Fit the GP Distribution(POT)
Fit the GP Distribution()所属R语言包：POT
Fitting a GPD to Peaks Over a Threshold
峰拟合GPD超过阈值
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Maximum (Penalized) Likelihood, Unbiased Probability Weighted Moments,Biased Probability Weighted Moments, Moments, Pickands', Minimum Density Power Divergence, Medians, Likelihood Moment and Maximum Goodness-of-Fit Estimators to fit Peaks Over a
最大似然（受罚），偏概率加权矩的，片面的概率加权矩矩，Pickands“，密度最小的功率发散，中位数，似然矩和最大的善良卜估计，以适应峰值超过一个
用法----------Usage----------
fitgpd(data, threshold, est = "mle", ...)
参数----------Arguments----------
参数：data
A numeric vector.
一个数值向量。
参数：threshold
A numeric value giving the threshold for the GPD. The 'mle' estimator allows varying threshold; so that threshold could be for this case a numeric vector. Be careful, varying thresholds are used cyclically if length doesn't match with data.
给阈值的GPD的数值。 'mle'估计允许不同的阈值，阈值可以为这种情况下，数字矢量。要小心，循环使用不同的阈值，如果长度不匹配data。
参数：est
A string giving the names of the estimator. It can be 'mle' (the default), 'mple', 'moments', 'pwmu', 'pwmb', 'mdpd', 'med', 'pickands', 'lme' and 'mgf' for the maximum likelihood, maximum penalized likelihood, moments, unbiased probability weighted moments, biased probability weigthed moments, minimum density power divergence, medians, Pickands', likelihood moment and maximum goodness-of-fit estimators respectively.
一个字符串，它给估计的名字。它可以是'mle'（默认值），'mple'，'moments'，'pwmu'，'pwmb'，'mdpd'，'med'， 'pickands'，'lme'和'mgf'为最大似然法，最大的惩罚的可能性，时刻，公正概率加权矩，有偏见的可能性。轻量化的时刻，最小功率密度的分歧，中位数，Pickands“，可能性的时刻，最大的善良的拟合估计。
参数：...
Other optional arguments to be passed to the optim function, allow hand fixed parameters (only for the mle, mple and mgf estimators) or passed several options to specific estimators - see the Note section.
其他可选的的参数传递给optim功能，让手固定的参数（仅适用于mle，mple和mgf估计），或通过几个选项，具体的估计 - 见注部分。
值----------Value----------
This function returns a list with components: <table summary="R valueblock"> <tr valign="top"><td>fitted.values</td> <td> A vector containing the estimated parameters.</td></tr> <tr valign="top"><td>std.err</td> <td> A vector containing the standard errors.</td></tr> <tr valign="top"><td>fixed</td> <td> A vector containing the parameters of the model that have been held fixed.</td></tr> <tr valign="top"><td>param</td> <td> A vector containing all parameters (optimized and fixed).</td></tr> <tr valign="top"><td>deviance</td> <td> The deviance at the maximum likelihood estimates.</td></tr> <tr valign="top"><td>corr</td> <td> The correlation matrix.</td></tr> <tr valign="top"><td>convergence, counts, message</td> <td> Components taken from the list returned by optim - for the mle method.</td></tr> <tr valign="top"><td>threshold</td> <td> The threshold passed to argument threshold.</td></tr> <tr valign="top"><td>nat, pat</td> <td> The number and proportion of exceedances.</td></tr> <tr valign="top"><td>data</td> <td> The data passed to the argument data.</td></tr> <tr valign="top"><td>exceed</td> <td> The exceedances, or the maxima of the clusters of exceedances.</td></tr> <tr valign="top"><td>scale</td> <td> The scale parameter for the fitted generalized Pareto distribution.</td></tr> <tr valign="top"><td>std.err.type</td> <td> The standard error type - for 'mle' only. That is Observed or Expected Information matrix of Fisher.</td></tr> <tr valign="top"><td>var.thresh</td> <td> Logical. Specify if the threshold is a varying one - 'mle' only. For other methods, threshold is always constant i.e. var.thresh = FALSE.</td></tr> </table>
