Evaluate the cumulative distribution function of a Cauchy distribution

Usage

# S3 method for Cauchy
cdf(d, x, drop = TRUE, elementwise = NULL, ...)

Arguments

d: A Cauchy object created by a call to Cauchy().
x: A vector of elements whose cumulative probabilities you would like to determine given the distribution d.
drop: logical. Should the result be simplified to a vector if possible?
elementwise: logical. Should each distribution in d be evaluated at all elements of x (elementwise = FALSE, yielding a matrix)? Or, if d and x have the same length, should the evaluation be done element by element (elementwise = TRUE, yielding a vector)? The default of NULL means that elementwise = TRUE is used if the lengths match and otherwise elementwise = FALSE is used.
...: Arguments to be passed to pcauchy. Unevaluated arguments will generate a warning to catch mispellings or other possible errors.

Value

In case of a single distribution object, either a numeric vector of length probs (if drop = TRUE, default) or a matrix with length(x) columns (if drop = FALSE). In case of a vectorized distribution object, a matrix with length(x) columns containing all possible combinations.

Examples


set.seed(27)

X <- Cauchy(10, 0.2)
X
#> [1] "Cauchy distribution (location = 10, scale = 0.2)"

mean(X)
#> [1] NaN
variance(X)
#> [1] NaN
skewness(X)
#> [1] NaN
kurtosis(X)
#> [1] NaN

random(X, 10)
#>  [1]  9.982203 10.053876  9.916324 10.336325 10.167877 10.626557 10.046357
#>  [8] 10.001540 10.091892 10.137681

pdf(X, 2)
#> [1] 0.0009940971
log_pdf(X, 2)
#> [1] -6.913676

cdf(X, 2)
#> [1] 0.00795609
quantile(X, 0.7)
#> [1] 10.14531

cdf(X, quantile(X, 0.7))
#> [1] 0.7
quantile(X, cdf(X, 7))
#> [1] 7