cauchy(VGAM)
cauchy()所属R语言包：VGAM
Cauchy Distribution Family Function
柯西分布家庭功能
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Estimates either the location parameter or both the location and scale parameters of the Cauchy distribution by maximum likelihood estimation.
估计无论是位置参数的位置和规模的Cauchy分布的参数极大似然估计。
用法----------Usage----------
cauchy(llocation="identity", lscale="loge", elocation=list(),
escale=list(), ilocation=NULL, iscale=NULL,
iprobs = seq(0.2, 0.8, by=0.2),
imethod=1, nsimEIM=NULL, zero=2)
cauchy1(scale.arg=1, llocation="identity",
elocation=list(), ilocation=NULL, imethod=1)
参数----------Arguments----------
参数：llocation, lscale
Parameter link functions for the location parameter a and the scale parameter b. See Links for more choices.
参数链接的位置参数a和尺度参数b。见Links更多的选择。
参数：elocation, escale
List. Extra argument for each link. See earg in Links for general information.
列表。每一个环节的额外参数。见earg中Links的一般信息。
参数：ilocation, iscale
Optional initial value for a and b. By default, an initial value is chosen internally for each.
可选初始值a和b。默认情况下，选择的初始值，为每个内部。
参数：imethod
Integer, either 1 or 2 or 3. Initial method, three algorithms are implemented. The user should try all possible values to help avoid converging to a local solution. Also, choose the another value if convergence fails, or use ilocation and/or iscale.
整数，1或2或3。初始方法，算法的实现。用户应尽量收敛到本地的解决方案，以帮助避免所有可能的值。另外，选择另一个值，如果收敛失败，或使用“ilocation和/或iscale。
参数：iprobs
Probabilities used to find the respective sample quantiles; used to compute iscale.
用来找到各样本分位数的概率;，用于计算iscale。
参数：zero, nsimEIM
See CommonVGAMffArguments for more information.
见CommonVGAMffArguments更多信息。
参数：scale.arg
Known (positive) scale parameter, called b below.
（正）尺度参数，称为b下面。
Details
详细信息----------Details----------
The Cauchy distribution has density function
柯西分布的密度函数
where y and a are real and finite, and b>0. The distribution is symmetric about a and has a heavy tail. Its median and mode are a but the mean does not exist. The fitted values are the estimates of a. Fisher scoring is the default but if nsimEIM is specified then Fisher scoring with simulation is used.
y和a是真实的，有限的，和b>0。约a和分布是对称的，有一个沉重的尾巴。它的中位数和模式是a但平均不存在。拟合值的估计a。费舍尔得分是默认值，但，如果nsimEIM指定Fisher评分与仿真。
If the scale parameter is known (cauchy1) then there may be multiple local maximum likelihood solutions for the location parameter. However, if both location and scale parameters are to be estimated (cauchy) then there is a unique maximum likelihood solution provided n > 2 and less than half the data are located at any one point.
如果被称为尺度参数（cauchy1），则有可能是多个本地最大似然解决方案的位置参数。但是，如果位置与刻度参数进行估计（cauchy），那么有最大的可能性是一个独特的解决方案提供n > 2和不到一半的数据在任何一个点。
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 ----------
It is well-known that the Cauchy distribution may have local maxima in its likelihood function; make full use of imethod, ilocation, iscale etc.
这是众所周知，柯西分布可有局部最大似然函数，充分利用imethod，ilocation，iscale等
注意----------Note----------
Good initial values are needed. By default these VGAM family functions search for a starting value for a on a grid. It also pays to select a wide range of initial values via the ilocation and/or iscale and/or imethod arguments.
良好的初始值是必要的。默认情况下，这些VGAM家庭功能的起始值a在网格上搜索。这也要付出代价，通过ilocation和/或iscale和/或imethod参数的初始值选择范围广泛。
（作者）----------Author(s)----------
T. W. Yee
参考文献----------References----------
Statistical Distributions, New York: Wiley-Interscience, Third edition.
Evaluation of the maximum-likehood estimator where the likelihood equation has multiple roots. Biometrika, 53, 151–165.
On the unimodality of the likelihood for the Cauchy distribution. Biometrika, 62, 701–704.
Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information. Biometrika, 65, 457–481.
参见----------See Also----------
Cauchy, cauchit, studentt.
Cauchy，cauchit，studentt。
实例----------Examples----------
# Both location and scale parameters unknown[这两个位置和尺度参数未知]
cdata1 <- data.frame(x = runif(nn <- 1000))
cdata1 <- transform(cdata1, loc = exp(1+0.5*x), scale = exp(1))
cdata1 <- transform(cdata1, y = rcauchy(nn, loc, scale))
fit <- vglm(y ~ x, cauchy(lloc="loge"), cdata1, trace = TRUE)
coef(fit, matrix = TRUE)
head(fitted(fit)) # Location estimates[位置估计]
summary(fit)
# Location parameter unknown[位置参数未知]
set.seed(123)
cdata2 <- data.frame(x = runif(nn <- 500))
cdata2 <- transform(cdata2, loc = 1+0.5*x, scale = 0.4)
cdata2 <- transform(cdata2, y = rcauchy(nn, loc, scale))
fit <- vglm(y ~ x, cauchy1(scale = 0.4), cdata2, trace = TRUE, crit = "c")
coef(fit, matrix = TRUE)
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。
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发表于 2012-10-1 15:28:54
