Uses of Class
dev.nm.analysis.function.rn2r1.univariate.AbstractUnivariateRealFunction
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Uses of AbstractUnivariateRealFunction in dev.nm.analysis.curvefit.interpolation
Subclasses of AbstractUnivariateRealFunction in dev.nm.analysis.curvefit.interpolation Modifier and Type Class Description classLinearInterpolatorDefine a univariate function by linearly interpolating between adjacent points.classNevilleTableNeville's algorithm is a polynomial interpolation algorithm. -
Uses of AbstractUnivariateRealFunction in dev.nm.analysis.differentiation.univariate
Subclasses of AbstractUnivariateRealFunction in dev.nm.analysis.differentiation.univariate Modifier and Type Class Description classDBetaRegularizedThis is the first order derivative function of the Regularized Incomplete Beta function,BetaRegularized, w.r.t the upper limit, x.classDErfThis is the first order derivative function of the Error function,Erf.classDfdxThe first derivative is a measure of how a function changes as its input changes.classDGammaThis is the first order derivative function of the Gamma function, \({d \mathrm{\Gamma}(x) \over dx}\).classDGaussianThis is the first order derivative function of aGaussianfunction, \({d \mathrm{\phi}(x) \over dx}\).classDPolynomialThis is the first order derivative function of aPolynomial, which, again, is a polynomial.classFiniteDifferenceA finite difference (divided by a small increment) is an approximation of the derivative of a function. -
Uses of AbstractUnivariateRealFunction in dev.nm.analysis.function.polynomial
Subclasses of AbstractUnivariateRealFunction in dev.nm.analysis.function.polynomial Modifier and Type Class Description classCauchyPolynomialThe Cauchy's polynomial of a polynomial takes this form:classPolynomialA polynomial is aUnivariateRealFunctionthat represents a finite length expression constructed from variables and constants, using the operations of addition, subtraction, multiplication, and constant non-negative whole number exponents.classQuadraticMonomialA quadratic monomial has this form: x2 + ux + v.classScaledPolynomialThis constructs a scaled polynomial that has neither too big or too small coefficients, hence avoiding overflow or underflow. -
Uses of AbstractUnivariateRealFunction in dev.nm.analysis.function.rn2r1.univariate
Subclasses of AbstractUnivariateRealFunction in dev.nm.analysis.function.rn2r1.univariate Modifier and Type Class Description classContinuedFractionA continued fraction representation of a number has this form: \[ z = b_0 + \cfrac{a_1}{b_1 + \cfrac{a_2}{b_2 + \cfrac{a_3}{b_3 + \cfrac{a_4}{b_4 + \ddots\,}}}} \] ai and bi can be functions of x, which in turn makes z a function of x.classStepFunctionA step function (or staircase function) is a finite linear combination of indicator functions of intervals. -
Uses of AbstractUnivariateRealFunction in dev.nm.analysis.function.special.beta
Subclasses of AbstractUnivariateRealFunction in dev.nm.analysis.function.special.beta Modifier and Type Class Description classBetaRegularizedThe Regularized Incomplete Beta function is defined as: \[ I_x(p,q) = \frac{B(x;\,p,q)}{B(p,q)} = \frac{1}{B(p,q)} \int_0^x t^{p-1}\,(1-t)^{q-1}\,dt, p > 0, q > 0 \]classBetaRegularizedInverseThe inverse of the Regularized Incomplete Beta function is defined at: \[ x = I^{-1}_{(p,q)}(u), 0 \le u \le 1 \] -
Uses of AbstractUnivariateRealFunction in dev.nm.analysis.function.special.gamma
Subclasses of AbstractUnivariateRealFunction in dev.nm.analysis.function.special.gamma Modifier and Type Class Description classDigammaThe digamma function is defined as the logarithmic derivative of the gamma function.classGammaGergoNemesThe Gergo Nemes' algorithm is very simple and quick to compute the Gamma function, if accuracy is not critical.classGammaLanczosLanczos approximation provides a way to compute the Gamma function such that the accuracy can be made arbitrarily precise.classGammaLanczosQuickLanczos approximation, computations are done indouble.classLogGammaThe log-Gamma function, \(\log (\Gamma(z))\), for positive real numbers, is the log of the Gamma function.classTrigammaThe trigamma function is defined as the logarithmic derivative of the digamma function. -
