Kurtosis

Description

Compute the kurtosis (Fisher or Pearson) of a dataset.

Usage

<Expr>$kurtosis(fisher = TRUE, bias = TRUE)

Arguments

`fisher`	If `TRUE` (default), Fisher’s definition is used (normal, centered at 0). Otherwise, Pearson’s definition is used (normal, centered at 3).
`bias`	If `FALSE`, the calculations are corrected for statistical bias.

Details

Kurtosis is the fourth central moment divided by the square of the variance. If Fisher’s definition is used, then 3 is subtracted from the result to give 0 for a normal distribution.

If bias is FALSE, then the kurtosis is calculated using k statistics to eliminate bias coming from biased moment estimators.

Value

Expr

Examples

library("polars")

pl$DataFrame(a = c(1:3, 2:1))$
  with_columns(kurt = pl$col("a")$kurtosis())

#> shape: (5, 2)
#> ┌─────┬───────────┐
#> │ a   ┆ kurt      │
#> │ --- ┆ ---       │
#> │ i32 ┆ f64       │
#> ╞═════╪═══════════╡
#> │ 1   ┆ -1.153061 │
#> │ 2   ┆ -1.153061 │
#> │ 3   ┆ -1.153061 │
#> │ 2   ┆ -1.153061 │
#> │ 1   ┆ -1.153061 │
#> └─────┴───────────┘