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grep rough audit - static analysis tool
v2.8 written by @Wireghoul
=================================[justanotherhacker.com]===
r-cran-evd-2.3-3/inst/doc/Multivariate_Extremes.Rnw-195-
r-cran-evd-2.3-3/inst/doc/Multivariate_Extremes.Rnw:196:We now consider all the $1500$ observations on liability claims. We assume that the data are distributed according to the distribution function $F$, and we are interested in $F(z)$ where $z=(z_1,z_2)$ is in some sense large. The methods we use assume that $F$ is in the domain of attraction of some bivariate extreme value distribution $G$, and we focus on large data points to estimate features of $G$, and hence of $F(z)$ for large $z$.
r-cran-evd-2.3-3/inst/doc/Multivariate_Extremes.Rnw-197-
r-cran-evd-2.3-3/inst/doc/Multivariate_Extremes.Rnw:198:Typically we focus on points $z$ that lie above a certain threshold. The functions \texttt{tcplot} and \texttt{mrlplot} can be used for producing plots on each margin to help determine thresholds $u_1$ and $u_2$ for methods that focus primarily on points $z$ such that $z_1 > u_1$ and $z_2 > u_2$. Alternatively, the function \texttt{bvtcplot} can be used to help determine a single threshold $u^{*}$ for methods that focus on points $z$ such that $r(z) > u^{*}$, where $r(z) = x_1(z_1) + x_2(z_2)$, and $x_j(z_j) = -1/\log \hat{F}_j(z_j)$ for $j=1,2$ where $F_j$ is estimated empirically.
r-cran-evd-2.3-3/inst/doc/Multivariate_Extremes.Rnw-199-
r-cran-evd-2.3-3/inst/doc/Multivariate_Extremes.Rnw:200:Following Segers and Vandewalle (2004), a sensible choice for threshold $u^{*}$ might be found from Figure \ref{bvtc} by taking the $k$th largest $r(z)$, where $k$ is the largest value for which the y-axis is close to two. Figure \ref{bvtc} is plotted below using \texttt{bvtcplot}. The value of $k$ is returned invisibly. Setting \texttt{spectral = TRUE} uses the $k$th largest points to plot a nonparametric estimate of $H([0,\omega])$ where $H$ is the spectral measure of $G$.
r-cran-evd-2.3-3/inst/doc/Multivariate_Extremes.Rnw-201-
##############################################
r-cran-evd-2.3-3/inst/doc/Multivariate_Extremes.Rnw-217-\vspace{-1cm}
r-cran-evd-2.3-3/inst/doc/Multivariate_Extremes.Rnw:218:\caption{A plot of $(k/n)r_{(n-k)}$ as a function of $k$, where $r_{(1)} \leq \dots \leq r_{(n)}$ are the ordered values of $r$. The y-axis provides an estimate of $H([0,1]) = 2$ for the spectral measure $H$ of $G$.}
r-cran-evd-2.3-3/inst/doc/Multivariate_Extremes.Rnw-219-\label{bvtc}
##############################################
r-cran-evd-2.3-3/inst/doc/guide22.txt-193-\end{equation}
r-cran-evd-2.3-3/inst/doc/guide22.txt:194:where ($\mu,\sigma,\xi$) are the location, scale and shape parameters respectively, $\sigma > 0$ and $h_{+}=\max(h,0)$.
r-cran-evd-2.3-3/inst/doc/guide22.txt-195-When $\xi>0$ the GEV distribution has a finite lower end point, given by $\mu - \sigma/\xi$.
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r-cran-evd-2.3-3/inst/doc/guide22.txt-206-\end{equation*}
r-cran-evd-2.3-3/inst/doc/guide22.txt:207:for $z > \mu$, where ($\mu,\sigma,\xi$) are the location, scale and shape parameters respectively, $\sigma > 0$ and $h_{+}=\max(h,0)$.
r-cran-evd-2.3-3/inst/doc/guide22.txt-208-The GPD has a finite lower end point, given by $\mu$.
