Binomial

The binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. Such a success/failure experiment is also called a Bernoulli experiment or Bernoulli trial; when n = 1, the binomial distribution is a Bernoulli distribution.

The Binomial distribution is an n times repeated Bernoulli trial. The binomial distribution is the basis for the popular binomial test of statistical significance.

This topic contains the following sections:

Constructor
Methods
Properties

Constructor

Constructor	Description	Performance
set success probability and number of trials	Creates new instance of Binomial with user specified parameters. Binomial(Int32, Double)

Description

Performance

set success probability and number of trials

Creates new instance of Binomial with user specified parameters.

method Binomial(Int32, Double)

Methods

Method	Description	Performance
pmf	Probability mass function. Pmf(Int32) Static probability mass function. Pmf(Int32, Int32, Double)
cdf	Cumulative distribution function. Cdf(Int32) Static cumulative distribution function. Cdf(Int32, Int32, Double)
inverse cdf	Inverse cumulative distribution function. Is useful for quantile calculation. Function will return value of random variable such that likelihood for this random variable to occur less than or equal to returned value equal to specified pvalue parameter. InverseCdf(Double, Int32, Double)

Method

Description

Performance

pmf

Probability mass function.

method Pmf(Int32)

Static probability mass function.

Static Pmf(Int32, Int32, Double)

cdf

Cumulative distribution function.

method Cdf(Int32)

Static cumulative distribution function.

Static Cdf(Int32, Int32, Double)

inverse cdf

Inverse cumulative distribution function. Is useful for quantile calculation. Function will return value of random variable such that likelihood for this random variable to occur less than or equal to returned value equal to specified pvalue parameter.

Static InverseCdf(Double, Int32, Double)

Properties

Property	Description	Performance
number of trials	Number of trials n. NumberOfTrials
success probability	Success probability in each trial p. SuccessProbability
mean	Mean of the distribution. Mean
median	Median is the numerical value separating the higher half of a probability distribution, from the lower half. Median
mode	Mode of distribution. Mode
kurtosis	Excess Kurtosis of distribution. Kurtosis
skewness	Skewness of distribution. Skewness
variance	Variance of the distribution. Variance