Uses of AbstractUnivariateRealFunction in dev.nm.analysis.function.special.gaussian
Subclasses of AbstractUnivariateRealFunction in dev.nm.analysis.function.special.gaussian Modifier and Type Class Description classCumulativeNormalHastingsHastings algorithm is faster but less accurate way to compute the cumulative standard Normal.classCumulativeNormalInverseThe inverse of the cumulative standard Normal distribution function is defined as: \[ N^{-1}(u) /]classCumulativeNormalMarsagliaMarsaglia is about 3 times slower but is more accurate to compute the cumulative standard Normal.classErfThe Error function is defined as: \[ \operatorname{erf}(x) = \frac{2}{\sqrt{\pi}}\int_{0}^x e^{-t^2} dt \]classErfcThis complementary Error function is defined as: \[ \operatorname{erfc}(x) = 1-\operatorname{erf}(x) = \frac{2}{\sqrt{\pi}} \int_x^{\infty} e^{-t^2}\,dt \]classErfInverseThe inverse of the Error function is defined as: \[ \operatorname{erf}^{-1}(x) \]classGaussianThe Gaussian function is defined as: \[ f(x) = a e^{- { \frac{(x-b)^2 }{ 2 c^2} } } \] -
Uses of AbstractUnivariateRealFunction in dev.nm.stat.evt.evd.univariate.fitting.acer
Subclasses of AbstractUnivariateRealFunction in dev.nm.stat.evt.evd.univariate.fitting.acer Modifier and Type Class Description classACERFunctionThe ACER (Average Conditional Exceedance Rate) function \(\epsilon_k(\eta)\) approximates the probability \[ \epsilon_k(\eta) = Pr(X_k > \eta | X_1 \le \eta, X_2 \le \eta, ..., X_{k-1} \le \eta) \] for a sequence of stochastic process observations \(X_i\) with a k-step memory.classACERInverseFunctionThe inverse of the ACER function.classACERLogFunctionThe ACER function in log scale (base e), i.e., \(log(\epsilon_k(\eta))\).classACERReturnLevelGiven an ACER function, compute the return level \(\eta\) for a given return period \(R\). -
Uses of AbstractUnivariateRealFunction in dev.nm.stat.evt.function
Subclasses of AbstractUnivariateRealFunction in dev.nm.stat.evt.function Modifier and Type Class Description classReturnLevelGiven a GEV distribution of a random variable \(X\), the return level \(\eta\) is the value that is expected to be exceeded on average once every interval of time \(T\), with a probability of \(1 / T\).classReturnPeriodThe return period \(R\) of a level \(\eta\) for a random variable \(X\) is the mean number of trials that must be done for \(X\) to exceed \(\eta\). -
Uses of AbstractUnivariateRealFunction in dev.nm.stat.stochasticprocess.univariate.filtration
Subclasses of AbstractUnivariateRealFunction in dev.nm.stat.stochasticprocess.univariate.filtration Modifier and Type Class Description classBtThis is aFiltrationFunctionthat returns \(B(t_i)\), the Brownian motion value at the i-th time point.classF_Sum_BtDtThis represents a function of this integral \[ I = \int_{0}^{1} B(t)dt \]classF_Sum_tBtDtThis represents a function of this integral \[ \int_{0}^{1} (t - 0.5) * B(t) dt \]classFiltrationFunctionA filtration function, parameterized by a fixed filtration, is a function of time, \(f(\mathfrak{F_{t_i}})\). -
Uses of AbstractUnivariateRealFunction in tech.nmfin.portfoliooptimization.lai2010.ceta
Subclasses of AbstractUnivariateRealFunction in tech.nmfin.portfoliooptimization.lai2010.ceta Modifier and Type Class Description classCetaThe function C(η) to be maximized (Eq. -
Uses of AbstractUnivariateRealFunction in tech.nmfin.portfoliooptimization.lai2010.ceta.maximizer
Subclasses of AbstractUnivariateRealFunction in tech.nmfin.portfoliooptimization.lai2010.ceta.maximizer Modifier and Type Class Description static classCetaMaximizer.NegCetaFunction
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