# Uses of Classdev.nm.analysis.function.rn2r1.AbstractBivariateRealFunction

• ## Uses of AbstractBivariateRealFunction in dev.nm.analysis.differentiation.univariate

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Description
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This is the first order derivative function of the Beta function w.r.t x, $${\partial \over \partial x} \mathrm{B}(x, y)$$.
• ## Uses of AbstractBivariateRealFunction in dev.nm.analysis.function.special.beta

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Description
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The beta function defined as: $B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}= \int_0^1t^{x-1}(1-t)^{y-1}\,dt, x > 0, y > 0$
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This class represents the log of Beta function log(B(x, y)).
• ## Uses of AbstractBivariateRealFunction in dev.nm.analysis.function.special.gamma

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Description
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The Lower Incomplete Gamma function is defined as: $\gamma(s,x) = \int_0^x t^{s-1}\,e^{-t}\,{\rm d}t = P(s,x)\Gamma(s)$ P(s,x) is the Regularized Incomplete Gamma P function.
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The Regularized Incomplete Gamma P function is defined as: $P(s,x) = \frac{\gamma(s,x)}{\Gamma(s)} = 1 - Q(s,x), s \geq 0, x \geq 0$
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The inverse of the Regularized Incomplete Gamma P function is defined as: $x = P^{-1}(s,u), 0 \geq u \geq 1$ When s > 1, we use the asymptotic inversion method. When s <= 1, we use an approximation of P(s,x) together with a higher-order Newton like method. In both cases, the estimated value is then improved using Halley's method, c.f., HalleyRoot.
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The Regularized Incomplete Gamma Q function is defined as: $Q(s,x)=\frac{\Gamma(s,x)}{\Gamma(s)}=1-P(s,x), s \geq 0, x \geq 0$ The algorithm used for computing the regularized incomplete Gamma Q function depends on the values of s and x.
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The Upper Incomplete Gamma function is defined as: $\Gamma(s,x) = \int_x^{\infty} t^{s-1}\,e^{-t}\,{\rm d}t = Q(s,x) \times \Gamma(s)$ The integrand has the same form as the Gamma function, but the lower limit of the integration is a variable.
• ## Uses of AbstractBivariateRealFunction in dev.nm.stat.timeseries.linear.univariate

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Description
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This is the auto-correlation function of a univariate time series {xt}.
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This is the auto-covariance function of a univariate time series {xt}.
• ## Uses of AbstractBivariateRealFunction in dev.nm.stat.timeseries.linear.univariate.sample

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Description
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This is the sample Auto-Correlation Function (ACF) for a univariate data set.
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This is the sample Auto-Covariance Function (ACVF) for a univariate data set.
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This is the sample partial Auto-Correlation Function (PACF) for a univariate data set.
• ## Uses of AbstractBivariateRealFunction in dev.nm.stat.timeseries.linear.univariate.stationaryprocess.arma

Modifier and Type
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Description
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Compute the Auto-Correlation Function (ACF) for an AutoRegressive Moving Average (ARMA) model, assuming that EXt = 0.
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Computes the Auto-CoVariance Function (ACVF) for an AutoRegressive Moving Average (ARMA) model by recursion.