Discrete distributions
[Random number generation]

Functions
SIM_API int	intuniform (int a, int b, int rng=0)
int	bernoulli (double p, int rng=0)
SIM_API int	binomial (int n, double p, int rng=0)
SIM_API int	geometric (double p, int rng=0)
SIM_API int	negbinomial (int n, double p, int rng=0)
SIM_API int	poisson (double lambda, int rng=0)

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Function Documentation

int bernoulli	(	double	p,
		int	rng = 0
	)			[inline]

Returns the result of a Bernoulli trial with probability p, that is, 1 with probability p and 0 with probability (1-p).

Generation is using elementary look-up.

Parameters:

	p	0=<p<=1
	rng	the underlying random number generator

References genk_dblrand().

SIM_API int binomial	(	int	n,
		double	p,
		int	rng = 0
	)

Returns a random integer from the binomial distribution with parameters n and p, that is, the number of successes in n independent trials with probability p.

Generation is using the relationship to Bernoulli distribution (runtime is proportional to n).

Parameters:

	n	n>=0
	p	0<=p<=1
	rng	the underlying random number generator

SIM_API int geometric	(	double	p,
		int	rng = 0
	)

Returns a random integer from the geometric distribution with parameter p, that is, the number of independent trials with probability p until the first success.

This is the n=1 special case of the negative binomial distribution.

Generation uses inverse transform.

Parameters:

	p	0<p<=1
	rng	the underlying random number generator

SIM_API int intuniform	(	int	a,
		int	b,
		int	rng = 0
	)

Returns a random integer with uniform distribution in the range [a,b], inclusive.

(Note that the function can also return b.)

Parameters:

	a,b	the interval, a<b
	rng	the underlying random number generator

SIM_API int negbinomial	(	int	n,
		double	p,
		int	rng = 0
	)

Returns a random integer from the negative binomial distribution with parameters n and p, that is, the number of failures occurring before n successes in independent trials with probability p of success.

Generation is using the relationship to geometric distribution (runtime is proportional to n).

Parameters:

	n	n>=0
	p	0<p<1
	rng	the underlying random number generator

SIM_API int poisson	(	double	lambda,
		int	rng = 0
	)

Returns a random integer from the Poisson distribution with parameter lambda, that is, the number of arrivals over unit time where the time between successive arrivals follow exponential distribution with parameter lambda.

Lambda is also the mean (and variance) of the distribution.

Generation method depends on value of lambda:

• 0<lambda<=30: count number of events
• lambda>30: Acceptance-Rejection due to Atkinson (see Banks, page 166)

Parameters:

	lambda	> 0
	rng	the underlying random number generator