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Introduction

The density function of the Exponential distribution:

$$ f(x; \lambda) = \lambda \exp(-\lambda x) \times \mathbf{1}[ x \geq 0] $$

Parameters:

• rate_par is $\lambda$. Note: this need not be an integer.

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Density

Definition:

 
template<typename Ta, typename Tb>
statslib_constexpr
return_t<Ta> dexp(const Ta x, const Tb rate_par, const bool log_form = false);

Computes the density function.

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Examples:

// parameters
double rate = 14.0;

// standard input
double dens_val = stats::dexp(0.5,rate);
double log_dens_val = stats::dexp(0.5,rate,true);

// Armadillo input
arma::mat X(10,1);
X.fill(0.5);

arma::mat dens_vals_mat = stats::dexp(X,rate);
arma::mat log_dens_vals_mat = stats::dexp(X,rate,true);

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Probability

Definition:

 
template<typename Ta, typename Tb>
statslib_constexpr
return_t<Ta> pexp(const Ta x, const Tb rate_par, const bool log_form = false);

Computes the cumulative distribution function (CDF).

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Examples:

// parameters
double rate = 14.0;

// standard input
double prob_val = stats::pexp(0.5,rate);
double log_prob_val = stats::pexp(0.5,rate,true);

// Armadillo input
arma::mat X(10,1);
X.fill(0.5);

arma::mat prob_vals_mat = stats::pexp(X,rate);
arma::mat log_prob_vals_mat = stats::pexp(X,rate,true);

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Quantile

Definition:

 
template<typename Ta, typename Tb>
statslib_constexpr
Ta qexp(const Ta p, const Tb rate_par);

Computes the quantile function.

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Examples:

// parameters
double rate = 14.0;

// standard input
double quant_val = stats::qexp(0.7,rate);

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

arma::mat quant_vals_mat = stats::qexp(X,rate);

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Random Sampling

Definition:

 
// random engine seeding
template<typename T>
statslib_inline
return_t<T> rexp(const T rate_par, rand_engine_t& engine);

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

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

Generates pseudo-random draws.

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Examples:

// parameters
double rate = 14.0;

// standard input
double rand_val = stats::rexp(rate);

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

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