Introduction

The density function of the Bernoulli distribution:

Parameters:

• prob_par is $p$

Density

Definition:

 
template<typename T>
statslib_constexpr
T dbern(const uint_t x, const T prob_par, const bool log_form = false);

Computes the density function.

Examples:

 
// parameters
double prob_par = 0.6;

// standard input
double dens_val = stats::dbern(1,prob_par);
double log_dens_val = stats::dbern(1,prob_par,true);

// Armadillo input
arma::mat X(10,1);
X.fill(1);

arma::mat dens_vals_mat = stats::dbern(X,prob_par);
arma::mat log_dens_vals_mat = stats::dbern(X,prob_par,true);

Probability

Definition:

 
template<typename T>
statslib_constexpr
T pbern(const uint_t x, const T prob_par, const bool log_form = false);

Computes the cumulative distribution function (CDF).

Examples:

// parameters
double prob_par = 0.6;

// standard input
double prob_val = stats::pbern(0,prob_par);
double log_prob_val = stats::pnorm(0,prob_par,true);

// Armadillo input
arma::mat X(10,1);
X.fill(0);

arma::mat prob_vals_mat = stats::pbern(X,prob_par);
arma::mat log_prob_vals_mat = stats::pbern(X,prob_par,true);

Quantile

Definition:

 
template<typename Ta, typename Tb, typename Tc = uint_t>
statslib_constexpr
Tc qbern(const Ta p, const Tb prob_par);

Computes the quantile function.

Examples:

// parameters
double prob_par = 0.6;

// standard input
int quant_val = stats::qbern(0.7,prob_par);

// Armadillo input
arma::mat X(10,1);
X.fill(0.7);

arma::mat quant_vals_mat = stats::qbern(X,prob_par);

Random Sampling

Definition:

 
// random engine seeding
template<typename T>
statslib_inline
uint_t rbern(const T prob_par, rand_engine_t& engine);

// seeding values
template<typename T>
statslib_inline
uint_t rbern(const T prob_par, uint_t seed_val = std::random_device{}());

// matrix output
template<typename mT, typename eT>
statslib_inline
mT rbern(const uint_t n, const uint_t k, const eT prob_par);

Generates pseudo-random draws.

Examples:

 
// parameters
double prob_par = 0.6;

// standard input
double rand_val = stats::rbern(prob_par);

// Armadillo output: 10 x 1 matrix
arma::mat rand_mat = stats::rbern<arma::mat>(10,1,prob_par);