2Location and Scale

2.1 The location model

For a systematic treatment of the situations considered in Chapter 1, we need to represent them by probability‐based statistical models. We assume that the outcome c02-i0001 of each observation depends on the “true value” c02-i0002 of the unknown parameter (in Example 1.1, the copper content of the whole flour batch) and also on some random error process. The simplest assumption is that the error acts additively:


where the errors c02-i0003 are random variables. This is called the location model.

If the observations are independent replications of the same experiment under equal conditions, it may be assumed that

  • c02-i0004 have the same distribution function c02-i0005
  • c02-i0006 are independent.

It follows that are independent, with common distribution function


and we say that the are i.i.d ...

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