# tails_i: Interval-Based Tails Comparison In funtimes: Functions for Time Series Analysis

 tails_i R Documentation

## Interval-Based Tails Comparison

### Description

Compare right tails of two sample distributions using an interval-based approach (IBA); see \insertCiteChu_etal_2015_insurance;textualfuntimes and \insertCiteLyubchich_Gel_2017_insurance;textualfuntimes.

### Usage

``````tails_i(x0, x1, d = NULL)
``````

### Arguments

 `x0, x1` vectors of the same length (preferably). Tail in `x1` is compared against the tail in `x0`. `d` a threshold defining the tail. The threshold is the same for both `x0` and `x1`. Default is `quantile(x0, probs = 0.99)`.

### Details

Sturges' formula is used to calculate the number of intervals (`k`) for `x0` `\ge` `d`, then interval width is derived. The tails, `x0` `\ge` `d` and `x1` `\ge` `d`, are divided into intervals. The number of `x1`-values within each interval is compared with the number of `x0`-values within the same interval (this difference is reported as `Nk`).

### Value

A list with two elements:

 `Nk` vector that tells how many more `x1`-values compared with `x0`-values there are within each interval. `Ck` vector of the intervals' centers.

### Author(s)

Calvin Chu, Yulia R. Gel, Vyacheslav Lyubchich

### References

\insertAllCited

`q.tails`

### Examples

``````x0 <- rnorm(1000)
x1 <- rt(1000, 5)
tails_i(x0, x1)

``````

funtimes documentation built on March 31, 2023, 7:35 p.m.