Investment Studio > Expressions > Functions > Statistical > BINOMDIST

float binomdist(integer successes, integer trials, float success_probability, boolean cumulative = TRUE)

Returns the binomial probability function.

successes >= 0 is the number of successful outcomes of a series of independent trials, where each trial can only result in success or failure (Bernoulli trials).

trials >= successes is the total number of trials.

success_probability Î [0, 1] is the probability of success in a single trial.

If cumulative = TRUE, the CDF (Cumulative Distribution Function) is returned (equal to the probability that successes is >= a stochastic variable with binomial distribution); otherwise, the PDF (Probability Density Function) is returned. If cumulative is omitted, it defaults to TRUE.

The binomial PDF is

f(successes, trials, success_probability) = combin(trials, successes) * success_probability^successes * (1 - success_probability)^(trials - successes)

and the CDF is

The binomial distribution plays a fundamental role in statistics. When both trials and trials * success_probability are large, its PDF reduces to the normal distribution (function normdist) with standard deviation = sqrt(trials * success_probability * (1 - success_probability)). When trials ® ¥ and success_probability ® 0, in such a way that trials * success_probability remains finite, it reduces to the Poisson distribution (function poisson) with mean = trials * success_probability.

Example

The probability of 10 flips of an evenly balanced coin resulting in 3 heads (and hence 7 tails) is

=binomdist(3, 10, 0.5, FALSE)

» 11.7%. The probability of the same series of trials resulting in at most 3 heads is

=binomdist(3, 10, 0.5)

» 17.2%.

See also combin, critbinom, fact, hypgeomdist, negbinomdist, permut, prob.