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R语言 smoothtail包 smoothtail-package()函数中文帮助文档(中英文对照)

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发表于 2012-9-30 10:34:13 | 显示全部楼层 |阅读模式
smoothtail-package(smoothtail)
smoothtail-package()所属R语言包:smoothtail

                                        Smooth Estimation of GPD Shape Parameter
                                         GPD形状参数的平滑估计

                                         译者:生物统计家园网 机器人LoveR

描述----------Description----------

Given independent and identically distributed observations X_1 < &hellip; < X_n from a  Generalized Pareto distribution with shape parameter &gamma; \in [-1,0], this package offers three  methods to compute estimates of &gamma;. The estimates are based on the principle of replacing the order  statistics X_{(1)}, &hellip;, X_{(n)} of the sample by quantiles \hat X_{(1)}, &hellip;, \hat X_{(n)} of the distribution function \hat F_n based on the  log&ndash;concave density estimator \hat f_n. This procedure is justified by the fact that the GPD density is
鉴于独立同分布的观测X_1 < &hellip; < X_n从广义帕累托分布形状参数&gamma; \in [-1,0]的,这个包提供了三种方法计算估计&gamma;。的估计是基于更换次序统计量的原则,X_{(1)}, &hellip;, X_{(n)}的样品位数\hat X_{(1)}, &hellip;, \hat X_{(n)}的分布函数\hat F_n的基础上对数凹密度估计\hat f_n。本程序是合理的的的GPD密度是一个事实,即


Details

详细信息----------Details----------

Package:
包装方式:

</td><td align="left"> smoothtail
</ TD> <TD ALIGN="LEFT"> smoothtail

Type:
类型:

</td><td align="left"> Package
</ TD> <TD ALIGN="LEFT">包装

Version:
版本:

</td><td align="left"> 2.0.1
</ TD> <TD ALIGN="LEFT"> 2.0.1

Date:
日期:

</td><td align="left"> 2011-11-29
</ TD> <TD ALIGN="LEFT"> 2011-11-29

License:
许可:

</td><td align="left"> GPL (>=2)
</ TD> <TD ALIGN="LEFT"> GPL(> = 2)

Use this package to estimate the shape parameter &gamma; of a Generalized Pareto Distribution (GPD). In  extreme value theory, &gamma; is denoted tail index. We offer three new estimators, all based on the fact  that the density function of the GPD is log&ndash;concave if &gamma; \in [-1,0], see Mueller and Rufibach (2009).  The functions for estimation of the tail index are:
用这个包来估计形状参数&gamma;的广义Pareto分布(GPD)。在极值理论,&gamma;表示尾部指数。我们提供了三种新的估计,所有的GPD的密度函数是对数凹的事实,如果&gamma; \in [-1,0],看到穆勒和Rufibach的(2009)的基础上。功能的尾部指数的估计是:

pickands <br> falk<br> falkMVUE<br> generalizedPick
pickands参考falk参考falkMVUE参考generalizedPick

This package depends on the package logcondens for estimation of a log&ndash;concave density: all the above functions take as first argument a dlc object as generated by logConDens in logcondens.
这个软件包依赖于包logcondens的log凹密度:估计所有上述功能需要一个dlc对象作为第一个参数所产生的logConDens中logcondens。

Additionally, functions for density, distribution function, quantile function and random number generation for a GPD with location parameter 0, shape parameter &gamma; and scale parameter &sigma; are provided:
此外,功能密度,分布函数,分位数函数和随机数生成的GPD的位置参数,形状参数&gamma;和规模参数&sigma;提供:

dgpd<br> pgpd<br> qgpd<br> rgpd.
dgpd参考pgpd参考qgpd参考rgpd。

Let us shortly clarify what we mean with log&ndash;concave density estimation. Suppose we are given an ordered sample Y_1 < &hellip; < Y_n of i.i.d. random variables having density function f, where f = \exp \varphi for a concave function \varphi : [-&infin;, &infin;) \to R. Following the development in  Duembgen and Rufibach (2009), it is then possible to get an estimator \hat f_n = \exp \hat \varphi_n  of f via the maximizer \hat \varphi_n of
让我们在短期内澄清我们的意思log凹密度估计。假定我们有一个有序的样品Y_1 < &hellip; < Y_n独立同分布随机变量的密度函数f,其中f = \exp \varphi的凹函数\varphi : [-&infin;, &infin;) \to R。继发展在Duembgen和Rufibach(2009年),它是那么可能得到的估计\hat f_n = \exp \hat \varphi_nf通过最大化\hat \varphi_n

over all concave functions \varphi. It turns out that \hat \varphi_n is piecewise linear, with  knots only at (some of the) observation points. Therefore, the infinite-dimensional optimization problem of finding  the function \hat \varphi_n boils down to a finite dimensional problem of finding the vector (\hat \varphi_n(Y_1),&hellip;,\hat \varphi(Y_n)).  How to solve this problem is described in Rufibach (2006, 2007) and in a more general setting in Duembgen, Huesler, and Rufibach (2010). The distribution function based on \hat f_n is defined as
以上所有凹函数\varphi。事实证明,这\hat \varphi_n是分段线性的,只在一些观测点与结。因此,无限维的优化问题,发现的功能\hat \varphi_n归结为一个有限维问题寻找向量(\hat \varphi_n(Y_1),&hellip;,\hat \varphi(Y_n))。如何解决这个问题的描述Rufibach(2006年,2007年),在一般设置在Duembgen,Huesler,并Rufibach的(2010)。分布函数的基础上\hat f_n被定义为

for x a real number. The definition of \hat F_n is justified by the fact that \hat F_n(Y_1) = 0.
x一个实数。 \hat F_n的事实,\hat F_n(Y_1) = 0是有道理的。


