MTH397

Computational Formulas for R

The Binomial Distribution

Event	R formula
exactly k successes	`dbinom(k,n,p)`
k or fewer successes	`pbinom(k,n,p)`
at least k successes	`1-pbinom(k-1,n,p)`
more than k successes	`1-pbinom(k,n,p)`
fewer than k successes	`pbinom(k-1,n,p)`
fewer than j or more than k successes	`1+pbinom(j-1,n,p)-pbinom(k,n,p)`
between j and k successes (inclusive)	`pbinom(k,n,p)-pbinom(j-1,n,p)`

The Geometric Distribution

Event	R formula
first success on the k^th trial	`dgeom(k-1,p)`
first success on or before the k^th trial	`pgeom(k-1,p)`
first success before the k^thtrial	`pgeom(k-2,p)`
first success on or after the k^thtrial	`1-pgeom(k-2,p)`
first success after the k^thtrial	`1-pgeom(k-1,p)`
first success between the j^th and k^th trial, inclusive	`pgeom(k-1,p)-pgeom(j-2,p)`
first success before the j^th trial or after the k^th trial	`1+pgeom(j-2,p)-pgeom(k-1,p)`

The Negative Binomial Distribution

Event	R formula
r^th success on the k^th trial	`dnbinom(k-r,r,p)`
r^th success on or before the k^th trial	`pnbinom(k-r,r,p)`
r^th success before the k^thtrial	`pnbinom(k-r-1,r,p)`
r^th success on or after the k^thtrial	`1-pnbinom(k-r-1,r,p)`
r^th success after the k^thtrial	`1-pnbinom(k-r,r,p)`
r^th success between the j^th and k^th trial, inclusive	`pnbinom(k-r,r,p)-pnbinom(j-r-1,r,p)`
r^th success before the j^th trial or after the k^th trial	`1-pnbinom(k-r,r,p)+pnbinom(j-r-1,r,p)`

The Poisson Distribution

Event	R formula
exactly k	`dpois(k,l)`
k or less	`ppois(k,l)`
at least k	`1-ppois(k-1,l)`
more than k	`1-ppois(k,l)`
less than k	`ppois(k-1,l)`
less than j or more than k	`1+ppois(j-1,l)-ppois(k,l)`
between j and k (inclusive)	`ppois(k,l)-ppois(j-1,l)`

The Normal Distribution

Event	R formula	Spreadsheet Formula
Y is less than y	`pnorm(y,mu,sigma)`	`=NORMDIST(y,mu,sigma,TRUE)`
Y is greater than y	`1-pnorm(y,mu,sigma)`	`=1-NORMDIST(y,mu,sigma,TRUE)`
Y is greater than y or less than z	`1-pnorm(y,mu,sigma)+pnorm(z,mu,sigma)`	`=1-NORMDIST(y,mu,sigma,TRUE)+NORMDIST(z,mu,sigma,TRUE)`
Y is between z and y	`pnorm(y,mu,sigma)-pnorm(z,mu,sigma)`	`=NORMDIST(y,mu,sigma,TRUE)-NORMDIST(z,mu,sigma,TRUE)`