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Concept in probability
stochastic processes, a part of the mathematical theory of probability, the variance gamma (VG) process, also known as Laplace motion, is a Lévy process determined
Variance_gamma_process
Stochastic process for effort or wear
gamma process produces a variance gamma process, and a variance gamma process can be written as the difference of two gamma processes. Moran process Klenke
Gamma_process
Continuous probability distribution
The variance-gamma distribution, generalized Laplace distribution or Bessel function distribution is a continuous probability distribution that is defined
Variance-gamma_distribution
Representation of a type of random process
{\begin{bmatrix}\gamma _{1}\\\gamma _{2}\\\gamma _{3}\\\vdots \\\gamma _{p}\\\end{bmatrix}}={\begin{bmatrix}\gamma _{0}&\gamma _{-1}&\gamma _{-2}&\cdots \\\gamma _{1}&\gamma
Autoregressive_model
Australian statistician
applications and history. He is known for the variance gamma model in financial mathematics (the variance gamma process). He was Professor, School of Mathematics
Eugene_Seneta
Cadlag in probability theory
is the variance gamma SSD, the Sato process obtained starting from the variance gamma process. The characteristic function of the Variance gamma at time
Additive_process
Probability distribution
random time.[citation needed] Increments of Laplace motion or a variance gamma process evaluated over the time scale also have a Laplace distribution.
Laplace_distribution
Important algorithms in numerical statistics
Algorithms for calculating variance play a major role in computational statistics. A key difficulty in the design of good algorithms for this problem is
Algorithms for calculating variance
Algorithms_for_calculating_variance
Two-parameter family of continuous probability distributions
the variance, which allows the gamma distribution to be used directly as a conjugate prior. Other Bayesians prefer to parametrize the inverse gamma distribution
Inverse-gamma_distribution
Thermodynamic process in which no mass or heat is exchanged with surroundings
V_{0}^{\gamma }=P\ V^{\gamma }={\mathsf {constant}}~.} At the same time, the work done by the pressure–volume changes as a result from this process, is equal
Adiabatic_process
American financial economist (born 1946)
the University of Maryland. Madan is most known for his work on the variance gamma model, the fast Fourier transform method for option pricing, and the
Dilip_Madan
time change which follows a gamma process, Γ ( t ; 1 , ν ) {\displaystyle \Gamma (t;1,\nu )} , the variance gamma process will follow: X V G ( t ; σ
Subordinator_(mathematics)
Solution to a stochastic differential equation
statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion processes are stochastic
Diffusion_process
Stochastic process modeling random walk with friction
=(k_{B}T/k)\exp[-(k/\gamma )|t-t'|]} with variance independent from γ {\displaystyle \gamma } and relaxation time-scale γ / k {\displaystyle \gamma /k} as expected
Ornstein–Uhlenbeck_process
Pricing model
In mathematical finance, the constant elasticity of variance model (CEV) is a stochastic volatility model, although technically it would be classed more
Constant elasticity of variance model
Constant_elasticity_of_variance_model
Probability distribution
{\displaystyle \ \mu \ } and unknown variance, with an inverse gamma distribution placed over the variance with parameters a = ν 2 {\textstyle a={\frac
Student's_t-distribution
Probability distribution
the gamma distribution itself. The closely related inverse-gamma distribution is used as a conjugate prior for scale parameters, such as the variance of
Gamma_distribution
Probability distribution
\gamma )={\frac {1}{\pi \gamma \left[1+\left({\frac {x-x_{0}}{\gamma }}\right)^{2}\right]}}={1 \over \pi }\left[{\gamma \over (x-x_{0})^{2}+\gamma ^{2}}\right]
Cauchy_distribution
Measure of frequency stability in clocks and oscillators
due to noise processes and not that of systematic errors or imperfections such as frequency drift or temperature effects. The Allan variance and Allan deviation
Allan_variance
analysis Variance Variance decomposition of forecast errors Variance gamma process Variance inflation factor Variance-gamma distribution Variance reduction
List_of_statistics_articles
Measure of the error of an estimator
moment (about the origin) of the error, and thus incorporates both the variance of the estimator (how widely spread the estimates are from one data sample
