Benford(VGAM)
Benford()所属R语言包：VGAM
Benford's Distribution
本福德的分布
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 Benford's distribution.
密度，分布函数，本福德分布的分位数函数，随机生成的。
用法----------Usage----------
dbenf(x, ndigits = 1, log = FALSE)
pbenf(q, ndigits = 1, log.p = FALSE)
qbenf(p, ndigits = 1)
rbenf(n, ndigits = 1)
参数----------Arguments----------
参数：x, q
Vector of quantiles. See ndigits.
向量的位数。见ndigits。
参数：p
vector of probabilities.
向量的概率。
参数：n
number of observations. A single positive integer. Else if length(n) > 1 then the length is taken to be the number required.
若干意见。一个正整数。否则，如果length(n) > 1的长度是所需的数量。
参数：ndigits
Number of leading digits, either 1 or 2. If 1 then the support of the distribution is {1,...,9}, else {10,...,99}.
领先的数字数，1或2。如果为1，然后分布的支持是{1，...，9}，{10，...，99}。
参数：log, log.p
Logical. If log.p = TRUE then all probabilities p are given as log(p).
逻辑。如果log.p = TRUE然后所有的概率p是log(p)。
Details
详细信息----------Details----------
Benford's Law (aka the significant-digit law) is the empirical observation that in many naturally occuring tables of numerical data, the leading significant (nonzero) digit is not uniformly distributed in 1:9. Instead, the leading significant digit (=D, say) obeys the law
本福德“（又名的有效位数法）的经验观察，在许多自然产生的数字数据的表，领先的显着性（非零）数字并非均匀分布在1:9。相反，领先的有效位数（=D，说的）守法
for d=1,…,9. This means the probability the first significant digit is 1 is approximately 0.301, etc.
d=1,…,9。这意味着第一个显着的数字是1的概率是大约0.301等
Benford's Law was apparently first discovered in 1881 by astronomer/mathematician S. Newcombe. It started by the observation that the pages of a book of logarithms were dirtiest at the beginning and progressively cleaner throughout. In 1938, a General Electric physicist called F. Benford rediscovered the law on this same observation. Over several years he collected data from different sources as different as atomic weights, baseball statistics, numerical data from Reader's Digest, and drainage areas of rivers.
本福德“显然是首次发现于1881年由天文学家/数学家S.纽康。由观察开始，对数的一本书的页面是最脏的开始，并逐步清洁整个。 1938年，通用电气的物理学家名为F.福德的重新发现法律在此相同的观察。在过去几年中，他收集了来自不同数据源的数据为不同的原子量，棒球统计数据，数值数据“读者文摘”，以及对河流的流域面积。
Applications of Benford's Law has been as diverse as to the area of fraud detection in accounting and the design computers.
本福德定律的应用已经作为不同的会计欺诈检测和设计电脑的区域。
值----------Value----------
dbenf gives the density, pbenf gives the distribution function, and qbenf gives the quantile function, and rbenf generates random deviates.
dbenf给出了密度，pbenf给出了分布函数，qbenf给分位数的功能，和rbenf随机产生的偏离。
（作者）----------Author(s)----------
T. W. Yee
参考文献----------References----------
The Law of Anomalous Numbers. Proceedings of the American Philosophical Society, 78, 551–572.
Note on the Frequency of Use of the Different Digits in Natural Numbers. American Journal of Mathematics, 4, 39–40.
实例----------Examples----------
dbenf(x <- c(0:10, NA, NaN, -Inf, Inf))
pbenf(x)
## Not run: [＃不运行：]
xx = 1:9; # par(mfrow=c(2,1))[面值（mfrow = C（2,1））]
barplot(dbenf(xx), col = "lightblue", las = 1, xlab = "Leading digit",
ylab = "Probability", names.arg = as.character(xx),
main = paste("Benford's distribution", sep = ""))
hist(rbenf(n = 1000), border = "blue", prob = TRUE,
main = "1000 random variates from Benford's distribution",
xlab = "Leading digit", sub="Red is the true probability",
breaks = 0:9 + 0.5, ylim = c(0, 0.35), xlim = c(0, 10.0))
lines(xx, dbenf(xx), col = "red", type = "h")
points(xx, dbenf(xx), col = "red")
## End(Not run)[＃（不执行）]
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 15:25:25