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r-cran-evd-2.3-3/inst/doc/guide22.txt-381-This distribution can be extended to an asymmetric form.
r-cran-evd-2.3-3/inst/doc/guide22.txt:382:Let $B$ be the set of all non-empty subsets of $\{1,\dots,d\}$, let $B_1=\{b \in B:|b|=1\}$, where $|b|$ denotes the number of elements in the set $b$, and let $B_{(i)}=\{b \in B:i \in b\}$.
r-cran-evd-2.3-3/inst/doc/guide22.txt-383-The multivariate asymmetric logistic model \citep{tawn90} is given by
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r-cran-evd-2.3-3/inst/doc/guide22.txt-530-\end{equation*}
r-cran-evd-2.3-3/inst/doc/guide22.txt:531:where $(y_1,\dots,y_d)$ is defined by the transformations \eqref{mtrans}. It follows that $A(\omega)=-\log\{G(y_1^{-1}(\omega_1),\dots,y_d^{-1}(\omega_d))\}$, defined on the simplex $S_d =\{\omega \in \mathbb{R}^d_+: \sum_{j=1}^d \omega_j = 1\}$.
r-cran-evd-2.3-3/inst/doc/guide22.txt-532-$A(\cdot)$ is known as the dependence function. The dependence function characterises the dependence structure of $G$.
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r-cran-evd-2.3-3/inst/doc/guide22.txt-598-
r-cran-evd-2.3-3/inst/doc/guide22.txt:599:%where $H_n(x)$ is the empirical distribution function of $x_1,\dots,x_n$, with $x_i = y_{i1} / (y_{i1} + y_{i2})$ for $i=1,\dots,n$, and $p(\cdot)$ is any bounded function on $[0,1]$, which can be specified using the argument \verb+wf+.
r-cran-evd-2.3-3/inst/doc/guide22.txt-600-%By default $p(\cdot)$ is the identity function.
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r-cran-evd-2.3-3/inst/doc/guide22.txt-796-
r-cran-evd-2.3-3/inst/doc/guide22.txt:797:By default the maximum likelihood estimates are calculated under the assumption that the data to be fitted are the observed values of independent random variables $Z_1,\dots,Z_n$, where $Z_i \sim \text{GEV}(\mu,\sigma,\xi)$ for each $i=1,\dots,n$. The \verb+nsloc+ argument allows non-stationary models of the form $Z_i \sim \text{GEV}(\mu_i,\sigma,\xi)$, where
r-cran-evd-2.3-3/inst/doc/guide22.txt-798-\begin{equation*}
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r-cran-evd-2.3-3/inst/doc/guide22.txt-800-\end{equation*}
r-cran-evd-2.3-3/inst/doc/guide22.txt:801:The parameters $(\beta_0,\dots,\beta_k)$ are to be estimated. In matrix notation $\boldsymbol{\mu} = \boldsymbol{\beta_0} + X \boldsymbol{\beta} $, where $ \boldsymbol{\mu}= (\mu_1,\dots,\mu_n)^T$, $\boldsymbol{\beta_0} = (\beta_0,\dots,\beta_0)^T$, $\boldsymbol{\beta} = (\beta_1,\dots,\beta_k)^T$ and $X$ is the $n \times k$ covariate matrix (excluding the intercept) with $ij$th element $x_{ij}$.
r-cran-evd-2.3-3/inst/doc/guide22.txt-802-
##############################################
r-cran-evd-2.3-3/inst/doc/guide22.txt-837-Arguments of the optimisation function \verb+optim+ can also be specified.
r-cran-evd-2.3-3/inst/doc/guide22.txt:838:The example given below produces maximum likelihood estimates for the distribution \eqref{maxdens}, where $m = 365$ and $F$ is the normal distribution.
r-cran-evd-2.3-3/inst/doc/guide22.txt-839-
##############################################
r-cran-evd-2.3-3/inst/doc/guide22.txt-851-The \verb+forder+ function yields maximum likelihood estimates for the distribution \eqref{orderdens} given integers $m$ and $j \in \{1,\dots,m\}$, and an arbitrary distribution function $F$.