Mean_squared_error
Continuous probability distribution
) = W ( t ) + γ t {\displaystyle W^{(\gamma )}(t)=W(t)+\gamma t} , we can define the inverse Gaussian process A t = inf { s > 0 : W ( γ ) ( s ) = δ t
Normal-inverse Gaussian distribution
Normal-inverse_Gaussian_distribution
Stochastic process in probability theory
Brownian motion process, and the Poisson process. Further important examples include the Gamma process, the Pascal process, and the Meixner process. Aside from
Lévy_process
Family of optimization algorithms
(Stochastic) variance reduction is an algorithmic approach to minimizing functions that can be decomposed into finite sums. By exploiting the finite sum
Stochastic_variance_reduction
Probability distribution
{\Gamma (r+k)}{k!\,\Gamma (r)}}\left({\frac {r}{r+m}}\right)^{r}\left({\frac {m}{r+m}}\right)^{k}\quad {\text{for }}k=0,1,2,\dotsc } The variance can
Negative binomial distribution
Negative_binomial_distribution
Probability distribution and special case of gamma distribution
infinity, a Gamma distribution converges towards a normal distribution with expectation μ = α θ {\displaystyle \mu =\alpha \theta } and variance σ 2 = α θ
Chi-squared_distribution
Family of probability distributions
directly relate to the variance-to-mean power law. Regional organ blood flow can thus be modelled by the Tweedie compound Poisson–gamma distribution., In this
Tweedie_distribution
Probability distribution
40% in the mean and 549% in the variance. If X and Y are independent, with X ∼ Γ ( α , θ ) {\displaystyle X\sim \Gamma (\alpha ,\theta )} and Y ∼ Γ ( β
Beta_distribution
Measure of variation in statistics
data set or probability distribution is the square root of its variance (the variance being the average of the squared deviations from the mean). A useful
Standard_deviation
Probability distribution
and unknown variance σ2, a combined (multivariate) conjugate prior is placed over the mean and variance, consisting of a normal-inverse-gamma distribution
Normal_distribution
Smooth function in statistics
statistics, the variance function is a smooth function that depicts the variance of a random quantity as a function of its mean. The variance function is
Variance_function
Stochastic volatility model used in derivatives markets
_{\text{impl}}=\alpha \;{\frac {\log(F_{0}/K)}{D(\zeta )}}\;\left\{1+\left[{\frac {2\gamma _{2}-\gamma _{1}^{2}+1/\left(F_{\text{mid}}\right)^{2}}{24}}\;\left({\frac {\sigma
SABR_volatility_model
Stochastic process generalizing Brownian motion
distributed with mean 0 and variance u. W has almost surely continuous paths: Wt is almost surely continuous in t. That the process has independent increments
Wiener_process
Spatial statistics function
_{i=1}^{N}\sum _{j=1}^{N}w_{i}\gamma (\mathbf {s} _{i},\mathbf {s} _{j})w_{j}\leq 0,} which corresponds to the fact that the variance var ( X ) {\displaystyle
Variogram
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
distribution) are considered low-variance, while those with CV > 1 (such as a hyper-exponential distribution) are considered high-variance[citation needed]. Some
Coefficient_of_variation
Type of option contract
Then, using the Bondesson series representation to generate the variance gamma process can increase the computational performance of the Asian option pricer
Asian_option
Compound probability distribution
to the Poisson distribution where mean and variance are the same. In practice, almost only densities of gamma distributions, logarithmic normal distributions
Mixed_Poisson_distribution
Name for several different families of probability distributions
Halliwell, L. J. (2021). The log-gamma distribution and non-normal error. Variance 2(13). https://www.casact.org/abstract/log-gamma-distribution-and-non-normal-error
Generalized logistic distribution
Generalized_logistic_distribution
Stochastic process used in biology to describe finite populations
important differences to deterministic processes which cannot model random events. The expected value and the variance of the number of A individuals X(t)
Moran_process
Discrete probability distribution
distribution Gamma distribution Hermite distribution Index of dispersion Negative binomial distribution Poisson clumping Poisson point process Poisson regression
Poisson_distribution
Degradation of AI models trained on synthetic data
in closed form, but the mean and variance of the square root of gamma distribution are expressed in terms of gamma functions, making the result quite
