Functions to compute the probability density function, cumulative distribution function, and quantile function for the Weibull distribution.
Usage
weibull_distribution(shape, scale = 1)
weibull_pdf(x, shape, scale = 1)
weibull_lpdf(x, shape, scale = 1)
weibull_cdf(x, shape, scale = 1)
weibull_lcdf(x, shape, scale = 1)
weibull_quantile(p, shape, scale = 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
# Weibull distribution with shape = 1, scale = 1
dist <- weibull_distribution(1, 1)
# Apply generic functions
cdf(dist, 0.5)
#> [1] 0.3934693
logcdf(dist, 0.5)
#> [1] -0.9327521
pdf(dist, 0.5)
#> [1] 0.6065307
logpdf(dist, 0.5)
#> [1] -0.5
hazard(dist, 0.5)
#> [1] 1
chf(dist, 0.5)
#> [1] 0.5
mean(dist)
#> [1] 1
median(dist)
#> [1] 0.6931472
mode(dist)
#> [1] 0
range(dist)
#> [1] 0.000000e+00 1.797693e+308
quantile(dist, 0.2)
#> [1] 0.2231436
standard_deviation(dist)
#> [1] 1
support(dist)
#> [1] 2.225074e-308 1.797693e+308
variance(dist)
#> [1] 1
skewness(dist)
#> [1] 2
kurtosis(dist)
#> [1] 9
kurtosis_excess(dist)
#> [1] 6
# Convenience functions
weibull_pdf(1, shape = 1, scale = 1)
#> [1] 0.3678794
weibull_lpdf(1, shape = 1, scale = 1)
#> [1] -1
weibull_cdf(1, shape = 1, scale = 1)
#> [1] 0.6321206
weibull_lcdf(1, shape = 1, scale = 1)
#> [1] -0.4586751
weibull_quantile(0.5, shape = 1, scale = 1)
#> [1] 0.6931472