### Name: birthday
### Title: Probability of coincidences
### Aliases: qbirthday pbirthday
### Keywords: distribution

### ** Examples

require(graphics)

 ## the standard version
qbirthday()
 ## same 4-digit PIN number
qbirthday(classes=10^4)
 ## 0.9 probability of three coincident birthdays
qbirthday(coincident=3, prob=0.9)
## Chance of 4 coincident birthdays in 150 people
pbirthday(150,coincident=4)
## 100 coincident birthdays in 1000 people: *very* rare:
pbirthday(1000, coincident=100)

## Accuracy compared to exact calculation
x1<-  sapply(10:100, pbirthday)
x2<- 1-sapply(10:100, function(n)prod((365:(365-n+1))/rep(365,n)))
par(mfrow=c(2,2))
plot(x1, x2, xlab="approximate", ylab="exact")
abline(0,1)
plot(x1, x1-x2, xlab="approximate", ylab="error")
abline(h=0)
plot(x1, x2, log="xy", xlab="approximate", ylab="exact")
abline(0,1)
plot(1-x1, 1-x2, log="xy", xlab="approximate", ylab="exact")
abline(0,1)