Model_collapse
Procedure to estimate standard deviation from a sample
the observed sample variance by the correction factor γ 1 {\displaystyle \gamma _{1}} gives an unbiased estimate of the variance. Similarly, re-writing
Unbiased estimation of standard deviation
Unbiased_estimation_of_standard_deviation
distributed variables with finite mean and variance is approximately normal. The normal-exponential-gamma distribution The normal-inverse Gaussian distribution
List of probability distributions
List_of_probability_distributions
Probability distribution
dz={\frac {4}{\pi }}\;\Gamma ^{2}{\Big (}{\frac {3}{2}}{\Big )}=1} A much simpler result, stated in a section above, is that the variance of the product of
Distribution of the product of two random variables
Distribution_of_the_product_of_two_random_variables
Time series model
the variance of the current error term or innovation as a function of the actual sizes of the previous time periods' error terms; often the variance is
Autoregressive conditional heteroskedasticity
Autoregressive_conditional_heteroskedasticity
Method of interpolation
\gamma (\mathbf {h} )} , valid in all field of analysis of Z ( x ) {\displaystyle Z(x)} , then we can write an expression for the estimation variance of
Kriging
Reinforcement learning algorithms
\sum _{0\leq i\leq T}(\gamma ^{i}R_{i})} . γ j ∑ j ≤ i ≤ T ( γ i − j R i ) {\textstyle \gamma ^{j}\sum _{j\leq i\leq T}(\gamma ^{i-j}R_{i})} : the REINFORCE
Actor-critic_algorithm
statistics, a continuous-time stochastic process, or a continuous-space-time stochastic process is a stochastic process for which the index variable takes a
Continuous-time stochastic process
Continuous-time_stochastic_process
Continuous probability distribution
normal-inverse gamma distribution (NI) G H ( λ , α , β , 0 , μ ) {\displaystyle \mathrm {GH} (\lambda ,\alpha ,\beta ,0,\mu )\,} is a variance-gamma distribution
Generalised hyperbolic distribution
Generalised_hyperbolic_distribution
Probability distribution
and variance of the inverse-gamma distribution, Inv-Gamma ( n , λ ) {\textstyle {\mbox{Inv-Gamma}}(n,\lambda )} . The uniformly minimum-variance unbiased
Exponential_distribution
Instrument used for measuring ionizing radiation
installed "area gamma" alarms for personnel protection, as well as in process measurement and interlock applications. The processing electronics of such
Geiger_counter
Mathematical model in optimal trade execution
the liquidation of a large position over a fixed time horizon as a mean-variance trade-off between market impact costs (incurred by trading too quickly)
Almgren–Chriss_model
Statistical model
In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that
Gaussian_process
Linear regression model with a single explanatory variable
mean β and variance σ 2 / ∑ i ( x i − x ¯ ) 2 , {\textstyle \sigma ^{2}\left/\sum _{i}(x_{i}-{\bar {x}})^{2}\right.,} where σ2 is the variance of the error
Simple_linear_regression
When variance is a random variable
statistics, stochastic volatility models are those in which the variance of a stochastic process is itself randomly distributed. They are used in the field
Stochastic_volatility
Fourth standardized moment in statistics
For non-normal samples, the variance of the sample variance depends on the kurtosis; for details, please see variance. Pearson's definition of kurtosis
Kurtosis
Method in Itô calculus
approximation converges strongly with order γ s {\displaystyle \gamma _{s}} to the continuous process X {\displaystyle X} ; likewise, X ^ {\displaystyle {\hat
Euler–Maruyama_method
Concept in statistics
functions of the variables. A one-dimensional GRF is also called a Gaussian process. An important special case of a GRF is the Gaussian free field. With regard
Gaussian_random_field
Class of statistical models
response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized
Generalized_linear_model
Range to estimate an unknown parameter
{\displaystyle \mu } and variance σ 2 . {\displaystyle \sigma ^{2}.} Define the sample mean X ¯ {\displaystyle {\bar {X}}} and unbiased sample variance S 2 {\displaystyle
Confidence_interval
Class of reinforcement learning algorithms
\sum _{\tau =t}^{T}(\gamma ^{\tau }R_{\tau })=\gamma ^{t}V^{\pi _{\theta _{i}}}(S_{t})} , this could significantly decrease variance in the gradient estimation
Policy_gradient_method
Estimate of an interval in which future observations will fall
