λ= 1.0 (60cpm相当)

[1] " 59.2 ±   6.3 [cpm], err1 = 49"
[1] " 59.1 ±   6.3 [cpm], err2 = 50"

λ= 5.0 (300cpm相当)

[1] "293.9 ±  13.3 [cpm], err1 = 60"
[1] "292.4 ±  13.2 [cpm], err2 = 50"

λ=10.0 (600cpm相当)

[1] "586.6 ±  19.9 [cpm], err1 = 44"
[1] "580.8 ±  19.7 [cpm], err2 = 59"

λ=20.0 (1200cpm相当)

[1] "1170.9 ±  31.8 [cpm], err1 = 64"
[1] "1147.6 ±  30.9 [cpm], err2 = 66"

# 関数：乱数による計数列生成
# 戻値：時間間隔毎計数列
# sampling(
#   num,	総数
#   rat,	平均到着率[1/s]
#   dt,		計測時間間隔[s]
#   dead	不感時間[s]
# )
# 1. 指数分布乱数により待ち時間生成
# 2. パルス時刻列作成
# 3. 時間間隔内の計数列作成
sampling <- function( num, rat, dt, dead ) {
  waitings <- rexp( num, rate=rat )
  times <- numeric( num )
  i <- 1
  for ( t in waitings ) {
    if ( i == 1 ) times[i] <- t
    else times[i] <- times[i-1] + t
    i <- i + 1
  }
  n <- ceiling( max( times ) / dt )
  freq <- numeric( n )
  for ( t in times ) {
    i <- ceiling( t / dt )
    freq[i] <- freq[i] + 1
  }
  i <- 1
  tmp <- 0
  for ( t in waitings ) {
    if ( i == 1 ) {
      times2 <- c(t)
      i <- i + 1
    } else {
      if ( t > dead ) {
        times2 <- c(times2, times2[i-1] + t + tmp)
        tmp <- 0
        i <- i + 1
      } else {
        tmp <- tmp + t
      }
    }
  }
  n <- ceiling( max( times2 ) / dt )
  freq2 <- numeric( n )
  for ( t in times2 ) {
    i <- ceiling( t / dt )
    freq2[i] <- freq2[i] + 1
  }
  return( list(freq, freq2) )
}
 
# 関数：計数表から測定、χ^2適合度検定を行なう。
# 戻値：測定結果表
# measure(
#   r		計数表
# )
# 1. χ^2適合度検定
# 2. (λ,自由度,χ^2,右側確率,cpm)を戻す
measure <- function( r ) {
  n <- length( r )
  k <- max( r ) + 1
  o <- numeric( k )
  for ( i in r ) {
    o[i+1] <- o[i+1] + 1
  }
  x <- 0:(k-1)
  l <- sum( o * x ) / n
  p <- exp(-l) * l^x / factorial(x)
  p[k] <- 1 - sum( p[-k] )
  e <- n * p
  while ( e[1] < 5 ) {
    o[2] <- o[2] + o[1]
    e[2] <- e[2] + e[1]
    o <- o[-1]
    e <- e[-1]
    k <- k - 1
  }
  while ( e[k] < 5 ) {
    o[k-1] <- o[k-1] + o[k]
    e[k-1] <- e[k-1] + e[k]
    o <- o[-k]
    e <- e[-k]
    k <- k - 1
  }
  z <- sum( (o - e)^2 / e )
  q <- pchisq( z, (k-2), lower.tail=FALSE )
  if ( is.nan(q) ) q = -1
  return( c( n, l, (k-2), z, q ) )
}
 
# メインルーチン
# 指定パラメータで測定シミュレーションを繰り返し、
# 平均値、分散、χ^2検定棄却数を表示する。
dead <- 0.001
rat <- 20.0
if ( rat <= 1.0 ) {
  num <- 100
} else {
  num <- 100 * rat
}
dt  <- 5
len <- 1000
cpm1 <- numeric( len )
cpm2 <- numeric( len )
err1 <- 0
err2 <- 0
for ( i in 1:len ) {
  r <- sampling( num, rat, dt, dead )
  dat1 <- measure( r[[1]] )
  dat2 <- measure( r[[2]] )
  cpm1[i] <- sum( r[[1]] ) * 60 / ( dat1[1] * dt )
  if ( dat1[5] < 0.05 ) err1 <- err1 + 1
  cpm2[i] <- sum( r[[2]] ) * 60 / ( dat2[1] * dt )
  if ( dat2[5] < 0.05 ) err2 <- err2 + 1
}
sprintf( "%5.1f ± %5.1f [cpm], err1 = %d",
  mean( cpm1 ), sd( cpm1 ), err1 )
sprintf( "%5.1f ± %5.1f [cpm], err2 = %d",
  mean( cpm2 ), sd( cpm2 ), err2 )