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Random Number Utilities
Random Number Generation » Random Number GeneratorsRandom Number Generation » | Random Number Distributions » Uniform Distributions » Bernoulli Distributions
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A discrete Poisson random number distribution.

The formula for the Poisson probability density function is $p(i|\mu) = \frac{\mu^i}{i!} e^{-\mu}$ where $\mu$ is the parameter of the distribution.

The type of the range of the distribution.

Parameter type.

Resets the distribution state.

Returns the distribution parameter mean.

Returns the parameter set of the distribution.

Sets the parameter set of the distribution.

Parameters
__paramThe new parameter set of the distribution.

Returns the greatest lower bound value of the distribution.

Returns the least upper bound value of the distribution.

Generating functions.

Return true if two Poisson distributions have the same parameters and the sequences that would be generated are equal.

Inserts a poisson_distribution random number distribution __x into the output stream __os.

Parameters
__osAn output stream.
__xA poisson_distribution random number distribution.
Returns
The output stream with the state of __x inserted or in an error state.

Extracts a poisson_distribution random number distribution __x from the input stream __is.

Parameters
__isAn input stream.
__xA poisson_distribution random number generator engine.
Returns
The input stream with __x extracted or in an error state.

Return true if two Poisson distributions are different.

An exponential continuous distribution for random numbers.

The formula for the exponential probability density function is $p(x|\lambda) = \lambda e^{-\lambda x}$.

Distribution Statistics
Mean$\frac{1}{\lambda}$
Median$\frac{\ln 2}{\lambda}$
Mode$zero$
Range$[0, \infty]$
Standard Deviation$\frac{1}{\lambda}$

The type of the range of the distribution.

Parameter type.

Constructs an exponential distribution with inverse scale parameter $\lambda$.

Resets the distribution state.

Has no effect on exponential distributions.

Returns the inverse scale parameter of the distribution.

Returns the parameter set of the distribution.

Sets the parameter set of the distribution.

Parameters
__paramThe new parameter set of the distribution.

Returns the greatest lower bound value of the distribution.

Returns the least upper bound value of the distribution.

Generating functions.

Return true if two exponential distributions have the same parameters.

Return true if two exponential distributions have different parameters.

Inserts a exponential_distribution random number distribution __x into the output stream __os.

Parameters
__osAn output stream.
__xA exponential_distribution random number distribution.
Returns
The output stream with the state of __x inserted or in an error state.

Extracts a exponential_distribution random number distribution __x from the input stream __is.

Parameters
__isAn input stream.
__xA exponential_distribution random number generator engine.
Returns
The input stream with __x extracted or in an error state.

A weibull_distribution random number distribution.

The formula for the normal probability density function is:

\[ p(x|\alpha,\beta) = \frac{\alpha}{\beta} (\frac{x}{\beta})^{\alpha-1} \exp{(-(\frac{x}{\beta})^\alpha)} \]

The type of the range of the distribution.

Parameter type.

Resets the distribution state.

Return the $a$ parameter of the distribution.

Return the $b$ parameter of the distribution.

Returns the parameter set of the distribution.

Sets the parameter set of the distribution.

Parameters
__paramThe new parameter set of the distribution.

Returns the greatest lower bound value of the distribution.

Returns the least upper bound value of the distribution.

Generating functions.

Return true if two Weibull distributions have the same parameters.

Return true if two Weibull distributions have different parameters.

Inserts a weibull_distribution random number distribution __x into the output stream __os.

Parameters
__osAn output stream.
__xA weibull_distribution random number distribution.
Returns
The output stream with the state of __x inserted or in an error state.

Extracts a weibull_distribution random number distribution __x from the input stream __is.

Parameters
__isAn input stream.
__xA weibull_distribution random number generator engine.
Returns
The input stream with __x extracted or in an error state.

A extreme_value_distribution random number distribution.

The formula for the normal probability mass function is

\[ p(x|a,b) = \frac{1}{b} \exp( \frac{a-x}{b} - \exp(\frac{a-x}{b})) \]

The type of the range of the distribution.

