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Bernoulli Distributions
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Modules

 Random Number Utilities
 

Detailed Description

A normal continuous distribution for random numbers.

The formula for the normal probability density function is

\[ p(x|\mu,\sigma) = \frac{1}{\sigma \sqrt{2 \pi}} e^{- \frac{{x - \mu}^ {2}}{2 \sigma ^ {2}} } \]

The type of the range of the distribution.

Parameter type.

Constructs a normal distribution with parameters $mean$ and standard deviation.

Resets the distribution state.

Returns the mean of the distribution.

Returns the standard deviation 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 normal distributions have the same parameters and the sequences that would be generated are equal.

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

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

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

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

Return true if two normal distributions are different.

A lognormal_distribution random number distribution.

The formula for the normal probability mass function is

\[ p(x|m,s) = \frac{1}{sx\sqrt{2\pi}} \exp{-\frac{(\ln{x} - m)^2}{2s^2}} \]

The type of the range of the distribution.

Parameter type.

Resets the distribution state.

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 lognormal distributions have the same parameters and the sequences that would be generated are equal.

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

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

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

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

Return true if two lognormal distributions are different.

A gamma continuous distribution for random numbers.

The formula for the gamma probability density function is:

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

The type of the range of the distribution.

Parameter type.

Constructs a gamma distribution with parameters $\alpha$ and $\beta$.

Resets the distribution state.

Returns the $\alpha$ of the distribution.

Returns the $\beta$ 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 gamma distributions have the same parameters and the sequences that would be generated are equal.

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

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

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

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

Return true if two gamma distributions are different.

A chi_squared_distribution random number distribution.

The formula for the normal probability mass function is $p(x|n) = \frac{x^{(n/2) - 1}e^{-x/2}}{\Gamma(n/2) 2^{n/2}}$

The type of the range of the distribution.

Parameter type.

Resets the distribution state.

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 Chi-squared distributions have the same parameters and the sequences that would be generated are equal.

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

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

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

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

Return true if two Chi-squared distributions are different.

A cauchy_distribution random number distribution.

The formula for the normal probability mass function is $p(x|a,b) = (\pi b (1 + (\frac{x-a}{b})^2))^{-1}$

The type of the range of the distribution.

Parameter type.

Resets the distribution state.

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 Cauchy distributions have the same parameters.

Return true if two Cauchy distributions have different parameters.

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

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

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

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

A fisher_f_distribution random number distribution.

The formula for the normal probability mass function is

\[ p(x|m,n) = \frac{\Gamma((m+n)/2)}{\Gamma(m/2)\Gamma(n/2)} (\frac{m}{n})^{m/2} x^{(m/2)-1} (1 + \frac{mx}{n})^{-(m+n)/2} \]

The type of the range of the distribution.

Parameter type.

Resets the distribution state.

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 Fisher f distributions have the same parameters and the sequences that would be generated are equal.

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

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

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

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

Return true if two Fisher f distributions are different.

A student_t_distribution random number distribution.

The formula for the normal probability mass function is:

\[ p(x|n) = \frac{1}{\sqrt(n\pi)} \frac{\Gamma((n+1)/2)}{\Gamma(n/2)} (1 + \frac{x^2}{n}) ^{-(n+1)/2} \]

The type of the range of the distribution.

Parameter type.

Resets the distribution state.

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 Student t distributions have the same parameters and the sequences that would be generated are equal.

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

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

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

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

Return true if two Student t distributions are different.