a_j {countSTAR}

Inverse rounding function

Description

Define the intervals associated with y = j based on the flooring function. The function returns -Inf for j = 0 (or smaller) and Inf for any j >= y_max + 1, where y_max is a known upper bound on the data y (if specified).

Usage

a_j(j, y_max = Inf)

Arguments

j

the integer-valued input(s)

y_max

a fixed and known upper bound for all observations; default is Inf

Value

The (lower) interval endpoint(s) associated with j.

Examples

# Standard cases:
a_j(1)
a_j(20)

# Boundary cases:
a_j(0)
a_j(20, y_max = 15)