(作者)----------Author(s)----------



Kaspar Rufibach (maintainer), <a href="mailto:kaspar.rufibach@gmail.com">kaspar.rufibach@gmail.com</a> , <br> <a href="http://www.kasparrufibach.ch">http://www.kasparrufibach.ch</a>

Samuel Mueller, <a href="mailto:s.mueller@maths.usyd.edu.au">s.mueller@maths.usyd.edu.au</a>, <br> <a href="http://www.maths.usyd.edu.au/ut/people?who=S_Mueller">http://www.maths.usyd.edu.au/ut/people?who=S_Mueller</a>

Kaspar Rufibach acknowledges support by the Swiss National Science Foundation SNF, <a href="http://www.snf.ch">http://www.snf.ch</a>




参考文献----------References----------

Maximum likelihood estimation of a log&ndash;concave density and its distribution function: basic properties and uniform consistency.  Bernoulli, 15(1), 40&ndash;68.  
Active set and EM algorithms for log-concave densities based on complete and censored data. Technical report 61, IMSV, Univ. of Bern, available at http://arxiv.org/abs/0707.4643.
Smooth tail index estimation. J. Stat. Comput. Simul., 79, 1155&ndash;1167.
On the max&ndash;domain of attraction of distributions with log&ndash;concave densities. Statist. Probab. Lett., 78, 1440&ndash;1444.
PhD Thesis, University of Bern, Switzerland and Georg-August University of Goettingen, Germany, 2006. <br> Available at http://www.stub.unibe.ch/download/eldiss/06rufibach_k.pdf.
Computing maximum likelihood estimators of a log-concave density function. J. Stat. Comput. Simul., 77, 561&ndash;574.

参见----------See Also----------

Package logcondens.
包装logcondens。


实例----------Examples----------


# generate ordered random sample from GPD[形成有序的随机抽样GPD]
set.seed(1977)
n <- 20
gam <- -0.75
x <- rgpd(n, gam)

# compute known endpoint[计算已知端点]
omega <- -1 / gam

# estimate log-concave density, i.e. generate dlc object[估计数凹密度,即产生DLC对象]
est <- logConDens(x, smoothed = FALSE, print = FALSE, gam = NULL, xs = NULL)

# plot distribution functions[图分布函数]
s <- seq(0.01, max(x), by = 0.01)
plot(0, 0, type = 'n', ylim = c(0, 1), xlim = range(c(x, s))); rug(x)
lines(s, pgpd(s, gam), type = 'l', col = 2)
lines(x, 1:n / n, type = 's', col = 3)
lines(x, est$Fhat, type = 'l', col = 4)
legend(1, 0.4, c('true', 'empirical', 'estimated'), col = c(2 : 4), lty = 1)

# compute tail index estimators for all sensible indices k[计算尾部指数估计,所有敏感指数K表]
falk.logcon <- falk(est)
falkMVUE.logcon <- falkMVUE(est, omega)
pick.logcon <- pickands(est)
genPick.logcon <- generalizedPick(est, c = 0.75, gam0 = -1/3)

# plot smoothed and unsmoothed estimators versus number of order statistics[图平滑和平滑的估计与顺序统计数]
plot(0, 0, type = 'n', xlim = c(0,n), ylim = c(-1, 0.2))
lines(1:n, pick.logcon[, 2], col = 1); lines(1:n, pick.logcon[, 3], col = 1, lty = 2)
lines(1:n, falk.logcon[, 2], col = 2); lines(1:n, falk.logcon[, 3], col = 2, lty = 2)
lines(1:n, falkMVUE.logcon[,2], col = 3); lines(1:n, falkMVUE.logcon[,3], col = 3,
    lty = 2)
lines(1:n, genPick.logcon[, 2], col = 4); lines(1:n, genPick.logcon[, 3], col = 4,
    lty = 2)
abline(h = gam, lty = 3)
legend(11, 0.2, c("Pickands", "Falk", "Falk MVUE", "Generalized Pickands'"),
    lty = 1, col = 1:8)

转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。


注:
注1:为了方便大家学习,本文档为生物统计家园网机器人LoveR翻译而成,仅供个人R语言学习参考使用,生物统计家园保留版权。
注2:由于是机器人自动翻译,难免有不准确之处,使用时仔细对照中、英文内容进行反复理解,可以帮助R语言的学习。
注3:如遇到不准确之处,请在本贴的后面进行回帖,我们会逐渐进行修订。
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