NegBinomial(stats)
NegBinomial()所属R语言包：stats
The Negative Binomial Distribution
负二项分布
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Density, distribution function, quantile function and random generation for the negative binomial distribution with parameters size and prob.
密度分布函数，分位数函数和随机生成的负二项分布参数size和prob。
用法----------Usage----------
dnbinom(x, size, prob, mu, log = FALSE)
pnbinom(q, size, prob, mu, lower.tail = TRUE, log.p = FALSE)
qnbinom(p, size, prob, mu, lower.tail = TRUE, log.p = FALSE)
rnbinom(n, size, prob, mu)
参数----------Arguments----------
参数：x
vector of (non-negative integer) quantiles.
矢量（非负整数）位数。
参数：q
vector of quantiles.
位数的向量。
参数：p
vector of probabilities.
概率向量。
参数：n
number of observations. If length(n) > 1, the length is taken to be the number required.
观测数。如果length(n) > 1，长度是所需的数量。
参数：size
target for number of successful trials, or dispersion parameter (the shape parameter of the gamma mixing distribution). Must be strictly positive, need not be integer.
试验取得成功，或分散的目标参数（伽玛混合分布的形状参数）。必须严格正，不必为整数。
参数：prob
probability of success in each trial. 0 < prob <= 1.
在每次试验成功的概率。 0 < prob <= 1。
参数：mu
alternative parametrization via mean: see "Details".
替代参数化通过的意思是：看到“详细资料”。
参数：log, log.p
logical; if TRUE, probabilities p are given as log(p).
逻辑;如果为TRUE，概率P日志（P）。
参数：lower.tail
logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x].
逻辑;如果是TRUE（默认），概率P[X ≤ x]，否则，“P[X > x]。
Details
详情----------Details----------
The negative binomial distribution with size = n and prob = p has density
size= n和prob= p有密度的负二项分布
for x = 0, 1, 2, …, n > 0 and 0 < p ≤ 1.
x = 0, 1, 2, …，n > 0和0 < p ≤ 1。
This represents the number of failures which occur in a sequence of Bernoulli trials before a target number of successes is reached. The mean is n(1-p)/p and variance n(1-p)/p^2.
这代表伯努利试验序列中的故障发生之前，一个成功的目标数量达到数。平均n(1-p)/p和方差n(1-p)/p^2。
A negative binomial distribution can also arise as a mixture of Poisson distributions with mean distributed as a gamma distribution (seepgamma) with scale parameter (1 - prob)/prob and shape parameter size. (This definition allows non-integer values of size.)
负二项分布也出现与平均分布为伽玛分布的泊松分布的混合物（见pgamma）规模参数(1 - prob)/prob和形状参数size。 （这个定义允许非整数的值size）。
An alternative parametrization (often used in ecology) is by the mean mu, and size, the dispersion parameter, where prob = size/(size+mu). The variance is mu + mu^2/size in this parametrization.
另一种参数化（通常是在生态环境中使用）是由平均mu，size，色散参数，其中prob=size/(size+mu)。方差是mu + mu^2/size在这个参数化。
If an element of x is not integer, the result of dnbinom is zero, with a warning.
如果一个元素x是不是整数，结果“dnbinom是零，警告。
The quantile is defined as the smallest value x such that F(x) ≥ p, where F is the distribution function.
位数被定义为最小的值x等F(x) ≥ p，其中F是分布函数。
值----------Value----------
dnbinom gives the density, pnbinom gives the distribution function, qnbinom gives the quantile function, and rnbinom generates random deviates.
dnbinom给人的密度，pnbinom给出了分布函数，qnbinom给人的分量功能，rnbinom产生随机的偏离。
Invalid size or prob will result in return value NaN, with a warning.
无效size或prob将导致返回值NaN警告。
源----------Source----------
dnbinom computes via binomial probabilities, using code contributed by Catherine Loader (see dbinom).
dnbinom通过二项式概率计算，使用由凯瑟琳装载机贡献的代码（见dbinom）。
pnbinom uses pbeta.
pnbinom使用pbeta的。
qnbinom uses the Cornish–Fisher Expansion to include a skewness correction to a normal approximation, followed by a search.
qnbinom使用康沃尔-Fisher展开，包括偏校正到正常的逼近，搜索。
rnbinom uses the derivation as a gamma mixture of Poissons, see
rnbinom使用伽玛混合的泊松推导，见
Devroye, L. (1986) Non-Uniform Random Variate Generation. Springer-Verlag, New York. Page 480.
devroye，L.（1986）非均匀随机变量生成。施普林格出版社，纽约。页480。
参见----------See Also----------
Distributions for standard distributions, including dbinom for the binomial, dpois for the Poisson and dgeom for the geometric distribution, which is a special case of the negative binomial.
为标准的分布，包括分布dbinom二项式，dpois泊松和dgeom几何分布，这是一个负二项分布的特例。
举例----------Examples----------
require(graphics)
x <- 0:11
dnbinom(x, size = 1, prob = 1/2) * 2^(1 + x) # == 1[== 1]
126 / dnbinom(0:8, size = 2, prob = 1/2) #- theoretically integer[ - 理论上的整数]
## Cumulative ('p') = Sum of discrete prob.s ('d'); Relative error :[＃累积（P）= SUM的离散prob.s（D）;相对误差：]
summary(1 - cumsum(dnbinom(x, size = 2, prob = 1/2)) /
pnbinom(x, size = 2, prob = 1/2))
x <- 0:15
size <- (1:20)/4
persp(x,size, dnb <- outer(x, size, function(x,s) dnbinom(x,s, prob= 0.4)),
xlab = "x", ylab = "s", zlab="density", theta = 150)
title(tit <- "negative binomial density(x,s, pr = 0.4) vs. x & s")
image (x,size, log10(dnb), main= paste("log [",tit,"]"))
contour(x,size, log10(dnb),add=TRUE)
## Alternative parametrization[＃替代参数化]
x1 <- rnbinom(500, mu = 4, size = 1)
x2 <- rnbinom(500, mu = 4, size = 10)
x3 <- rnbinom(500, mu = 4, size = 100)
h1 <- hist(x1, breaks = 20, plot = FALSE)
h2 <- hist(x2, breaks = h1$breaks, plot = FALSE)
h3 <- hist(x3, breaks = h1$breaks, plot = FALSE)
barplot(rbind(h1$counts, h2$counts, h3$counts),
beside = TRUE, col = c("red","blue","cyan"),
names.arg = round(h1$breaks[-length(h1$breaks)]))
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
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发表于 2012-2-16 18:59:57