and variance may be calculated from γ = P ( ℓ < X < u ) = P ( ℓ − μ σ < X − μ σ < u − μ σ ) = P ( ℓ − μ σ < Z < u − μ σ ) , {\displaystyle \gamma =P(\ell
Prediction_interval
Machine learning technique
of BatchNorm: import numpy as np def batchnorm(x, gamma, beta, epsilon=1e-9): # Mean and variance of each feature mu = np.mean(x, axis=0) # shape (N
Normalization (machine learning)
Normalization_(machine_learning)
IID variables, their sum will be normally distributed with mean nμ and variance nσ2. The probability that the crack does not exceed a critical length ω
Birnbaum–Saunders distribution
Birnbaum–Saunders_distribution
How many standard deviations apart from the mean an observed datum is
with high probability γ {\displaystyle \gamma } , i.e. Pr ( L < X < U ) = γ , {\displaystyle \Pr(L<X<U)=\gamma ,} For the standard score Z of X it gives:
Standard_score
Class of financial models with stochastic volatility and jumps
introducing both a stochastic variance process and a jump component—typically modeled via a Poisson process or more general Lévy processes—SVJ models allow for
Stochastic volatility jump models
Stochastic_volatility_jump_models
Probability distribution
distribution Variance-gamma distribution Generalised hyperbolic distribution O.E Barndorff-Nielsen, J. Kent and M. Sørensen (1982): "Normal variance-mean mixtures
Normal_variance-mean_mixture
Type of Borel measure
with finite, non-zero variance are called non-degenerate Gaussian measures. The standard Gaussian measure γ n {\displaystyle \gamma ^{n}} on R n {\displaystyle
Gaussian_measure
Predictive filter
interval T {\displaystyle T} , the process variance σ w 2 {\displaystyle \sigma _{w}^{2}} and the noise variance σ v 2 {\displaystyle \sigma _{v}^{2}}
Alpha_beta_filter
Probability distribution
Assuming that each component is uncorrelated, normally distributed with equal variance, and zero mean, then the overall wind speed (vector magnitude) will be
Rayleigh_distribution
Mathematical model for neuron networks
himself was influenced by Hédi Soula. Galves and Löcherbach referred to the process that Cessac described as "a version in a finite dimension" of their own
Galves–Löcherbach_model
Concept in statistics
with variance distributed according to a gamma distribution yields a variance-gamma distribution. Compounding a Gaussian distribution with variance distributed
Compound probability distribution
Compound_probability_distribution
Measure of linear correlation
{\displaystyle r_{xy}} by substituting estimates of the covariances and variances based on a sample into the formula above. Given paired data { ( x 1 ,
Pearson correlation coefficient
Pearson_correlation_coefficient
Probability distribution
[R^{p}]&=\left.{\frac {\Gamma (\alpha +p)\Gamma (\beta -p)}{\Gamma (\alpha +\beta )}}\right/{\frac {\Gamma (\alpha )\Gamma (\beta )}{\Gamma (\alpha +\beta )}}\\[
Ratio_distribution
Value at risk Variance gamma process / spr Vasicek model Volatility Boltzmann factor Brownian motion / (U:C) Brownian ratchet Cosmic variance Critical phenomena
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Overview of and topical guide to probability
process Compound Poisson process Wiener process Geometric Brownian motion Fractional Brownian motion Brownian bridge Ornstein–Uhlenbeck process Gamma
Outline_of_probability
Probability distribution on the circle
variance that grows linearly in time. On the other hand, the von Mises distribution is the stationary distribution of a drift and diffusion process on
Von_Mises_distribution
Continuous probability distribution
{\displaystyle \gamma _{2}={\frac {-6\Gamma _{1}^{4}+12\Gamma _{1}^{2}\Gamma _{2}-3\Gamma _{2}^{2}-4\Gamma _{1}\Gamma _{3}+\Gamma _{4}}{[\Gamma _{2}-\Gamma _{1}^{2}]^{2}}}}
Weibull_distribution
Three-parameter family of continuous probability distributions
distribution, the usual shape parameter. K-distribution is a special case of variance-gamma distribution, which in turn is a special case of generalised hyperbolic
K-distribution
Family of probability distributions often used to model tails or extreme values
relative variance of the fluctuations of exponential scale, Λ {\displaystyle \Lambda } . Notice however, that since the parameters for the Gamma distribution
Generalized Pareto distribution
Generalized_Pareto_distribution
Aspect of probability theory
Compound Poisson process Hermite distribution Negative binomial distribution Geometric distribution Geometric Poisson distribution Gamma distribution Neyman
Compound_Poisson_distribution
