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searching for Closed-form expression 68 found (153 total)

Holtsmark distribution (1,483 words) [view diff] no match in snippet view article find links to article

is one of the few examples of a stable distribution for which a closed form expression of the probability density function is known. However, its probability

Fibonacci word (1,938 words) [view diff] no match in snippet view article find links to article

trivially, by swapping 0s for 1s and shifting the positions by one. A closed form expression for the so-called rabbit sequence: The nth digit of the word is

Elementary cellular automaton (2,819 words) [view diff] no match in snippet view article find links to article

2 x ) {\displaystyle {\frac {1+2x}{(1+x)(1-2x)}}} . It has the closed form expression a ( t ) = 4 ⋅ 2 t − ( − 1 ) t 3 {\displaystyle a(t)={\frac {4\cdot

Skew normal distribution (1,365 words) [view diff] exact match in snippet view article find links to article

closed-form expression for the estimates is available unless α = 0 {\displaystyle \alpha =0} . In contrast, the method of moments has a closed-form expression

Delannoy number (1,163 words) [view diff] exact match in snippet view article find links to article

n-k}}={\binom {m+n-k}{m}}{\binom {m}{k}}} . Hence, one gets the closed-form expression D ( m , n ) = ∑ k = 0 min ( m , n ) ( m + n − k m ) ( m k ) . {\displaystyle

Thurstonian model (1,454 words) [view diff] no match in snippet view article find links to article

applicability scoring. In Chapter 7 of this book[citation needed], a closed form expression, derived in 1988, is given for a Euclidean-Gaussian similarity model

Generalized chi-squared distribution (2,076 words) [view diff] exact match in snippet view article find links to article

\\\mathbb {R} {\text{ otherwise.}}\end{cases}}} PDF no closed-form expression CDF no closed-form expression Mean ∑ j w j ( k j + λ j ) + m {\displaystyle \sum

Glaisher–Kinkelin constant (2,969 words) [view diff] no match in snippet view article find links to article

role both in mathematics and in physics. It appears when giving a closed form expression for Porter's constant, when estimating the efficiency of the Euclidean

Fejér kernel (1,183 words) [view diff] no match in snippet view article find links to article

kernel F n ( x ) {\displaystyle F_{n}(x)} may also be written in a closed form expression as follows F n ( x ) = 1 n ( sin ⁡ ( n x 2 ) sin ⁡ ( x 2 ) ) 2 =

Superellipsoid (2,307 words) [view diff] exact match in snippet view article find links to article

is its conciseness and expressiveness in shape. Furthermore, a closed-form expression of the Minkowski sum between two superellipsoids is available. This

Cantor distribution (811 words) [view diff] exact match in snippet view article find links to article

1 8 . {\displaystyle \operatorname {var} (X)={\frac {1}{8}}.} A closed-form expression for any even central moment can be found by first obtaining the

Polynomial root-finding (3,355 words) [view diff] exact match in snippet view article find links to article

It involves determining either a numerical approximation or a closed-form expression of the roots of a univariate polynomial, i.e., determining approximate

Total harmonic distortion (2,987 words) [view diff] exact match in snippet view article find links to article

expressions may be quite laborious to obtain. For example, the closed-form expression for the THDF of the sawtooth wave filtered by the first-order Butterworth

Nonlinear regression (1,394 words) [view diff] exact match in snippet view article find links to article

§§ Transformation, below, for more details. In general, there is no closed-form expression for the best-fitting parameters, as there is in linear regression

Directivity (2,877 words) [view diff] no match in snippet view article find links to article

The actual result is in fact, 33.1 dBi. For antenna arrays, the closed form expression for Directivity for progressively phased array of isotropic sources

Logistic regression (20,645 words) [view diff] exact match in snippet view article find links to article

estimated by maximum-likelihood estimation (MLE). This does not have a closed-form expression, unlike linear least squares; see § Model fitting. Logistic regression

Beta wavelet (1,861 words) [view diff] exact match in snippet view article find links to article

(b-t)^{\beta -1},} a ≤ t ≤ b {\displaystyle a\leq t\leq b} . A closed-form expression for first-order beta wavelets can easily be derived. Within their

Spline wavelet (7,879 words) [view diff] no match in snippet view article find links to article

