Exponential distribution

Distribution function and quantile function of the exponential distribution.

cdfexp(x, para = c(0, 1))
quaexp(f, para = c(0, 1))

Arguments

x

Vector of quantiles.

f

Vector of probabilities.

para

Numeric vector containing the parameters of the distribution, in the order \(\xi, \alpha\) (location, scale).

Details

The exponential distribution with parameters \(\xi\) (lower bound) and \(\alpha\) (mean) has distribution function $$F(x)=1-\exp\lbrace-(x-\xi)/\alpha\rbrace$$ for \(x\ge0\), and quantile function $$x(F)=\xi-\alpha\log(1-F).$$

Value

cdfexp gives the distribution function; quaexp gives the quantile function.

Note

The functions expect the distribution parameters in a vector, rather than as separate arguments as in the standard R functions pexp and qexp.

See also

pexp for the standard R version of the exponential distribution. cdfgam for the gamma distribution, cdfgpa for the generalized Pareto distribution, cdfkap for the kappa distribution, cdfpe3 for the Pearson type III distribution, and cdfwak for the Wakeby distribution, all of which generalize the exponential distribution.

Examples

# Random sample from the exponential distribution
# with lower bound 0 and mean 3.
quaexp(runif(100), c(0,3))
#>   [1]  2.75458428  0.51310684  0.02228086  1.88428979  2.06613543  1.02648761
#>   [7]  3.96019417  4.44209880  6.22875576  0.57689978  0.10452391  1.15868968
#>  [13]  1.54414071  0.65323632  1.55021982  0.19733453  1.47650877 11.13310959
#>  [19]  1.02701587  3.40315765  3.98769664  0.65430659 11.81813245  4.05882862
#>  [25]  0.15845055  2.26642421  3.57044520  3.49960723  0.09518517  0.76685509
#>  [31]  1.07358754  3.03564418  1.95615708  1.69780625  3.67695672  8.90298449
#>  [37]  0.59659247  0.73348416  3.41983059  2.07252319  3.07898106  3.23893900
#>  [43]  0.30285793  4.35218076  4.40478922 14.03719697 10.57222152  1.47887245
#>  [49]  1.85515714  1.13606828  0.57593734  2.27512848  2.04150452  4.53297015
#>  [55]  0.68514050  3.74897481  0.20231974  1.31182785  5.23232851  0.95986483
#>  [61]  2.53222384  1.22715044  2.72097324  0.63779071  8.85594653  2.34580672
#>  [67]  2.35975973  0.97967270  1.77557817  1.39331114  0.08538662  1.88200636
#>  [73]  1.48304333  0.06080777  1.41948629  2.46234744  5.83648601  1.45747094
#>  [79]  2.25180161  2.75365744  0.90888000  1.02768288  1.96221313  7.57739392
#>  [85]  1.53607996  0.71923953  3.34209299  0.18120642 17.49737335  0.48415449
#>  [91]  2.19290003  5.61474767  3.80041540  0.82850195  2.37587668  5.40182822
#>  [97]  0.08506270  1.90115174  4.91474746  5.04685351