pawed’ (from pat(t)e ‘paw’), a nickname, applied presumably to a man with large and clumsy hands and feet.German : nickname for a trustworthy man, from Middle High German pate, Middle Low German pade ‘godfather’, ‘male relative’ (see Paeth), or alternatively from a personal name Bado, probably meaning ‘battle’, ‘fight’.
Female
English
Variant spelling of English Kate, CATE means "pure."
Surname or Lastname
English
English : topographic name for someone who lived by a pass or narrow valley, from Old English hraca ‘throat’, or a habitational name from any of the minor places deriving their name from this word, such as Rake in Devon or The Rake in Sussex.English and Dutch : from Middle English, Middle Dutch rake ‘rake’, applied as a metonymic occupational name for a maker of such implements or as a nickname for a tall thin man. (The expression ‘lean as a rake’ is found in Chaucer.)
Female
Portuguese
Portuguese form of Hebrew Ruth, RUTE means "appearance" or "friendship."
Surname or Lastname
English (now rare)
English (now rare) : occupational name for a furrier, Middle English pel(e)ter.
RATE FUNCTION
RATE FUNCTION
Boy/Male
Hindu
Lord Ganesh, Gift
Boy/Male
Indian, Tamil
King of the World
Girl/Female
Hindu, Indian
Goddess Laxmi
Boy/Male
Australian, Portuguese
Strong; Healthy
Girl/Female
Indian
Tasty
Boy/Male
Hindu, Indian, Sanskrit
Idea
Surname or Lastname
English
English : variant of Good.Dutch : metonymic occupational name for a goldsmith, from goud ‘gold’.
Male
Dutch
, supplanter.
Boy/Male
Hindu, Indian, Marathi, Oriya
Joyous Person
Boy/Male
Hindu, Indian
Welcome
RATE FUNCTION
RATE FUNCTION
RATE FUNCTION
RATE FUNCTION
RATE FUNCTION
a.
Alt. of Rathe
n.
One who rates or scolds.
n.
One who rates or estimates.
v. t.
To settle the relative scale, rank, position, amount, value, or quality of; as, to rate a ship; to rate a seaman; to rate a pension.
a.
Of the second size, rank, quality, or value; as, a second-rate ship; second-rate cloth; a second-rate champion.
v. t.
To pack in a crate or case for transportation; as, to crate a sewing machine; to crate peaches.
n.
A salt of uric acid; as, sodium urate; ammonium urate.
n.
The fruit of the date palm; also, the date palm itself.
v. t.
To supply with a gate.
n.
The order or class to which a war vessel belongs, determined according to its size, armament, etc.; as, first rate, second rate, etc.
n.
A gate. See 1st Gate.
v. t.
To assess for the payment of a rate or tax.
n.
The gain or loss of a timepiece in a unit of time; as, daily rate; hourly rate; etc.
adv.
Alt. of Rathe
n.
A tax or sum assessed by authority on property for public use, according to its income or value; esp., in England, a local tax; as, parish rates; town rates.
imp. & p. p.
of Rate
v. t.
To raze.
n.
That which is established as a measure or criterion; degree; standard; rank; proportion; ratio; as, a slow rate of movement; rate of interest is the ratio of the interest to the principal, per annum.
v. t.
To run a race with.