gev(VGAM)
gev()所属R语言包：VGAM
Generalized Extreme Value Distribution Family Function
广义极值分布的家庭功能
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Maximum likelihood estimation of the 3-parameter generalized extreme value (GEV) distribution.
最大似然估计的三参数广义极值分布（GEV）。
用法----------Usage----------
gev(llocation = "identity", lscale = "loge", lshape = "logoff",
elocation = list(), escale = list(),
eshape = if (lshape == "logoff") list(offset = 0.5) else
if (lshape == "elogit") list(min = -0.5, max = 0.5) else list(),
percentiles = c(95, 99), iscale=NULL, ishape = NULL,
imethod = 1, gshape=c(-0.45, 0.45), tolshape0 = 0.001,
giveWarning = TRUE, zero = 3)
egev(llocation = "identity", lscale = "loge", lshape = "logoff",
elocation = list(), escale = list(),
eshape = if (lshape == "logoff") list(offset = 0.5) else
if (lshape == "elogit") list(min = -0.5, max = 0.5) else list(),
percentiles = c(95, 99), iscale=NULL, ishape = NULL,
imethod = 1, gshape=c(-0.45, 0.45), tolshape0 = 0.001,
giveWarning = TRUE, zero = 3)
参数----------Arguments----------
参数：llocation, lscale, lshape
Parameter link functions for mu, sigma and xi respectively. See Links for more choices.
参数的链接功能，mu，sigma和xi分别。见Links更多的选择。
参数：elocation, escale, eshape
List. Extra argument for the respective links. See earg in Links for general information. For the shape parameter, if the logoff link is chosen then the offset is called A below; and then the linear/additive predictor is log(xi+A) which means that xi > -A. For technical reasons (see Details) it is a good idea for A = 0.5.
列表。额外的参数，相应的链接。见earg中Links的一般信息。对于的形状参数，如果logoff链接被选择，则偏移量被称为A下面;，然后线性/添加剂的预测是log(xi+A)这意味着xi > -A。由于技术上的原因（见详情），它是一个好主意，A = 0.5。
参数：percentiles
Numeric vector of percentiles used for the fitted values. Values should be between 0 and 100. However, if percentiles=NULL, then the mean mu + sigma * (gamma(1-xi)-1)/xi is returned, and this is only defined if xi<1.
用于拟合值的百分位数的数字矢量。值应该介于0和100之间。但是，如果percentiles=NULL，然后平均mu + sigma * (gamma(1-xi)-1)/xi是回来了，而这仅仅是定义，如果xi<1。
参数：iscale, ishape
Numeric. Initial value for sigma and xi. A NULL means a value is computed internally. The argument ishape is more important than the other two because they are initialized from the initial xi. If a failure to converge occurs, or even to obtain initial values occurs, try assigning ishape some value (positive or negative; the sign can be very important). Also, in general, a larger value of iscale is better than a smaller value.
数字。 sigma和xi的初始值。 ANULL是指在内部计算的值。参数ishape比其他两个更重要的是，因为它们是从最初的xi初始化。如果收敛失败时，或即使获得初始值时，尝试分配ishape一定的价值（正或负的符号是非常重要的）。另外，在一般情况中，一个较大的值iscale是优于一个较小的值。
参数：imethod
Initialization method. Either the value 1 or 2. Method 1 involves choosing the best xi on a course grid with endpoints gshape. Method 2 is similar to the method of moments. If both methods fail try using ishape.
初始化方法。无论的值1或2。方法1，选择最好的xi在电网与端点gshape。方法2是类似矩量法。如果两种方法都失败尝试使用ishape。
参数：gshape
Numeric, of length 2. Range of xi used for a grid search for a good initial value for xi. Used only if imethod equals 1.
数字，长度为2。范围的xi一格寻找一个好的初始值xi使用。仅用于如果imethod等于1。
参数：tolshape0, giveWarning
Passed into dgev when computing the log-likelihood.
