The statistical distribution of the mean squared weighted deviation

The probability distribution of the mean squared weighted deviation (MSWD) is derived and its dependence on degrees of freedom f is shown. The expectation (or mean) value of MSWD=1 and is not a function of f. However, the +1σ range of the expectation value of the MSWD decreases with increasing f. The standard deviation of the MSWD is σ = ±(2/f)1/2. If MSWD 1+2(2/f)1/2, there is only <5% probability that the data define an isochron. Use of MSWD as a criterion for accepting or rejecting the assumption of an isochron may be applied only if analytical errors σxi and σyi are well known.