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as.prob <- function(weight){ | |
return(weight/sum(weight)) | |
} | |
expt.comp <- function(input){ | |
n <- length(input) | |
g <- function(i,n,input){ | |
(-1)**(n-1-i)*1/(1-apply(combn(input,i),2,sum)) | |
} | |
tmp <- sapply(seq(0,n-1),function(i){ |
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sapply(seq(1,50),function(n){ n*harmonic(n) }) | |
[1] [2] [3] [4] [5] | |
[1] 1.000000 3.000000 5.500000 8.333333 11.416667 | |
[2] 14.700000 18.150000 21.742857 25.460714 29.289683 | |
[3] 33.218651 37.238528 41.341739 45.521873 49.773435 | |
[4] 54.091664 58.472393 62.911945 67.407053 71.954793 | |
[5] 76.552533 81.197892 85.888705 90.622996 95.398954 | |
[6] 100.214913 105.069332 109.960789 114.887960 119.849614 | |
[7] 124.844601 129.871846 134.930341 140.019140 145.137350 |
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harmonic <- function(n){ | |
sum(sapply(seq(1,n),function(n){ return(1/n) })) | |
} | |
res <- 44*harmonic(44) # res = 192.399 |
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# hand calculation での注意:二項分布の同等性検定は2×2の分割表によるχ^2検定に等しいのでそちらの計算方法を採用。 | |
# Q1.はサンプル数が少ないのでイェツの補正を行っている。 | |
###################################### | |
# Q1. | |
# Head Tail S | |
# A 4 6 10 | |
# B 6 4 10 | |
# S 10 10 20 | |
# |
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> calc.p <- function(n) { rbinom(1,n,1/2)/n } # n回試行での表の出る確率 | |
> x <- seq(1,1000) | |
> y <- sapply(x, calc.p) | |
> x | |
[1] 1 2 3 4 5 6 7 8 9 10 | |
... | |
[995] 995 996 997 998 999 1000 | |
> y | |
[1] 1.0000000 0.5000000 1.0000000 0.7500000 0.6000000 | |
... |
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# 10回のコイン投げを100セット繰り返したときの,表の出た回数の分布。 | |
> n <- 10; x <- seq(0,10); set <- 100; | |
> hist(rbinom(set,n,0.5), breaks=x, probability=TRUE, xlab='set=100,n=10') | |
> lines(x, dnorm(x, n/2, sqrt(n*0.5*0.5)), col="red") | |
# 20回のコイン投げを100セット繰り返したときの,表の出た回数の分布。 | |
> n <- 20; x <- seq(0,20); set <- 100; | |
> hist(rbinom(set,n,0.5), breaks=x, probability=TRUE, xlab='set=100,n=10') | |
> lines(x, dnorm(x, n/2, sqrt(n*0.5*0.5)), col="red") |
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# Normal Distiribution | |
# Sequence between -4 and 4 with 0.1 steps | |
x <- seq(-4, 4, 0.1) | |
# Plot an empty chart with tight axis boundaries, and axis lines on bottom and left | |
plot(x, type="n", xaxs="i", yaxs="i", xlim=c(-4, 4), ylim=c(0, 0.4), | |
bty="l", xaxt="n", xlab="z-value", ylab="probability density") | |
# Function to plot each coloured portion of the curve, between "a" and "b" as a | |
# polygon; the function "dnorm" is the normal probability density function |
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> samples <- rnorm(100) | |
> table(round(samples)) | |
-3 -2 -1 0 1 2 3 | |
1 4 26 36 25 7 1 |
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## harmonic number ## | |
harmonic <- function(n){ | |
sum(sapply(seq(1,n),function(n){ return(1/n) })) | |
} | |
## expectation of partly complete case ## | |
expt.partly_comp1 <- function(m,n){ | |
if (n < m) { | |
m * ( harmonic(m) - harmonic(m-n) ) | |
}else{ | |
m * harmonic(m) |
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as.prob <- function(weight){ | |
return(weight/sum(weight)) | |
} | |
expt.partly_comp2 <- function(vec.prob, n){ | |
m <- length(vec.prob) | |
g <- function(m, n, i, vec.prob){ | |
(-1)**(n-1-i)*choose(m-i-1, m-n)*1/(1-apply(combn(vec.prob, i), 2, sum)) | |
} | |
tmp <- sapply(seq(0,n-1),function(i){ | |
g( m, n, i, vec.prob) |