Probability distributions

Probability distributions

Generates a nonparametric distribution.

Usage

LogNormal(meanlog, sdlog, mean, sd, ...)

Gamma(shape, rate, scale, mean, sd, ...)

Normal(mean, sd, ...)

Exp(rate, mean, ...)

Weibull(shape, scale, mean, sd, ...)

NonParametric(pmf, ...)

Fixed(value, ...)

Arguments

meanlog, sdlog

mean and standard deviation of the distribution on the log scale with default values of 0 and 1 respectively.

mean, sd

mean and standard deviation of the distribution

...

arguments to define the limits of the distribution that will be passed to bound_dist()

shape, scale

shape and scale parameters. Must be positive, scale strictly.

rate

an alternative way to specify the scale.

pmf

Probability mass of the given distribution; this is passed as a zero-indexed numeric vector (i.e. the fist entry represents the probability mass of zero). If not summing to one it will be normalised to sum to one internally.

value

Value of the fixed (delta) distribution

Value

A dist_spec representing a distribution of the given specification.

Details

Probability distributions are ubiquitous in EpiNow2, usually representing epidemiological delays (e.g., the generation time for delays between becoming infecting and infecting others; or reporting delays)

They are generated using functions that have a name corresponding to the probability distribution that is being used. They generated dist_spec objects that are then passed to the models underlying EpiNow2. All parameters can be given either as fixed values (a numeric value) or as uncertain values (a dist_sepc). If given as uncertain values, currently only normally distributed parameters (generated using Normal()) are supported.

Each distribution has a representation in terms of "natural" parameters (the ones used in stan) but can sometimes also be specified using other parameters such as the mean or standard deviation of the distribution. If not given as natural parameters then these will be calculated from the given parameters. If they have uncertainty, this will be done by random sampling from the given uncertainty and converting resulting parameters to their natural representation.

Currently available distributions are lognormal, gamma, normal, fixed (delta) and nonparametric. The nonparametric is a special case where the probability mass function is given directly as a numeric vector.

See also

vignette("delays") for an overview of how delay distributions are used in EpiNow2

Examples

LogNormal(mean = 4, sd = 1)
#> - lognormal distribution:
#>   meanlog:
#>     1.4
#>   sdlog:
#>     0.25
LogNormal(mean = 4, sd = 1, max = 10)
#> - lognormal distribution (max: 10):
#>   meanlog:
#>     1.4
#>   sdlog:
#>     0.25
# If specifying uncertain parameters, use the natural parameters
LogNormal(meanlog = Normal(1.5, 0.5), sdlog = 0.25, max = 10)
#> - lognormal distribution (max: 10):
#>   meanlog:
#>     - normal distribution:
#>       mean:
#>         1.5
#>       sd:
#>         0.5
#>   sdlog:
#>     0.25
Gamma(mean = 4, sd = 1)
#> - gamma distribution:
#>   shape:
#>     16
#>   rate:
#>     4
Gamma(shape = 16, rate = 4)
#> - gamma distribution:
#>   shape:
#>     16
#>   rate:
#>     4
Gamma(shape = Normal(16, 2), rate = Normal(4, 1))
#> - gamma distribution:
#>   shape:
#>     - normal distribution:
#>       mean:
#>         16
#>       sd:
#>         2
#>   rate:
#>     - normal distribution:
#>       mean:
#>         4
#>       sd:
#>         1
Normal(mean = 4, sd = 1)
#> - normal distribution:
#>   mean:
#>     4
#>   sd:
#>     1
Normal(mean = 4, sd = 1, max = 10)
#> - normal distribution (max: 10):
#>   mean:
#>     4
#>   sd:
#>     1
Exp(rate = 1)
#> - exp distribution:
#>   rate:
#>     1
Exp(mean = 4)
#> - exp distribution:
#>   rate:
#>     0.25
Weibull(shape = 1, scale = 1)
#> - weibull distribution:
#>   shape:
#>     1
#>   scale:
#>     1
Weibull(shape = 1, scale = 1, max = 10)
#> - weibull distribution (max: 10):
#>   shape:
#>     1
#>   scale:
#>     1
Weibull(mean = 4, sd = 1)
#> - weibull distribution:
#>   shape:
#>     4.5
#>   scale:
#>     4.4
NonParametric(c(0.1, 0.3, 0.2, 0.4))
#> - nonparametric distribution
#>   PMF: [0.1 0.3 0.2 0.4]
NonParametric(c(0.1, 0.3, 0.2, 0.1, 0.1))
#> - nonparametric distribution
#>   PMF: [0.12 0.37 0.25 0.12 0.12]
Fixed(value = 3)
#> - fixed value:
#>   3
Fixed(value = 3.5)
#> - fixed value:
#>   3.5