这个函数返回一个列表的组件：<table summary="R valueblock"> <tr valign="top"> <TD> fitted.values </ TD> <td>一个向量参数的估计。</ TD > </ TR> <tr valign="top"> <TD>std.err </ TD> <td>一个向量的标准误差。</ TD> </ TR> <TR VALIGN =“顶” > <TD> fixed </ TD> <td>一个向量的模式，已举办的参数固定的。</ TD> </ TR> <tr valign="top"> <TD> param </ TD> <TD>一个向量，包含所有参数（优化和修复）。</ TD> </ TR> <tr valign="top"> <TD> deviance</ TD> <TD>的最大似然估计的偏差。</ TD> </ TR> <tr valign="top"> <TD>corr</ TD> <TD>的相关性矩阵。</ TD> </ TR> <tr valign="top"> <TD> convergence, counts, message </ TD> <TD>组件从列表中返回的optim - mle方法。 / TD> </ TR> <tr valign="top"> <TD>threshold </ TD> <TD>的阈值传递给参数threshold。</ TD> </ TR> < TR VALIGN =“顶”> <TD>nat, pat </ TD> <TD>超标的数量和比例。</ TD> </ TR> <tr valign="top"> <TD> X> </ TD> <TD>的数据传递给该参数data。</ TD> </ TR> <tr valign="top"> <TD> data</ TD> <TD>超标，或聚类超标的最大值。</ TD> </ TR> <tr valign="top"> <TD>exceed </ TD> <TD>的规模参数广义帕累托分布的拟合。</ TD> </ TR> <tr valign="top"> <TD>scale </ TD> <TD>标准的错误类型 - std.err.type只。这是'mle'或Observed信息矩阵的费舍尔。</ TD> </ TR> <tr valign="top"> <TD> Expected</ TD> <TD>逻辑。指定如果阈值是不同的1 - var.thresh只。对于其它的方法，阈值始终是不变的，即'mle'。</ TD> </ TR> </表>
注意----------Note----------
The Maximum Likelihood estimator is obtained through a slightly modified version of Alec Stephenson's fpot.norm function in the evd package.
最大似然估计是通过略加修改的版本亚历克·斯蒂芬森的fpot.norm函数evd包。
For the 'mple' estimator, the likelihood function is penalized using the following function :
'mple'估计，似然函数，使用下面的函数处罚：
1)^alpha], if 0 < xi < 1, 0 if xi ≥ 1</i>
1）^α]，当0 <XI <1，0如果xi≥1 </ I>
The 'lme' estimator has a special parameter 'r'. Zhang (2007) shows that a value of -0.5 should be accurate in most of the cases. However, other values such as r < 0.5 can be explored. In particular, if r is approximatively equal to the opposite of the true shape parameter value, then the lme estimate is equivalent to the mle estimate.
'lme'估计有一个特殊的参数'r'。章（2007）表明，在大多数的情况下，应该是准确的值-0.5。但是，其他值如r < 0.5可以探索。特别是，如果r是近似相等的相反的真实形状参数值，然后lme估计相当于mle的估计。
The 'pwmb' estimator has special parameters 'a' and 'b'. These parameters are called the "plotting-position" values. Hosking and Wallis (1987) recommend the use of a = 0.35 and b = 0 (the default). However, different values can be tested.
'pwmb'估计有特殊参数'a'和'b'。这些参数被称为“绘图位置”值。霍斯和Wallis（1987）建议使用a = 0.35和b = 0（默认值）。然而，不同的值可以被测试。
For the 'pwmu' and 'pwmb' approaches, one can pass the option 'hybrid = TRUE' to use hybrid estimators as proposed by Dupuis and Tsao (1998). Hybrid estimators avoid to have no feasible points.
对于'pwmu'和'pwmb'的方法，人们可以通过选项“'hybrid = TRUE'使用杜普伊斯，曹（1998）所提出的混合估计。混合估计避免有没有可行的。
The mdpd estimator has a special parameter 'a'. This is a parameter of the "density power divergence". Juarez and Schucany (2004) recommend the use of a = 0.1, but any value of a such as a > 0 can be used (small values are recommend yet).
mdpd估计有一个特殊的参数'a'。这是一个参数的“密度功率发散”。 （2004年华雷斯和Schucany的）建议使用的a = 0.1，但任何价值的a如a > 0可以使用（小值还建议）。
The med estimator admits two extra arguments tol and maxit to control the "stopping-rule" of the optimization process.
