Functions for dealing with probability. More...

Functions
std::mt19937	generator (getpid())
	the global generator for the probability module.

template<typename T >
void	seed (T value)
	Set the seed for the random number generator. More...

template<typename T >
T	uniform_int (T min, T max)
	Sample a number from an integer-valued uniform distribution. More...

template<typename T >
T	uniform_real (T min, T max)
	Sample a number from a real-valued uniform distribution. More...

template<typename T >
T	normal (T mean, T stddev)
	Sample a number from a normal distribution. More...

template<typename T >
T	lognormal (T mean, T stddev)
	Sample a number from a log-normal distribution. More...

template<typename T >
T	power_law (T constant, T exponent)
	Sample a number sample from a power law distribution. More...

bool	boolean ()
	Return the result of a coin toss. More...

template<typename T >
bool	boolean (T P)
	Return true with given probability. More...

Detailed Description

Functions for dealing with probability.

Function Documentation

◆ boolean() [1/2]

bool Maths::Probability::boolean ( )

inline

Return the result of a coin toss.

Returns: \(y \sim \mathcal{U}\{0, 1\}\)

◆ boolean() [2/2]

template<typename T >

bool Maths::Probability::boolean ( T P )

inline

Return true with given probability.

Template Parameters

T	the class of the probability value

Parameters

P	the probability of sampling true, \(p_{true}\)

Returns: true with \(P(\texttt{true} = p_{true})\) and false with \(P(\texttt{false} = 1 - p_{true})\)

◆ lognormal()

template<typename T >

T Maths::Probability::lognormal	(	T	mean,
		T	stddev
	)

inline

Sample a number from a log-normal distribution.

Template Parameters

T	the class of the number to sample

Parameters

mean	the mean value \(\mu\) of the distribution
stddev	the standard deviation \(\sigma\) of the distribution

Returns: \(y \sim e^{\mu + \sigma \mathcal{U}(0, 1)}\)

◆ normal()

template<typename T >

T Maths::Probability::normal	(	T	mean,
		T	stddev
	)

inline

Sample a number from a normal distribution.

Template Parameters

T	the class of the number to sample

Parameters

mean	the mean value \(\mu\) of the distribution
stddev	the standard deviation \(\sigma\) of the distribution

Returns: \(y \sim \mathcal{N}(\mu, \sigma)\)

◆ power_law()

template<typename T >

T Maths::Probability::power_law	(	T	constant,
		T	exponent
	)

inline

Sample a number sample from a power law distribution.

Template Parameters

T	the class of the number to sample

Parameters

constant	the constant value \(k\) of the distribution
exponent	the exponent \(\alpha\)

Returns: \(y \sim k \cdot \mathcal{U}(0, 1)^{\alpha}\)

◆ seed()

template<typename T >

void Maths::Probability::seed ( T value )

inline

Set the seed for the random number generator.

Template Parameters

T	the class of the seed value

Parameters

value the seed for the random number generators

◆ uniform_int()

template<typename T >

T Maths::Probability::uniform_int	(	T	min,
		T	max
	)

inline

Sample a number from an integer-valued uniform distribution.

Template Parameters

T	the class of the number to sample

Parameters

min	the inclusive minimal value \(v_{min}\) to sample
max	the inclusive maximal value \(v_{max}\) to sample

Returns: \(y \sim \mathcal{U}\{v_{min}, v_{max}\}\)

◆ uniform_real()

template<typename T >

T Maths::Probability::uniform_real	(	T	min,
		T	max
	)

inline

Sample a number from a real-valued uniform distribution.

Template Parameters

T	the class of the number to sample

Parameters

min	the inclusive minimal value \(v_{min}\) to sample
max	the inclusive maximal value \(v_{max}\) to sample

Returns: \(y \sim \mathcal{U}(v_{min}, v_{max})\)