− 1 ) {\displaystyle \psi _{C,1}(x)=N_{1}(2x)-N_{1}(2x-1)} The closed form expression for compactly supported B-spline wavelet of order 1 is ψ C , 1 (

Poisson binomial distribution (2,600 words) [view diff] case mismatch in snippet view article find links to article

2018.01.007. ISSN 0167-9473. Fernandez, M.; S. Williams (2010). "Closed-Form Expression for the Poisson-Binomial Probability Density Function". IEEE Transactions

Stable distribution (6,796 words) [view diff] no match in snippet view article find links to article

parameter of the mixing distribution always equal to one). A general closed form expression for stable PDFs with rational values of α {\displaystyle \alpha

Vibrational partition function (773 words) [view diff] no match in snippet view article find links to article

frequency of the jth mode. Using this approximation we can derive a closed form expression for the vibrational partition function. Q vib ( T ) = ∏ j ∑ n e

Boltzmann distribution (2,495 words) [view diff] no match in snippet view article find links to article

not follow Maxwell–Boltzmann statistics, and there is no simple closed form expression for quantum gases in the canonical ensemble. In the grand canonical

Lattice model (physics) (1,478 words) [view diff] exact match in snippet view article

difficult due to non-linear interactions between sites. Models with a closed-form expression for the partition function are known as exactly solvable. Examples

Tsallis entropy (2,563 words) [view diff] exact match in snippet view article find links to article

(PDF). Kybernetika. 3 (1): 30–35. Nielsen, F.; Nock, R. (2012). "A closed-form expression for the Sharma–Mittal entropy of exponential families". Journal

Inverse kinematics (2,400 words) [view diff] exact match in snippet view article find links to article

problem). An analytic solution to an inverse kinematics problem is a closed-form expression that takes the end-effector pose as input and gives joint positions

Depth of field (4,439 words) [view diff] exact match in snippet view article find links to article

Field Method, in Depth of Field in Depth. Peterson does not give a closed-form expression for the minimum f-number, though such an expression obtains from

Square root of 5 (2,851 words) [view diff] no match in snippet view article find links to article

rectangle.) 5 {\displaystyle {\sqrt {5}}} then naturally figures in the closed form expression for the Fibonacci numbers, a formula which is usually written in

SABR volatility model (2,483 words) [view diff] no match in snippet view article find links to article

{\displaystyle \beta =0} and β = 1 {\displaystyle \beta =1} , no closed form expression for this probability distribution is known. The general case can

Acid–base titration (2,675 words) [view diff] exact match in snippet view article find links to article

the titration curve in terms of concentration: Writing a single closed-form expression for the titration curve for a variety of titrations without using

Riemann–Siegel theta function (1,521 words) [view diff] exact match in snippet view article find links to article

{\text{and}}\quad {\overline {\Gamma (z)}}=\Gamma ({\bar {z}})} to obtain the closed-form expression θ ( t ) = log ⁡ Γ ( 2 i t + 1 4 ) − log ⁡ Γ ( − 2 i t + 1 4 ) 2

Color appearance model (2,370 words) [view diff] exact match in snippet view article find links to article

CIEXYZ defined in 1974. The conversion to CIEXYZ, however, has no closed-form expression, making it hard to use in practice. SRLAB2 A 2009 modification of

Rényi entropy (3,526 words) [view diff] exact match in snippet view article find links to article

2159046. S2CID 14238708. Nielsen, Frank; Nock, Richard (2012). "A closed-form expression for the Sharma–Mittal entropy of exponential families". Journal

Channel capacity (4,845 words) [view diff] exact match in snippet view article find links to article

between the input and the output. The feedback capacity is known as a closed-form expression only for several examples such as the trapdoor channel, Ising channel

Plastic ratio (4,381 words) [view diff] no match in snippet view article find links to article

k_{r}=\lambda ^{*}(r)} for ⁠ r = 23 {\displaystyle r=23} ⁠ has closed form expression λ ∗ ( 23 ) = sin ⁡ ( arcsin ⁡ ( ( 2 4 ρ ) − 12 ) / 2 ) {\displaystyle

Maxwell–Jüttner distribution (2,911 words) [view diff] no match in snippet view article find links to article

in terms of its Lorentz factor. The integral simplifies to the closed- form expression: ⟨ v ⟩ MJ = 2 c θ ( θ + 1 ) e − 1 / θ K 2 ⁡ ( 1 θ ) {\displaystyle