med估计也承认两个额外的参数tol和maxit控制的优化过程中的“停止规则”。
The mgf approach uses goodness-of-fit statistics to estimate the GPD parameters. There are currently 8 different statitics: the Kolmogorov-Smirnov "KS", Cramer von Mises "CM", Anderson Darling "AD", right tail Anderson Darling "ADR", left tail Anderson Darling "ADL", right tail Anderson Darling (second degree) "AD2R", left tail Anderson Darling (second degree) "AD2L" and the Anderson Darling (second degree) "AD2" statistics.
mgf方法是使用适合的善良的统计信息来估计GPD参数。目前有8个不同的统计程序，柯尔莫哥洛夫 - 斯米尔诺夫"KS"，克莱姆·冯·米塞斯"CM"，安德森亲爱的"AD"，右侧尾部安德森亲爱的"ADR"，离开尾安德森亲爱的，"ADL"，右尾安德森亲爱的（第二级）"AD2R"，左尾安德森，达林（第二度）"AD2L"和安德森达林（第二级）"AD2"统计。
（作者）----------Author(s)----------
Mathieu Ribatet
参考文献----------References----------
Coles, S. (2001) An Introduction to Statistical Modelling of Extreme Values. Springer Series in Statistics. London.
Coles, S. and Dixon, M. (1999) Likelihood-Based Inference for Extreme Value Models. Extremes 2(1):5–23.
Dupuis, D. and Tsao (1998) M. A hybrid estimator for generalized Pareto and extreme-value distributions. Communications in Statistics-Theory and Methods 27:925–941.
Hosking, J. and Wallis, J. (1987) Parameters and Quantile Estimation for the Generalized Pareto Distribution. Technometrics 29:339–349.
Juarez, S. and Schucany, W. (2004) Robust and Efficient Estimation for the Generalized Pareto Distribution. Extremes 7:237–251.
Luceno, A. (2006) Fitting the generalized Pareto distribution to data using maximum goodness-of-fit estimators. Computational Statistics and Data Analysis 51:904–917.
Peng, L. and Welsh, A. (2001) Robust Estimation of the Generalized Pareto Distribution. Extremes 4:53–65.
Embrechts, P and Kluppelberg, C. and Mikosch, T (1997) Modelling Extremal Events for Insurance and Finance. Springers.
Pickands, J. (1975) Statistical Inference Using Extreme Order Statistics. Annals of Statistics. 3:119–131.
Zhang, J. (2007) Likelihood Moment Estimation for the Generalized Pareto Distribution. Australian and New Zealand Journal of Statistics. 49(1):69–77.
实例----------Examples----------
x <- rgpd(200, 1, 2, 0.25)
mle <- fitgpd(x, 1, "mle")$param
pwmu <- fitgpd(x, 1, "pwmu")$param
pwmb <- fitgpd(x, 1, "pwmb")$param
pickands <- fitgpd(x, 1, "pickands")$param ##Check if Pickands estimates[＃检查Pickands估计]
##are valid or not !!![＃是有效还是无效！]
med <- fitgpd(x, 1, "med", ##Sometimes the fitting algo is not[＃有时拟合算法是不]
start = list(scale = 2, shape = 0.25))$param ##accurate. So specify[＃准确。因此，指定]
##good starting values is[＃良好的初始值是]
##a good idea. [＃是一个好主意。]
mdpd <- fitgpd(x, 1, "mdpd")$param
lme <- fitgpd(x, 1, "lme")$param
mple <- fitgpd(x, 1, "mple")$param
ad2r <- fitgpd(x, 1, "mgf", stat = "AD2R")$param
print(rbind(mle, pwmu, pwmb, pickands, med, mdpd, lme,
mple, ad2r))
##Use PWM hybrid estimators[＃使用PWM混合估计]
fitgpd(x, 1, "pwmu", hybrid = FALSE)
##Now fix one of the GPD parameters[＃现在修复的GPD的参数之一]
##Only the MLE, MPLE and MGF estimators are allowed ![＃只有的MLE，MPLE和MGF估计是不允许的！]
fitgpd(x, 1, "mle", scale = 2)
fitgpd(x, 1, "mple", shape = 0.25)
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注：
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发表于 2012-9-24 07:05:56
