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 class
LinearInterpolator
Define a univariate function by linearly interpolating between adjacent points.class
NevilleTable
Neville'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 class
DBetaRegularized
This is the first order derivative function of the Regularized Incomplete Beta function,BetaRegularized
, w.r.t the upper limit, x.class
DErf
This is the first order derivative function of the Error function,Erf
.class
Dfdx
The first derivative is a measure of how a function changes as its input changes.class
DGamma
This is the first order derivative function of the Gamma function, \({d \mathrm{\Gamma}(x) \over dx}\).class
DGaussian
This is the first order derivative function of aGaussian
function, \({d \mathrm{\phi}(x) \over dx}\).class
DPolynomial
This is the first order derivative function of aPolynomial
, which, again, is a polynomial.class
FiniteDifference
A 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 class
CauchyPolynomial
The Cauchy's polynomial of a polynomial takes this form:class
Polynomial
A polynomial is aUnivariateRealFunction
that represents a finite length expression constructed from variables and constants, using the operations of addition, subtraction, multiplication, and constant non-negative whole number exponents.class
QuadraticMonomial
A quadratic monomial has this form: x2 + ux + v.class
ScaledPolynomial
This 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 class
ContinuedFraction
A 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.class
StepFunction
A 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 class
BetaRegularized
The Regularized Incomplete Beta function is defined as: \[ I_x(p,q) = \frac{B(x;\,p,q)}{B(p,q)} = \frac{1}{B(p,q)} \int_0^x t^{p-1}\,(1-t)^{q-1}\,dt, p > 0, q > 0 \]class
BetaRegularizedInverse
The 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 class
Digamma
The digamma function is defined as the logarithmic derivative of the gamma function.class
GammaGergoNemes
The Gergo Nemes' algorithm is very simple and quick to compute the Gamma function, if accuracy is not critical.class
GammaLanczos
Lanczos approximation provides a way to compute the Gamma function such that the accuracy can be made arbitrarily precise.class
GammaLanczosQuick
Lanczos approximation, computations are done indouble
.class
LogGamma
The log-Gamma function, \(\log (\Gamma(z))\), for positive real numbers, is the log of the Gamma function.class
Trigamma
The 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 class
CumulativeNormalHastings
Hastings algorithm is faster but less accurate way to compute the cumulative standard Normal.class
CumulativeNormalInverse
The inverse of the cumulative standard Normal distribution function is defined as: \[ N^{-1}(u) /]class
CumulativeNormalMarsaglia
Marsaglia is about 3 times slower but is more accurate to compute the cumulative standard Normal.class
Erf
The Error function is defined as: \[ \operatorname{erf}(x) = \frac{2}{\sqrt{\pi}}\int_{0}^x e^{-t^2} dt \]class
Erfc
This complementary Error function is defined as: \[ \operatorname{erfc}(x) = 1-\operatorname{erf}(x) = \frac{2}{\sqrt{\pi}} \int_x^{\infty} e^{-t^2}\,dt \]class
ErfInverse
The inverse of the Error function is defined as: \[ \operatorname{erf}^{-1}(x) \]class
Gaussian
The 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 class
ACERFunction
The 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.class
ACERInverseFunction
The inverse of the ACER function.class
ACERLogFunction
The ACER function in log scale (base e), i.e., \(log(\epsilon_k(\eta))\).class
ACERReturnLevel
Given 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 class
ReturnLevel
Given 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 \(1 / T\).class
ReturnPeriod
The 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 class
Bt
This is aFiltrationFunction
that returns \(B(t_i)\), the Brownian motion value at the i-th time point.class
F_Sum_BtDt
This represents a function of this integral \[ I = \int_{0}^{1} B(t)dt \]class
F_Sum_tBtDt
This represents a function of this integral \[ \int_{0}^{1} (t - 0.5) * B(t) dt \]class
FiltrationFunction
A 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 class
Ceta
The 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 class
CetaMaximizer.NegCetaFunction
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