A Simple Test for Changes in Statistical Distributions

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Abstract

It is often difficult to determine whether a variable is undergoing a systematic change. A conventional approach to determining whether a variable exhibits a long-term change in terms of its statistical properties is to apply a trend test or some kind of time series analysis involving various degrees of complexity. Here it is shown that it is possible to indicate, through a simple test based entirely on mathematical logic, whether a series of numbers consists of independent and identically distributed (i.i.d.) numbers.

Examples of the application of the i.i.d. test include testing monthly temperatures for new record values [Benestad, 2004], or studying future trends in extreme monthly precipitation based on large, multimodel ensembles of climate model simulations [Benestad, 2006].

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