Cumulative distribution function

cumulative_distribution_function evaluates the cumulative distribution function of a specific distribution dist at a point x.

Usage

cumulative_distribution_function(dist, x, n, theta, ...)

# S4 method for class 'Binomial,numeric,numeric,numeric'
cumulative_distribution_function(dist, x, n, theta, ...)

# S4 method for class 'ChiSquared,numeric,numeric,numeric'
cumulative_distribution_function(dist, x, n, theta, ...)

# S4 method for class 'NestedModels,numeric,numeric,numeric'
cumulative_distribution_function(dist, x, n, theta, ...)

# S4 method for class 'Normal,numeric,numeric,numeric'
cumulative_distribution_function(dist, x, n, theta, ...)

# S4 method for class 'Student,numeric,numeric,numeric'
cumulative_distribution_function(dist, x, n, theta, ...)

# S4 method for class 'Survival,numeric,numeric,numeric'
cumulative_distribution_function(dist, x, n, theta, ...)

Arguments

dist

a univariate distribution object

x

outcome

n

sample size

theta

distribution parameter

...

further optional arguments

Value

value of the cumulative distribution function at point x.

Details

If the distribution is Binomial, theta denotes the rate difference between intervention and control group. Then, the mean is assumed to be √ n theta.

If the distribution is Normal, then the mean is assumed to be √ n theta.

Examples

cumulative_distribution_function(Binomial(.1, TRUE), 1, 50, .3)
#> [1] 0.004310344

cumulative_distribution_function(Pearson2xK(3), 1, 30, get_tau_Pearson2xK(c(0.3,0.4,0.7,0.2)))
#> [1] 0.001966853
cumulative_distribution_function(ZSquared(TRUE), 1, 35, get_tau_ZSquared(0.4, 1))
#> [1] 0.2466166


cumulative_distribution_function(ANOVA(3), 1, 30, get_tau_ANOVA(c(0.3, 0.4, 0.7, 0.2)))
#> [1] 0.2402678

cumulative_distribution_function(Normal(), 1, 50, .3)
#> [1] 0.3085375

cumulative_distribution_function(Student(two_armed = FALSE), .75, 50, .9)
#> [1] 1.062003e-08

cumulative_distribution_function(Survival(0.6,TRUE),0.75,50,0.9)
#> [1] 0.899164