freund61(VGAM)
freund61()所属R语言包：VGAM
Freund's (1961) Bivariate Extension of the Exponential Distribution
弗氏（1961）二元指数分布扩展
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Estimate the four parameters of the Freund (1961) bivariate extension of the exponential distribution by maximum likelihood estimation.
弗氏（1961）二元指数分布扩展的四个参数估计的最大似然估计。
用法----------Usage----------
freund61(la = "loge", lap = "loge", lb = "loge", lbp = "loge",
ea = list(), eap = list(), eb = list(), ebp = list(),
ia = NULL, iap = NULL, ib = NULL, ibp = NULL,
independent = FALSE, zero = NULL)
参数----------Arguments----------
参数：la,lap,lb,lbp,ea,eap,eb,ebp
Link functions and extra arguments applied to the (positive) parameters alpha, alpha', beta and beta', respectively (the “p” stands for “prime”). See Links for more choices.
链接功能和额外的参数（正）参数alpha，alpha'，beta和beta'“（”p“代表“素”）。见Links更多的选择。
参数：ia,iap,ib,ibp
Initial value for the four parameters respectively. The default is to estimate them all internally.
初始值的四个参数分别。默认值是内部估计他们所有。
参数：independent
Logical. If TRUE then the parameters are constrained to satisfy alpha=alpha' and beta=beta', which implies that y1 and y2 are independent and each have an ordinary exponential distribution.
逻辑。如果TRUE然后参数的约束，以满足alpha=alpha'和beta=beta'，这意味着y1和y2是独立的，每个人都有一个普通的指数分布。
参数：zero
An integer-valued vector specifying which linear/additive predictors are modelled as intercepts only. The values must be from the set {1,2,3,4}. The default is none of them.
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{1,2,3,4}。在默认情况下是没有。
Details
详细信息----------Details----------
This model represents one type of bivariate extension of the exponential distribution that is applicable to certain problems, in particular, to two-component systems which can function if one of the components has failed. For example, engine failures in two-engine planes, paired organs such as peoples' eyes, ears and kidneys. Suppose y1 and y2 are random variables representing the lifetimes of two components A and B in a two component system. The dependence between y1 and y2 is essentially such that the failure of the B component changes the parameter of the exponential life distribution of the A component from alpha to alpha', while the failure of the A component changes the parameter of the exponential life distribution of the B component from beta to beta'.
此模型代表一种类型的指数分布，这是适用于某些问题，尤其是，可以如果已失败的组件之一起作用的双组分系统的二元扩展。例如，双引擎飞机发动机故障，人民的眼睛，耳朵和肾脏等器官配对。假设y1和y2是随机变量，代表两个组件的寿命A和B在双组分体系。 y1和y2本质上是这样的依赖关系，失败的B成分的变化Aalpha组件的指数寿命分布的参数alpha'，而失败的A成分的变化从B组件betabeta'指数寿命分布的参数。
The joint probability density function is given by
的联合概率密度函数由下式给出
for 0 < y1 < y2, and
0 < y1 < y2，
for 0 < y2 < y1. Here, all four parameters are positive, as well as the responses y1 and y2. Under this model, the probability that component A is the first to fail is alpha/(alpha+beta). The time to the first failure is distributed as an exponential distribution with rate alpha+beta. Furthermore, the distribution of the time from first failure to failure of the other component is a mixture of Exponential(alpha') and Exponential(beta') with proportions beta/(alpha+beta) and alpha/(alpha+beta) respectively.
0 < y2 < y1。在这里，所有的四个参数是积极的，以及响应y1和y2。在这种模式下，该组件A是第一个失败的概率是alpha/(alpha+beta)。第一次失败的时间，分布的指数分布率alpha+beta。此外，分配的时间，从第一个故障的故障的另一组分是一种混合物的指数（alpha'）和指数（beta'）与比例beta/(alpha+beta)和alpha/(alpha+beta)分别。
The marginal distributions are, in general, not exponential. By default, the linear/additive predictors are eta1=log(alpha), eta2=log(alpha'), eta3=log(beta), eta4=log(beta').
的边缘分布，在一般情况下，是不是指数。默认情况下，线性/对添加剂的预测是eta1=log(alpha)，eta2=log(alpha')，eta3=log(beta)，eta4=log(beta')。
A special case is when alpha=alpha' and beta'=beta', which means that y1 and y2 are independent, and both have an ordinary exponential distribution with means 1/alpha and 1/beta respectively.
一个特殊情况是，当alpha=alpha'和beta'=beta'，这意味着这y1，和y2是独立的，有一个普通的指数分布与手段1/alpha 1/beta“。
Fisher scoring is used, and the initial values correspond to the MLEs of an intercept model. Consequently, convergence may take only one iteration.
Fisher评分被使用，并且初始值对应于极大似然估计的截距模型。因此，收敛可能只需要一次迭代。
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和vgam。
注意----------Note----------
To estimate all four parameters, it is necessary to have some data where y1<y2 and y2<y1.
估计所有四个参数，它需要有一些数据y1<y2和y2<y1。
The response must be a two-column matrix, with columns y1 and y2. Currently, the fitted value is a matrix with two columns; the first column has values (alpha'+beta)/(alpha' * (alpha+beta)) for the mean of y1, while the second column has values (beta'+alpha)/(beta' * (alpha+beta)) for the mean of y2. The variance of y1 is
响应必须是一个两列的矩阵，与列y1和y2。目前，拟合的值是一个具有两列的矩阵的第一列中的值(alpha'+beta)/(alpha' * (alpha+beta))为平均值y1，而第二列具有值(beta'+alpha)/(beta' * (alpha+beta))<X的平均值>。的方差y2
the variance of y2 is
的方差y2
the covariance of y1 and y2 is
y1和y2是协方差
（作者）----------Author(s)----------
T. W. Yee
参考文献----------References----------
A bivariate extension of the exponential distribution. Journal of the American Statistical Association, 56, 971–977.
参见----------See Also----------
exponential.
exponential。
实例----------Examples----------
fdata = data.frame(y1 = rexp(nn <- 200, rate = 4))
fdata = transform(fdata, y2 = rexp(nn, rate = 8))
fit = vglm(cbind(y1, y2) ~ 1, fam = freund61, fdata, trace = TRUE)
coef(fit, matrix = TRUE)
Coef(fit)
vcov(fit)
head(fitted(fit))
summary(fit)
# y1 and y2 are independent, so fit an independence model[y1和y2是独立的，所以适合独立模式]
fit2 = vglm(cbind(y1, y2) ~ 1, fam = freund61(indep = TRUE),
fdata, trace = TRUE)
coef(fit2, matrix = TRUE)
constraints(fit2)
pchisq(2 * (logLik(fit)-logLik(fit2)), # p-value[p-值]
df = df.residual(fit2) - df.residual(fit), lower.tail = FALSE)
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 15:35:06
