From what I eventually found on familysearch and then what I subsequently found on Ancestry there is a lot of conflict here and, as usual, sources not given.
The one thing all the trees seem to agree on is that he was born 3/1/1861 in Thisted, Viborg, Denmark BUT there is no such birth entry on familysearch in that place! Plus, familysearch tree and ancestry trees show different parents!! Most of the ancestry trees show Peder's parents are Henrik Andersen and Karin Kirstine Ballzegen or Baltzersen BUT although this couple did have a son Peder born 3/1/1861 it was in Pjedsted, Vejle, Denmark!
Peder Anderson married Christine Schumacher 23/5/1886 in Midhirst, Stratford, Taranaki, New Zealand (the same place in which he died in 1909). The various trees all show that this was a second marriage for him and that first wife was a Charlotte who'd died in 1880. Again, if this marriage took place 1/11/1879 Denmark she died soon after. The trees also suggest she was born 1865 which would mean that Peder was 18 and Charlotte 14 when they married?? However, can find no trace of such a marriage.
In view of all the conflicting information I think some serious and thorough research needs to be done to confirm a) names of his parents, b) his correct birthplace and c) where the information regarding 1st wife 'Charlotte' has come from.
Annette