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# sindwem: sum of individual weighted means

This R package contains exactly one function, that calculates the "sum of individual weighted means" according to a methodology that is quite common among archaeologists and was first published in 1988 by Elisabeth Fentress and Philip Perkins.

The base data is usually made of a number of artefact types (in most cases, ceramic types): for each type, we know the time span (earliest known date of production, latest known date of production) and a quantity of items, that can be from a single site, from a region, etc.

The desired result is a plot with time on the X axis and a "trend" on the Y axis, based on the combination of all recorded types. The idea is that phases of abandonment can be easily spotted by local minima.

A naive approach would be to calculate the average date for each type, and assign the number of items to that date. This approach is not correct, since types have different time spans: a type dated from 400 to 200 BCE (200 years) would result in the same date as a type dated from 320 to 280 BCE (40 years).

A more correct approach is to assume a uniform distribution for the entire time span, and "weight" each type according to its actual time span. This is what this package does at the moment.

The best approach would be to model the time span according to a probability distribution of choice: there is no accepted standard but, as a suggestion, a normal distribution is perhaps better than a uniform distribution to model the quantity of items of a certain type produced over time.

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