Scale space implementation (3,290 words) [view diff] exact match in snippet view article find links to article

_{n=-M}^{M}f(x-n)\,T(n,t)} or can be implemented in the Fourier domain using a closed-form expression for its discrete-time Fourier transform: T ^ ( θ , t ) = ∑ n = −

Dottie number (1,076 words) [view diff] no match in snippet view article find links to article

and Bertrand's circle problems. The Dottie number appears in the closed form expression of some integrals: ∫ 0 ∞ ln ⁡ ( 4 ( x + sinh ⁡ x ) 2 + π 2 4 ( x

Gieseking manifold (1,152 words) [view diff] no match in snippet view article find links to article

equal to L ( 2 , χ − 4 ) {\displaystyle L(2,\chi _{-4})} Another closed form expression may be given in terms of the trigamma function: V = 3 3 ( ψ 1 (

Cauchy distribution (6,933 words) [view diff] exact match in snippet view article find links to article

and can be expressed as a function of the chi-squared divergence. Closed-form expression for the total variation, Jensen–Shannon divergence, Hellinger distance

Propagation graph (2,136 words) [view diff] no match in snippet view article find links to article

frequency as a geometric series of matrices. This observation yields a closed form expression for the transfer function as H ( f ) = D ( f ) + R ( f ) [ I − B

Multivariate normal distribution (9,594 words) [view diff] no match in snippet view article find links to article

estimating the parameters of a multivariate normal distribution has a closed form expression. This can be used, for example, to compute the Cramér–Rao bound

Supergolden ratio (2,981 words) [view diff] no match in snippet view article find links to article

k_{r}=\lambda ^{*}(r)} for ⁠ r = 31 {\displaystyle r=31} ⁠ has closed form expression λ ∗ ( 31 ) = sin ⁡ ( arcsin ⁡ ( ( 2 4 ψ ) − 12 ) / 2 ) {\displaystyle

Kane S. Yee (925 words) [view diff] case mismatch in snippet view article find links to article

1038/nphoton.2014.305. S2CID 56374370. Yee, Kane S. (February 1974). "A Closed-Form Expression for the Energy Dissipation in a Low-Loss Transmission Line". IEEE

Gauss–Kuzmin–Wirsing operator (3,078 words) [view diff] exact match in snippet view article find links to article

diagonalizing the upper-left n by n portion. There is no known closed-form expression that diagonalizes this operator; that is, there are no closed-form

Log-normal distribution (12,551 words) [view diff] exact match in snippet view article find links to article

_{j=1}^{n}X_{j}} . The distribution of Y {\displaystyle Y} has no closed-form expression, but can be reasonably approximated by another log-normal distribution

Low-rank approximation (3,884 words) [view diff] no match in snippet view article find links to article

{\displaystyle L} variable (a linear least squares problem) leads to the closed form expression of the approximation error as a function of P {\displaystyle P}

Jordan normal form (7,474 words) [view diff] exact match in snippet view article find links to article

function. For example, in principle the Jordan form could give a closed-form expression for the exponential exp(A). The number of Jordan blocks corresponding

Indefinite sum (2,767 words) [view diff] no match in snippet view article find links to article

n f ( k ) . {\displaystyle \sum _{k=1}^{n}f(k).} In this case a closed form expression F(k) for the sum is a solution of F ( x + 1 ) − F ( x ) = f ( x

Gijswijt's sequence (1,411 words) [view diff] exact match in snippet view article find links to article

. n − 1 {\displaystyle 2^{2^{3^{4^{5^{.^{.^{.{n-1}}}}}}}}} . A closed-form expression for the earliest index at which a given positive integer n {\displaystyle

Algebra of random variables (3,557 words) [view diff] no match in snippet view article find links to article

The first order term always vanishes but was kept to obtain a closed form expression. Then, E ⁡ [ f ( X ) ] ≈ ∑ n = 0 n max 1 n ! ( d n f d X n ) X =

Discrete Fourier transform (12,333 words) [view diff] no match in snippet view article find links to article

}\exp \left(-{\frac {\pi \cdot (m+N\cdot k)^{2}}{N}}\right).} The closed form expression for the series can be expressed by Jacobi theta functions as F (

