Editing Propagation of uncertainty (section)

====Reciprocal and shifted reciprocal====
{{main|Reciprocal normal distribution}}
In the special case of the inverse or reciprocal <math>1/B</math>, where <math>B=N(0,1)</math> follows a [[standard normal distribution]], the resulting distribution is a reciprocal standard normal distribution, and there is no definable variance.<ref name=Johnson>{{cite book
  | last1 = Johnson | first1 = Norman L.
  | last2 = Kotz    | first2 = Samuel
  | last3 = Balakrishnan | first3 = Narayanaswamy
  | title = Continuous Univariate Distributions, Volume 1
  | year = 1994
  | publisher = Wiley
  | isbn=0-471-58495-9
  | pages = 171
  }}</ref>

However, in the slightly more general case of a shifted reciprocal function <math>1/(p-B)</math> for <math>B=N(\mu,\sigma)</math> following a general normal distribution, then mean and variance statistics do exist in a [[principal value]] sense, if the difference between the pole <math>p</math> and the mean <math>\mu</math> is real-valued.<ref name=lecomte2013exact>{{Cite journal
| last1= Lecomte | first1 = Christophe
| title = Exact statistics of systems with uncertainties: an analytical theory of rank-one stochastic dynamic systems
| journal = Journal of Sound and Vibration
| volume = 332
| issue =  11
| date = May 2013
| pages = 2750–2776
| doi = 10.1016/j.jsv.2012.12.009
| bibcode = 2013JSV...332.2750L
}}</ref>