#include <boost/math/distributions/exponential.hpp>

template <class RealType = double,
          class Policy   = policies::policy<> >
class exponential_distribution;

typedef exponential_distribution<> exponential;

template <class RealType, class Policy>
class exponential_distribution
{
public:
   typedef RealType value_type;
   typedef Policy   policy_type;

   exponential_distribution(RealType lambda = 1);

   RealType lambda()const;
};

The exponential distribution is a continuous probability distribution with PDF:

It is often used to model the time between independent events that happen at a constant average rate.

The following graph shows how the distribution changes for different values of the rate parameter lambda:

Member Functions

exponential_distribution(RealType lambda = 1);

Constructs an Exponential distribution with parameter lambda. Lambda is defined as the reciprocal of the scale parameter.

Requires lambda > 0, otherwise calls domain_error.

RealType lambda()const;

Accessor function returns the lambda parameter of the distribution.

Non-member Accessors

All the usual non-member accessor functions that are generic to all distributions are supported: Cumulative Distribution Function, Probability Density Function, Quantile, Hazard Function, Cumulative Hazard Function, __logcdf, __logpdf, mean, median, mode, variance, standard deviation, skewness, kurtosis, kurtosis_excess, range and support.

The domain of the random variable is [0, +∞].

In this distribution the implementation of both logcdf, and logpdf are specialized to improve numerical accuracy.

Accuracy

The exponential distribution is implemented in terms of the standard library functions exp, log, log1p and expm1 and as such should have very low error rates.

Implementation

In the following table λ is the parameter lambda of the distribution, x is the random variate, p is the probability and q = 1-p.

references

(See also the reference documentation for the related Extreme Distributions.)