gengamma(VGAM)
gengamma()所属R语言包：VGAM
Generalized Gamma distribution family function
广义伽玛分布族的功能
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Estimation of the 3-parameter generalized gamma distribution proposed by Stacy (1962).
由Stacy（1962）提出的三参数广义伽玛分布的估计。
用法----------Usage----------
gengamma(lscale = "loge", ld = "loge", lk = "loge",
escale = list(), ed = list(), ek = list(),
iscale = NULL, id = NULL, ik = NULL, zero = NULL)
参数----------Arguments----------
参数：lscale, ld, lk
Parameter link function applied to each of the positive parameters b, d and k, respectively. See Links for more choices.
参数链接功能适用于每一个积极的参数b，d和k，分别。见Links更多的选择。
参数：escale, ed, ek
List. Extra argument for each of the links. See earg in Links for general information.
列表。每个环节的额外参数。见earg中Links的一般信息。
参数：iscale, id, ik
Initial value for b, d and k, respectively. The defaults mean an initial value is determined internally for each.
b，d和k，分别的初始值。默认的初始值确定为每个内部。
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}. The default value means none are modelled as intercept-only terms. See CommonVGAMffArguments for more information.
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}。默认值是指没有被建模为仅截距。见CommonVGAMffArguments更多信息。
Details
详细信息----------Details----------
The probability density function can be written
的概率密度函数可以写成
for scale parameter b > 0, and d > 0, k > 0, and y > 0. The mean of Y is b*k (returned as the fitted values).
为尺度参数b > 0，d > 0，k > 0和y > 0。平均Y是b*k（返回的拟合值）。
There are many special cases, as given in Table 1 of Stacey and Mihram (1965). In the following, the parameters are in the order b,d,k. The special cases are: Exponential f(y;b,1,1), Gamma f(y;b,1,k), Weibull f(y;b,d,1), Chi Squared f(y;2,1,a/2) with a degrees of freedom, Chi f(y;sqrt(2),2,a/2) with a degrees of freedom, Half-normal f(y;sqrt(2),2,1/2), Circular normal f(y;sqrt(2),2,1), Spherical normal f(y;sqrt(2),2,3/2), Rayleigh f(y;c sqrt(2),2,1) where c>0.
有许多特殊的情况下，如表1中给出的斯泰西和Mihram的（1965）。在下文中，该参数是在顺序b,d,k。特殊情况是：指数f(y;b,1,1)，伽玛f(y;b,1,k)，韦伯f(y;b,d,1)，卡方f(y;2,1,a/2)a自由度，智f(y;sqrt(2),2,a/2) a自由度，半正常f(y;sqrt(2),2,1/2)，圆形的正常f(y;sqrt(2),2,1)，球形普通的f(y;sqrt(2),2,3/2)，瑞利f(y;c sqrt(2),2,1)c>0。
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 ----------
Several authors have considered maximum likelihood estimation for the generalized gamma distribution and have found that the Newton-Raphson algorithm does not work very well and that the existence of solutions to the log-likelihood equations is sometimes in doubt. Although Fisher scoring is used here, it is likely that the same problems will be encountered. It appears that large samples are required, for example, the estimator of k became asymptotically normal only with 400 or more observations. It is not uncommon for maximum likelihood estimates to fail to converge even with two or three hundred observations. With covariates, even more observations are needed to increase the chances of convergence.
一些作者认为广义伽玛分布的最大似然估计，并已发现的牛顿 - 拉夫逊算法不很好地工作的解决方案，以对数似然方程的存在有时是毋庸置疑的。虽然这里使用的是Fisher评分，则很可能会遇到同样的问题。似乎是必需的，例如，大样本估计k成为只具有400或更多的观测渐近正常。这是不寻常的最大似然估计无法收敛甚至两三百元的意见。随着协变量，甚至更多的观测是必要的衔接，以增加成功的机会。
注意----------Note----------
The notation used here differs from Stacy (1962) and Prentice (1974). Poor initial values may result in failure to converge so if there are covariates and there are convergence problems, try using the zero argument (e.g., zero = 2:3) or the ik argument.
这里所用的符号不同于斯泰西（1962）和Prentice（1974）。差的初始值，可能会导致收敛失败，所以如果有协变量和有收敛的问题，请尝试使用zero参数（例如，zero = 2:3）ik参数。
（作者）----------Author(s)----------
T. W. Yee
参考文献----------References----------
A generalization of the gamma distribution. Annals of Mathematical Statistics, 33, 1187–1192.
Parameter estimation for a generalized gamma distribution. Technometrics, 7, 349–358.
A log gamma model and its maximum likelihood estimation. Biometrika, 61, 539–544.
参见----------See Also----------
rgengamma, gamma1, gamma2, prentice74.
rgengamma，gamma1，gamma2，prentice74。
实例----------Examples----------
k = exp(-1); Scale = exp(1)
gdata = data.frame(y = rgamma(1000, shape = k, scale = Scale))
fit = vglm(y ~ 1, gengamma, gdata, trace = TRUE)
coef(fit, matrix = TRUE)
# Another example[另一个例子]
gdata = data.frame(x = runif(nn <- 5000))
gdata = transform(gdata, Scale = exp(1), d = exp(0 + 1.2*x),
k = exp(-1 + 2*x))
gdata = transform(gdata, y = rgengamma(nn, scale = Scale, d = d, k = k))
fit = vglm(y ~ x, gengamma(zero = 1, iscale = 6), gdata, trace = TRUE)
fit = vglm(y ~ x, gengamma(zero = 1), gdata, trace = TRUE, maxit = 50)
coef(fit, matrix = TRUE)
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注：
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发表于 2012-10-1 15:36:03