Parameter type.

Resets the distribution state.

Return the $a$ parameter of the distribution.

Return the $b$ parameter of the distribution.

Returns the parameter set of the distribution.

Sets the parameter set of the distribution.

Parameters
__paramThe new parameter set of the distribution.

Returns the greatest lower bound value of the distribution.

Returns the least upper bound value of the distribution.

Generating functions.

Return true if two extreme value distributions have the same parameters.

Return true if two extreme value distributions have different parameters.

Inserts a extreme_value_distribution random number distribution __x into the output stream __os.

Parameters
__osAn output stream.
__xA extreme_value_distribution random number distribution.
Returns
The output stream with the state of __x inserted or in an error state.

Extracts a extreme_value_distribution random number distribution __x from the input stream __is.

Parameters
__isAn input stream.
__xA extreme_value_distribution random number generator engine.
Returns
The input stream with __x extracted or in an error state.

A discrete_distribution random number distribution.

The formula for the discrete probability mass function is

The type of the range of the distribution.

Parameter type.

Resets the distribution state.

Returns the probabilities of the distribution.

Returns the parameter set of the distribution.

Sets the parameter set of the distribution.

Parameters
__paramThe new parameter set of the distribution.

Returns the greatest lower bound value of the distribution.

Returns the least upper bound value of the distribution.

Generating functions.

Return true if two discrete distributions have the same parameters.

Inserts a discrete_distribution random number distribution __x into the output stream __os.

Parameters
__osAn output stream.
__xA discrete_distribution random number distribution.
Returns
The output stream with the state of __x inserted or in an error state.

Extracts a discrete_distribution random number distribution __x from the input stream __is.

Parameters
__isAn input stream.
__xA discrete_distribution random number generator engine.
Returns
The input stream with __x extracted or in an error state.

Return true if two discrete distributions have different parameters.

A piecewise_constant_distribution random number distribution.

The formula for the piecewise constant probability mass function is

The type of the range of the distribution.

Parameter type.

Resets the distribution state.

Returns a vector of the intervals.

Returns a vector of the probability densities.

Returns the parameter set of the distribution.

Sets the parameter set of the distribution.

Parameters
__paramThe new parameter set of the distribution.

Returns the greatest lower bound value of the distribution.

Returns the least upper bound value of the distribution.

Generating functions.

Return true if two piecewise constant distributions have the same parameters.

Inserts a piecewise_constant_distribution random number distribution __x into the output stream __os.

Parameters
__osAn output stream.
__xA piecewise_constant_distribution random number distribution.
Returns
The output stream with the state of __x inserted or in an error state.

Extracts a piecewise_constant_distribution random number distribution __x from the input stream __is.

Parameters
__isAn input stream.
__xA piecewise_constant_distribution random number generator engine.
Returns
The input stream with __x extracted or in an error state.

Return true if two piecewise constant distributions have different parameters.

A piecewise_linear_distribution random number distribution.

The formula for the piecewise linear probability mass function is

The type of the range of the distribution.

Parameter type.

Resets the distribution state.

Return the intervals of the distribution.

Return a vector of the probability densities of the distribution.

Returns the parameter set of the distribution.

Sets the parameter set of the distribution.

Parameters
__paramThe new parameter set of the distribution.

Returns the greatest lower bound value of the distribution.

Returns the least upper bound value of the distribution.

Generating functions.

Return true if two piecewise linear distributions have the same parameters.

Inserts a piecewise_linear_distribution random number distribution __x into the output stream __os.

Parameters
__osAn output stream.
__xA piecewise_linear_distribution random number distribution.
Returns
The output stream with the state of __x inserted or in an error state.

Extracts a piecewise_linear_distribution random number distribution __x from the input stream __is.

Parameters
__isAn input stream.
__xA piecewise_linear_distribution random number generator engine.
Returns
The input stream with __x extracted or in an error state.

Return true if two piecewise linear distributions have different parameters.