Functions to compute the probability density function, cumulative distribution function, and quantile function for the Exponential distribution.
With rate parameter \(\lambda > 0\), the PDF and CDF are
$$f(x; \lambda) = \lambda e^{-\lambda x}, \quad x \ge 0$$ $$F(x; \lambda) = 1 - e^{-\lambda x}$$
and the quantile is
$$F^{-1}(p; \lambda) = -\frac{\log(1-p)}{\lambda}$$
Usage
exponential_distribution(lambda = 1)
exponential_pdf(x, lambda = 1)
exponential_lpdf(x, lambda = 1)
exponential_cdf(x, lambda = 1)
exponential_lcdf(x, lambda = 1)
exponential_quantile(p, lambda = 1)Value
A single numeric value with the computed probability density, log-probability density, cumulative distribution, log-cumulative distribution, or quantile depending on the function called.
See also
Boost Documentation for more details on the mathematical background.
Examples
# Exponential distribution with rate parameter lambda = 2
dist <- exponential_distribution(2)
# Apply generic functions
cdf(dist, 0.5)
#> [1] 0.6321206
logcdf(dist, 0.5)
#> [1] -0.4586751
pdf(dist, 0.5)
#> [1] 0.7357589
logpdf(dist, 0.5)
#> [1] -0.3068528
hazard(dist, 0.5)
#> [1] 2
chf(dist, 0.5)
#> [1] 1
mean(dist)
#> [1] 0.5
median(dist)
#> [1] 0.3465736
mode(dist)
#> [1] 0
range(dist)
#> [1] 0 Inf
quantile(dist, 0.2)
#> [1] 0.1115718
standard_deviation(dist)
#> [1] 0.5
support(dist)
#> [1] 2.225074e-308 1.797693e+308
variance(dist)
#> [1] 0.25
skewness(dist)
#> [1] 2
kurtosis(dist)
#> [1] 9
kurtosis_excess(dist)
#> [1] 6
# Convenience functions
exponential_pdf(1, 2)
#> [1] 0.2706706
exponential_lpdf(1, 2)
#> [1] -1.306853
exponential_cdf(1, 2)
#> [1] 0.8646647
exponential_lcdf(1, 2)
#> [1] -0.1454135
exponential_quantile(0.5, 2)
#> [1] 0.3465736