Functions to compute the probability density function, cumulative distribution function, and quantile function for the Poisson distribution.
Usage
poisson_distribution(lambda = 1)
poisson_pdf(x, lambda = 1)
poisson_lpdf(x, lambda = 1)
poisson_cdf(x, lambda = 1)
poisson_lcdf(x, lambda = 1)
poisson_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
# Poisson distribution with lambda = 1
dist <- poisson_distribution(1)
# Apply generic functions
cdf(dist, 5)
#> [1] 0.9994058
logcdf(dist, 5)
#> [1] -0.0005943614
pdf(dist, 5)
#> [1] 0.003065662
logpdf(dist, 5)
#> [1] -5.787492
hazard(dist, 5)
#> [1] 5.159442
chf(dist, 5)
#> [1] 7.42832
mean(dist)
#> [1] 1
median(dist)
#> [1] 1
mode(dist)
#> [1] 1
range(dist)
#> [1] 0.000000e+00 1.797693e+308
quantile(dist, 0.2)
#> [1] 0
standard_deviation(dist)
#> [1] 1
support(dist)
#> [1] 0.000000e+00 1.797693e+308
variance(dist)
#> [1] 1
skewness(dist)
#> [1] 1
kurtosis(dist)
#> [1] 4
kurtosis_excess(dist)
#> [1] 1
# Convenience functions
poisson_pdf(0, 1)
#> [1] 0.3678794
poisson_lpdf(0, 1)
#> [1] -1
poisson_cdf(0, 1)
#> [1] 0.3678794
poisson_lcdf(0, 1)
#> [1] -1
poisson_quantile(0.5, 1)
#> [1] 1