doryokujin

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)

doryokujin

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)