r-cran-evd-2.3-3/inst/doc/guide22.txt:852:An example is given below, where $m = 365$, $j = 2$ and $F$ is the normal distribution.
r-cran-evd-2.3-3/inst/doc/guide22.txt-853-\begin{verbatim}
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r-cran-evd-2.3-3/inst/doc/guide22.txt-952-The fitted probability of an exceedance over $z > u$ is therefore $p(1 - G(z))$, where $p$ is the estimated probability of exceeding $u$, which is given by the empirical proportion of exceedances.
r-cran-evd-2.3-3/inst/doc/guide22.txt:953:The $m$-period return level $z_m$ satisfies $p(1 - G(z_m)) = 1/(mN\hat{\theta})$, where $N$ is the number of observations per period, and $\hat{\theta}$ is the estimate of the extremal index if cluster maxima are fitted, with $\hat{\theta} = 1$ otherwise. The value $N$ can be specified using the argument \verb+npp+. For example, if observations are recorded weekly and $\verb+npp+ = 52$, then $z_m$ is the $m$-year return level.
r-cran-evd-2.3-3/inst/doc/guide22.txt-954-If \verb+mper+ is \verb+Inf+, then $z_m$ is defined as the upper end point $u - \sigma/\xi$, and $\xi$ is then restricted to be negative.
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r-cran-evd-2.3-3/inst/doc/guide22.txt-1023-The first example given below produces maximum likelihood estimates for the (symmetric) logistic model.
r-cran-evd-2.3-3/inst/doc/guide22.txt:1024:The second example constrains the model at independence (where $\texttt{dep} = 1$).
r-cran-evd-2.3-3/inst/doc/guide22.txt-1025-The estimates produced in the second example are the same as those that would be produced if \verb+fgev+ was separately applied to each margin.
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r-cran-evd-2.3-3/inst/doc/guide22.txt-1067-%When the usual asymptotic properties do not hold the \verb+std.errors+ component will still be based on the inverse of the observed information matrix, but these values must be \emph{interpreted with caution} \citep{smit85}.
r-cran-evd-2.3-3/inst/doc/guide22.txt:1068:The value in the output labelled \verb+Dependence+ is the fitted estimate of $\chi = 2\{1-A(1/2)\} \in [0,1]$ \citep{coleheff99}, where $A(\cdot)$ denotes the dependence function \eqref{bvdepfn}. At independence $\chi = 0$, and at complete dependence $\chi = 1$.
r-cran-evd-2.3-3/inst/doc/guide22.txt-1069-
##############################################
r-cran-evd-2.3-3/inst/doc/guide22.txt-1532-\end{equation*}
r-cran-evd-2.3-3/inst/doc/guide22.txt:1533:where $\gamma=\gamma(y_1,y_2;\alpha,\beta)$ solves $(1-\alpha)y_1(1-\gamma)^\beta=(1-\beta)y_2\gamma^\alpha$.
r-cran-evd-2.3-3/inst/doc/guide22.txt-1534-The logistic model is obtained when $\alpha=\beta$.
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r-cran-evd-2.3-3/inst/doc/guide22.txt-1541-\end{equation*}
r-cran-evd-2.3-3/inst/doc/guide22.txt:1542:where $\gamma=\gamma(y_1,y_2;-\alpha_0,-\beta_0)$.
r-cran-evd-2.3-3/inst/doc/guide22.txt-1543-The negative logistic model is obtained when $\alpha_0=\beta_0$ (with $r = 1/\alpha_0 = 1/\beta_0$).
