Bernoulli distribution | Vose Software

Bernoulli distribution

Format: Bernoulli(p)


The Bernoulli distribution is a Binomial distribution with n = 1. The Bernoulli distribution returns a 1 with probability p and a zero otherwise.


The Bernoulli distribution, named after Swiss scientist Jakob Bernoulli, is very useful for modeling an event that may or may not occur. For example, if you believe that there is a 20% chance of a competitor enter your market you can model this as VoseBernoulli(0.2) or VoseBernoulli(20%): in 20% of the scenarios it will generate a 1 which you can use to build further logic on.

For a simple example, =VoseBernoulli(0.2)*VoseLognormal(12,72) models a risk event with a probability of 20% of occurring and an impact, should it occur, equal to Lognormal(12,72). In fact, a better way of modeling this is to use the VoseRiskEvent function.

ModelRisk functions added to Microsoft Excel for the Bernoulli distribution

VoseBernoulli generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseBernoulliObject constructs a distribution object for this distribution.

VoseBernoulliProb returns the probability mass or cumulative distribution function for this distribution.

VoseBernoulliProb10 returns the log10 of the probability mass or cumulative distribution function.

VoseBernoulliFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VoseBernoulliFitObject constructs a distribution object of this distribution fitted to data.

VoseBernoulliFitP returns the parameters of this distribution fitted to data.


Bernoulli distribution equations