...one of the most highly
regarded and expertly designed C++ library projects in the
world.
— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards
#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:
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.
All the usual nonmember accessor functions that are generic to all distributions are supported: Cumulative Distribution Function, Probability Density Function, Quantile, Hazard Function, Cumulative Hazard Function, mean, median, mode, variance, standard deviation, skewness, kurtosis, kurtosis_excess, range and support.
The domain of the random variable is [0, +∞].
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.
In the following table λ is the parameter lambda of the distribution, x is the random variate, p is the probability and q = 1p.
Function 
Implementation Notes 


Using the relation: pdf = λ * exp(λ * x) 
cdf 
Using the relation: p = 1  exp(x * λ) = expm1(x * λ) 
cdf complement 
Using the relation: q = exp(x * λ) 
quantile 
Using the relation: x = log(1p) / λ = log1p(p) / λ 
quantile from the complement 
Using the relation: x = log(q) / λ 
mean 
1/λ 
standard deviation 
1/λ 
mode 
0 
skewness 
2 
kurtosis 
9 
kurtosis excess 
6 
(See also the reference documentation for the related Extreme Distributions.)