##############################################
r-cran-evd-2.3-3/inst/doc/guide22.txt-1563-\end{equation*}
r-cran-evd-2.3-3/inst/doc/guide22.txt:1564:where both $\alpha$ and $\alpha + 3\beta$ are non-negative, and where both $\alpha + \beta$ and $\alpha + 2\beta$ are less than or equal to one. These constraints imply that $\beta \in [-0.5,0.5]$ and $\alpha \in [0,1.5]$, though $\alpha$ can only be greater than one if $\beta$ is negative. The (symmetric) mixed model is obtained when $\beta = 0$. Complete dependence cannot be obtained. Independence is obtained when $\alpha = \beta = 0$.
r-cran-evd-2.3-3/inst/doc/guide22.txt-1565-
##############################################
r-cran-evd-2.3-3/R/nonpar.R-14- epdata <- apply(data, 2, rank, na.last = "keep")
r-cran-evd-2.3-3/R/nonpar.R:15: nasm <- apply(data, 2, function(x) sum(!is.na(x)))
r-cran-evd-2.3-3/R/nonpar.R-16- epdata <- epdata / rep(nasm+1, each = nrow(data))
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r-cran-evd-2.3-3/R/nonpar.R-294- data <- apply(data, 2, rank, na.last = "keep")
r-cran-evd-2.3-3/R/nonpar.R:295: nasm <- apply(data, 2, function(x) sum(!is.na(x)))
r-cran-evd-2.3-3/R/nonpar.R-296- data <- data / rep(nasm+1, each = nrow(data))
##############################################
r-cran-evd-2.3-3/vignettes/Multivariate_Extremes.Rnw-195-
r-cran-evd-2.3-3/vignettes/Multivariate_Extremes.Rnw:196:We now consider all the $1500$ observations on liability claims. We assume that the data are distributed according to the distribution function $F$, and we are interested in $F(z)$ where $z=(z_1,z_2)$ is in some sense large. The methods we use assume that $F$ is in the domain of attraction of some bivariate extreme value distribution $G$, and we focus on large data points to estimate features of $G$, and hence of $F(z)$ for large $z$.
r-cran-evd-2.3-3/vignettes/Multivariate_Extremes.Rnw-197-
r-cran-evd-2.3-3/vignettes/Multivariate_Extremes.Rnw:198:Typically we focus on points $z$ that lie above a certain threshold. The functions \texttt{tcplot} and \texttt{mrlplot} can be used for producing plots on each margin to help determine thresholds $u_1$ and $u_2$ for methods that focus primarily on points $z$ such that $z_1 > u_1$ and $z_2 > u_2$. Alternatively, the function \texttt{bvtcplot} can be used to help determine a single threshold $u^{*}$ for methods that focus on points $z$ such that $r(z) > u^{*}$, where $r(z) = x_1(z_1) + x_2(z_2)$, and $x_j(z_j) = -1/\log \hat{F}_j(z_j)$ for $j=1,2$ where $F_j$ is estimated empirically.
r-cran-evd-2.3-3/vignettes/Multivariate_Extremes.Rnw-199-
r-cran-evd-2.3-3/vignettes/Multivariate_Extremes.Rnw:200:Following Segers and Vandewalle (2004), a sensible choice for threshold $u^{*}$ might be found from Figure \ref{bvtc} by taking the $k$th largest $r(z)$, where $k$ is the largest value for which the y-axis is close to two. Figure \ref{bvtc} is plotted below using \texttt{bvtcplot}. The value of $k$ is returned invisibly. Setting \texttt{spectral = TRUE} uses the $k$th largest points to plot a nonparametric estimate of $H([0,\omega])$ where $H$ is the spectral measure of $G$.
r-cran-evd-2.3-3/vignettes/Multivariate_Extremes.Rnw-201-
##############################################
r-cran-evd-2.3-3/vignettes/Multivariate_Extremes.Rnw-217-\vspace{-1cm}
r-cran-evd-2.3-3/vignettes/Multivariate_Extremes.Rnw:218:\caption{A plot of $(k/n)r_{(n-k)}$ as a function of $k$, where $r_{(1)} \leq \dots \leq r_{(n)}$ are the ordered values of $r$. The y-axis provides an estimate of $H([0,1]) = 2$ for the spectral measure $H$ of $G$.}
r-cran-evd-2.3-3/vignettes/Multivariate_Extremes.Rnw-219-\label{bvtc}