传递到dgev计算对数似然。
参数：zero
An integer-valued vector specifying which linear/additive predictors are modelled as intercepts only. The values must be from the set {1,2,3} corresponding respectively to mu, sigma, xi. If zero=NULL then all linear/additive predictors are modelled as a linear combination of the explanatory variables. For many data sets having zero = 3 is a good idea.
指定一个整数值向量线性/添加剂的预测模型仅作为拦截。这些值必须是从集合{1,2,3}，分别对应于mu，sigma，xi。如果zero=NULL然后所有的线性/添加剂预测因子建模作为解释变量的线性组合。对于许多数据集有zero = 3是一个好主意。
Details
详细信息----------Details----------
The GEV distribution function can be written
GEV分布函数可以写成
where sigma > 0, -Inf < mu < Inf, and 1 + xi*(y-mu)/sigma > 0. Here, x_+ = max(x,0). The mu, sigma, xi are known as the location, scale and shape parameters respectively. The cases xi>0, xi<0, xi = 0 correspond to the Frechet, Weibull, and Gumbel types respectively. It can be noted that the Gumbel (or Type I) distribution accommodates many commonly-used distributions such as the normal, lognormal, logistic, gamma, exponential and Weibull.
sigma > 0，-Inf < mu < Inf和1 + xi*(y-mu)/sigma > 0。在这里，x_+ = max(x,0)。 mu，sigma，xi的位置，大小和形状参数分别被称为。的情况下，xi>0，xi<0，xi = 0对应的导数，韦伯，和Gumbel分布类型分别。它可以指出的是，耿贝尔（或I型）发行可容纳许多常用的如正常，对数正态分布，MF，伽玛值，指数分布和Weibull分布。
For the GEV distribution, the kth moment about the mean exists if xi < 1/k. Provided they exist, the mean and variance are given by mu + sigma { Gamma(1-xi)-1} / xi and sigma^2 { Gamma(1-2 xi) - Gamma^2 (1- xi) } / xi^2 respectively, where Gamma is the gamma function.
k阶矩的平均GEV分布，如果xi < 1/k。只要他们存在，均值和方差mu + sigma { Gamma(1-xi)-1} / xi和sigma^2 { Gamma(1-2 xi) - Gamma^2 (1- xi) } / xi^2，其中Gamma是伽玛函数。
Smith (1985) established that when xi > -0.5, the maximum likelihood estimators are completely regular. To have some control over the estimated xi try using lshape = "logoff" and the eshape=list(offset = 0.5), say, or lshape = "elogit" and eshape=list(min = -0.5, max = 0.5), say.
史密斯（1985年）成立，当xi > -0.5，极大似然估计是完全正规的。有一些的估计xi控制尝试使用lshape = "logoff"和eshape=list(offset = 0.5)，说，或lshape = "elogit"和eshape=list(min = -0.5, max = 0.5)“说。
值----------Value----------
An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm, and vgam.
类的一个对象"vglmff"（见vglmff-class）。该对象被用于建模功能，如vglm，vgam。
警告----------Warning ----------
Currently, if an estimate of xi is too close to zero then an error will occur for gev() with multivariate responses. In general, egev() is more reliable than gev().
目前，如果xi的估计是太接近零，那么错误将发生gev()多元反应。在一般情况下，egev()是更可靠的比gev()。
Fitting the GEV by maximum likelihood estimation can be numerically fraught. If 1 + xi*(y-mu)/sigma <= 0 then some crude evasive action is taken but the estimation process can still fail. This is particularly the case if vgam with s is used; then smoothing is best done with vglm with regression splines (bs or ns) because vglm implements half-stepsizing whereas vgam doesn't (half-stepsizing helps handle the problem of straying outside the parameter space.)
