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#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 non-member 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 = 1-p.
| 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(1-p) / 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.)