vmtable: Rounds a contingency table of meteor magnitude frequencies

In vismeteor: Analysis of Visual Meteor Data

Rounds a contingency table of meteor magnitude frequencies

Description

The meteor magnitude contingency table of VMDB contains half meteor counts (e.g. 3.5). This function converts these frequencies to integer values.

Usage

vmtable(mt)

Arguments

mt	table; A two-dimensional contingency table of meteor magnitude frequencies.

Details

The contingency table of meteor magnitudes mt must be two-dimensional. The row names refer to the magnitude observations. Column names must be integer meteor magnitude values. Also, the columns must be sorted in ascending or descending order of meteor magnitude.

A sum-preserving algorithm is used for rounding. It ensures that the total frequency of meteors per observation is preserved. The marginal frequencies of the magnitudes are also preserved with the restriction that the deviation is at most \pm 0.5. If the total sum of a meteor magnitude is integer, then the deviation is \pm 0.

The algorithm is unbiased: for a fixed observation order it preserves the original totals without introducing systematic drift, even though each run follows the deterministic sequence dictated by the observed counts and their ordering.

Value

A rounded contingency table of meteor magnitudes is returned.

Note

Internally the counts are doubled to half-meteor units, leftover halves are alternated between rows so column margins stay within \pm 0.5, and when the grand total is odd the matrix is temporarily mirrored so the unavoidable surplus meteor originates from the opposite end of the magnitude scale rather than always favouring the faintest bin. The mirroring is only the initial condition; the loop then processes the table cell by cell so the rounding direction alternates between bright and faint magnitudes depending on the current row and column state.

Examples

# For example, create a contingency table of meteor magnitudes
mt <- as.table(matrix(
    c(
        0.0, 0.0, 2.5, 0.5, 0.0, 1.0,
        0.0, 1.5, 2.0, 0.5, 0.0, 0.0,
        1.0, 0.0, 0.0, 3.0, 2.5, 0.5
    ), nrow = 3, ncol = 6, byrow = TRUE
))
colnames(mt) <- seq(6)
rownames(mt) <- c('A', 'B', 'C')
mt
margin.table(mt, 1)
margin.table(mt, 2)

# contingency table with integer values
(mt.int <- vmtable(mt))
margin.table(mt.int, 1)
margin.table(mt.int, 2)

vismeteor documentation built on Nov. 5, 2025, 6:23 p.m.