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Introduction

The density function of the Binomial distribution:

$$ f(x; n, p) = \binom{n}{x} p^x (1-p)^{n-x} $$

Parameters:

• n_trials_par is $n$
• prob_par is $p$

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Density

Definition:

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

Computes the density function.

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Examples:

 
// parameters
double prob_par = 0.6;
unsigned int n_trials = 4;

// standard input
double dens_val = stats::dbinom(2,n_trials,prob_par);
double log_dens_val = stats::dbinom(2,n_trials,prob_par,true);

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

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

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Probability

Definition:

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

Computes the cumulative distribution function (CDF).

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Examples:

// parameters
double prob_par = 0.6;
unsigned int n_trials = 4;

// standard input
double prob_val = stats::pbinom(2,n_trials,prob_par);
double log_prob_val = stats::pnorm(2,n_trials,prob_par,true);

// Armadillo input
arma::mat X(10,1);
X.fill(2);

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

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Quantile

Definition:

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

Computes the quantile function.

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Examples:

// parameters
double prob_par = 0.6;
unsigned int n_trials = 4;

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

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

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

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Random Sampling

Definition:

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

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

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

Generates pseudo-random draws.

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Examples:

 
// parameters
double prob_par = 0.6;
unsigned int n_trials = 4;

// standard input
int rand_val = stats::rbinom(n_trials,prob_par);

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

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