Investment Studio > Expressions > Functions > Statistical > BETADIST

float betadist(float x, float alpha, float beta, float a = 0, float b = 1, boolean cumulative = TRUE)

Returns the standard Beta probability function for the scaled argument

x_scaled = (x - a) / (b - a)

x must be in the range [a, b].

b must be > a.

If a is omitted, it defaults to 0. If b is omitted, it defaults to 1. With default a and b, betadist reduces to the standard Beta probability function.

alpha and beta must be > 0.

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

Mathematically, the standard Beta PDF is

f(x, alpha, beta) = (1 - x)^{beta - 1} x^{alpha - 1} / beta(alpha, beta)

and the CDF is

Example

The probability of 0.5 being >= a stochastic variable with Beta(1, 3) distribution is

=betadist(0.5, 1, 3)

or 87.5%.

See also beta, betainv, gamma, gammadist, gammainv, gammaln.