拟合GEV可以通过最大似然估计数值充满。如果1 + xi*(y-mu)/sigma <= 0然后一些原油的规避动作，但仍然无法估计过程。这是特别的情况下，如果vgams，然后平滑最好的做法是vglm的回归样条（bs或ns）的，因为vglm实现半stepsizing的，而vgam不（半stepsizing帮助处理问题的参数空间的偏离外）。
注意----------Note----------
The VGAM family function gev can handle a multivariate (matrix) response. If so, each row of the matrix is sorted into descending order and NAs are put last. With a vector or one-column matrix response using egev will give the same result but be faster and it handles the xi = 0 case. The function gev implements Tawn (1988) while egev implements Prescott and Walden (1980).
VGAM家庭函数gev可以处理多元（矩阵）的反应。如果是这样，该矩阵的每一行被分成降序和NAs的把最后。用向量或一列的矩阵使用egev会得到相同的结果，但速度更快，处理xi = 0情况下的响应。的功能gev实现Tawn（1988年），而egev实现普雷斯科特和Walden（1980），。
The shape parameter xi is difficult to estimate accurately unless there is a lot of data. Convergence is slow when xi is near -0.5. Given many explanatory variables, it is often a good idea to make sure zero = 3. The range restrictions of the parameter xi are not enforced; thus it is possible for a violation to occur.
形状参数xi是很难准确地估计，除非有大量的数据。当xi附近-0.5收敛速度很慢。鉴于许多解释变量，它通常是一个好主意，以确保zero = 3。的范围限制的参数xi不执行，因此这是可能的违反发生。
Successful convergence often depends on having a reasonably good initial value for xi. If failure occurs try various values for the argument ishape, and if there are covariates, having zero = 3 is advised.
成功的收敛往往取决于有一个相当不错的初始值xi。如果发生故障尝试不同的参数值ishape，如果有协变量，zero = 3建议。
（作者）----------Author(s)----------
T. W. Yee
参考文献----------References----------
Vector generalized linear and additive extreme value models. Extremes, 10, 1–19.
An extreme-value theory model for dependent observations. Journal of Hydrology, 101, 227–250.
Maximum likelihood estimation of the parameters of the generalized extreme-value distribution. Biometrika, 67, 723–724.
Maximum likelihood estimation in a class of nonregular cases. Biometrika, 72, 67–90.
参见----------See Also----------
rgev, gumbel, egumbel, guplot, rlplot.egev, gpd, frechet2, elogit, oxtemp, venice.
rgev，gumbel，egumbel，guplot，rlplot.egev，gpd，frechet2，elogit，oxtemp，venice。
实例----------Examples----------
# Multivariate example[多变量示例]
fit1 = vgam(cbind(r1, r2) ~ s(year, df = 3), gev(zero = 2:3),
venice, trace = TRUE)
coef(fit1, matrix = TRUE)
head(fitted(fit1))
## Not run: [＃不运行：]
par(mfrow=c(1,2), las = 1)
plot(fit1, se = TRUE, lcol = "blue", scol = "forestgreen",
main = "Fitted mu(year) function (centered)", cex.main = 0.8)
with(venice, matplot(year, y[,1:2], ylab = "Sea level (cm)", col = 1:2,
main = "Highest 2 annual sea levels", cex.main = 0.8))
with(venice, lines(year, fitted(fit1)[,1], lty = "dashed", col = "blue"))
legend("topleft", lty = "dashed", col = "blue", "Fitted 95 percentile")
## End(Not run)[＃（不执行）]
# Univariate example[单因素例如]
(fit = vglm(maxtemp ~ 1, egev, oxtemp, trace = TRUE))
head(fitted(fit))
coef(fit, matrix = TRUE)
Coef(fit)
vcov(fit)
vcov(fit, untransform = TRUE)
sqrt(diag(vcov(fit))) # Approximate standard errors[近似的标准误]
## Not run: rlplot(fit) [＃不运行：rlplot的（适合）]
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
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发表于 2012-10-1 15:36:49