Frozen orbit (3,272 words) [view diff] no match in snippet view article find links to article

on the closed form expression for this " J 3 {\displaystyle J_{3}\,} perturbation". With the "modern theory" this explicit closed form expression is not

Image segmentation (9,662 words) [view diff] no match in snippet view article find links to article

modeled by a multivariate normal distribution whose entropy has a closed form expression. An interesting property of this model is that the estimated entropy

Precoding (3,895 words) [view diff] exact match in snippet view article find links to article

linear precoding). The optimal linear precoding does not have any closed-form expression, but it takes the form of a weighted MMSE precoding for single-antenna

Formal power series (10,130 words) [view diff] no match in snippet view article find links to article

number theory and combinatorics. For an example involving finding a closed form expression for the Fibonacci numbers, see the article on Examples of generating

David Penny (4,389 words) [view diff] exact match in snippet view article find links to article

Review in 2009, that "Penny's formula [remained] the most remarkable closed-form expression for any class of phylogenetic trees in evolutionary biology". Evolution

Rankine–Hugoniot conditions (4,062 words) [view diff] no match in snippet view article find links to article

sound in the fluid at upstream conditions. For shocks in solids, a closed form expression such as equation (15) cannot be derived from first principles. Instead

Lambert W function (12,429 words) [view diff] case mismatch in snippet view article find links to article

Napocensis. 62, IV: 607–616. F. Nielsen, "Jeffreys Centroids: A Closed-Form Expression for Positive Histograms and a Guaranteed Tight Approximation for

Universal enveloping algebra (8,954 words) [view diff] no match in snippet view article find links to article

Baker–Campbell–Hausdorff formula for the product of two elements of a Lie group. A closed form expression is given by p ( t ) ⋆ q ( t ) = exp ⁡ ( t i m i ( ∂ ∂ u , ∂ ∂ v

Bayesian quadrature (2,588 words) [view diff] exact match in snippet view article find links to article

embedding ν [ k ( ⋅ , x ) ] {\displaystyle \nu [k(\cdot ,x)]} has no closed-form expression for a general kernel k {\displaystyle k} and measure ν {\displaystyle

Marcum Q-function (7,425 words) [view diff] no match in snippet view article find links to article

half-integer values ν = n + 1 / 2 {\displaystyle \nu =n+1/2} , we have a closed form expression for the generalized Marcum Q-function as Q n + 1 / 2 ( a , b ) =

Quantile-parameterized distribution (2,913 words) [view diff] exact match in snippet view article find links to article

representation of known distributions whose CDFs otherwise have no closed-form expression. Keelin et al. (2019) apply this to the sum of independent identically

Minimum mean square error (9,310 words) [view diff] no match in snippet view article find links to article

expectation. While these numerical methods have been fruitful, a closed form expression for the MMSE estimator is nevertheless possible if we are willing

Soliton (optics) (6,762 words) [view diff] no match in snippet view article

solitons ( N > 1 {\displaystyle N>1} ) we can use the following closed form expression: a ( τ , ζ = 0 ) = N tanh ⁡ ( τ ) . {\displaystyle a(\tau ,\zeta

Hattendorff's theorem (1,655 words) [view diff] no match in snippet view article find links to article

{\displaystyle V_{h}=\mathbb {E} [L_{h}|K(x)\geq h]} which admits to the closed form expression V h = ∑ k = 0 ∞ ( v k + 1 b k + h + 1 − ∑ j = 0 k v j π j + h )

Biological neuron model (14,910 words) [view diff] exact match in snippet view article find links to article

method, but in the case of a pulse of stimulus, it yields a simple closed-form expression. y(t) is the input of the model and is interpreted as the neurotransmitter

Metalog distribution (7,310 words) [view diff] exact match in snippet view article find links to article

closed-form representation of known distributions whose CDFs have no closed-form expression. Keelin et al. (2019) apply this to the sum of independent identically

Supersilver ratio (3,010 words) [view diff] no match in snippet view article find links to article

59 {\displaystyle k_{r}=\lambda ^{*}(r){\text{ for }}r=59} has closed form expression λ ∗ ( 59 ) = sin ⁡ ( arcsin ⁡ ( G 59 − 12 ) / 2 ) {\displaystyle