Technique for the generative modeling of a continuous probability distribution
the case that the reverse process has variance equals to 0. In other words, the reverse process (and also the forward process) is deterministic. When using
Diffusion_model
Method of improving artificial neural network
unit variance. Let the transformed activation be z = γ y ^ + β {\displaystyle z=\gamma {\hat {y}}+\beta } , and suppose γ {\displaystyle \gamma } and
Batch_normalization
{x} )}}} The ratio of the variance and the arithmetic mean was proposed as a test statistic by Clapham. Since the variance is always ≥0 the contraharmonic
Contraharmonic_mean
Statistical method
estimated from the data. Bootstrapping assigns measures of accuracy (bias, variance, confidence intervals, prediction error, etc.) to sample estimates. This
Bootstrapping_(statistics)
Probability distribution
P(IV)(\mu ,\sigma ,\gamma ,1)=P(III)(\mu ,\sigma ,\gamma ).} The finiteness of the mean, and the existence and the finiteness of the variance depend on the
Pareto_distribution
Probability distribution
} },\nu )={\frac {\left|{\mathbf {\Psi } }\right|^{\nu /2}}{2^{\nu p/2}\Gamma _{p}({\frac {\nu }{2}})}}\left|\mathbf {X} \right|^{-(\nu +p+1)/2}e^{-{\frac
Inverse-Wishart_distribution
Statistical transformation
variable whose distribution is approximately normally distributed, with a variance that is stable over different values of r. Given a set of N bivariate sample
Fisher_transformation
Probability distribution
distributed Gamma distributions: Y 1 ∼ Gamma ( α 1 , 1 ) , … , Y K ∼ Gamma ( α K , 1 ) {\displaystyle Y_{1}\sim \operatorname {Gamma} (\alpha _{1}
Dirichlet_distribution
Fundamental theorem in probability theory and statistics
with expected value (average) μ {\displaystyle \mu } and finite positive variance σ 2 {\displaystyle \sigma ^{2}} , and let X ¯ n {\displaystyle {\bar {X}}_{n}}
Central_limit_theorem
Measure of the asymmetry of random variables
distributions converge to a normal distribution with mean 0 and variance 6 (Fisher, 1930). The variance of the sample skewness is thus approximately 6 / n {\displaystyle
Skewness
Model in theoretical ecology and statistical mechanics
variables (i.e., zero mean and unit variance) with ⟨ a i j a j i ⟩ = γ {\displaystyle \langle a_{ij}a_{ji}\rangle =\gamma } for i ≠ j {\displaystyle i\neq
Random generalized Lotka–Volterra model
Random_generalized_Lotka–Volterra_model
Applications", www.2-ept.com Madan, D., Carr, P., Chang, E. (1998) "The Variance Gamma Process and Option Pricing", European Finance Review 2: 79–105 2 -
2-EPT probability density function
2-EPT_probability_density_function
Statistical measure of reliability
_{y_{i}}^{2}} the variance associated with each part i; and σ X 2 {\displaystyle \sigma _{X}^{2}} the observed score variance (the variance associated with
Cronbach's_alpha
Branch of statistics
Uniformly minimum-variance unbiased estimators (UMVUE), sometimes called best unbiased estimators as well, are estimators that have minimum variance among all
Parametric_statistics
Branch of statistics
standard normal variables; useful e.g. for inference regarding the sample variance of normally distributed samples (see chi-squared test) Student's t distribution
Mathematical_statistics
Family of continuous probability distributions
m_{n}={\frac {b\Gamma (1+n/a)\Gamma (b)}{\Gamma (1+b+n/a)}}=bB(1+n/a,b)\,} where B is the Beta function and Γ(.) denotes the Gamma function. The variance, skewness
Kumaraswamy_distribution
Probability distribution that has the most entropy of a class
\Gamma (x)={\frac {\Gamma '(x)}{\Gamma (x)}}} is the digamma function, B ( p , q ) = Γ ( p ) Γ ( q ) Γ ( p + q ) {\displaystyle B(p,q)={\frac {\Gamma (p)\
Maximum entropy probability distribution
Maximum_entropy_probability_distribution
Method to draw shadows in computer graphic images
pdf VSM "Variance" http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.104.2569&rep=rep1&type=pdf SAVSM "Summed Area Variance" https://developer
Shadow_mapping
Machine learning technique
F_{m}(x)=F_{m-1}(x)+\gamma _{m}h_{m}(x),\quad \gamma _{m}={\underset {\gamma }{\operatorname {arg\,min} }}\sum _{i=1}^{n}L(y_{i},F_{m-1}(x_{i})+\gamma h_{m}(x_{i}))
Gradient_boosting
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VARIANCE GAMMA-PROCESS
VARIANCE GAMMA-PROCESS
VARIANCE GAMMA-PROCESS
VARIANCE GAMMA-PROCESS
VARIANCE GAMMA-PROCESS
VARIANCE GAMMA-PROCESS
VARIANCE GAMMA-PROCESS
VARIANCE GAMMA-PROCESS
VARIANCE GAMMA-PROCESS
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