@Bernard Girma

I might be able to help you, if you haven't found them yet, but I would need some more information.

I guess that they maybe didn't come from Farsund, but from some other nearby parishes. And their last names might be something else way back in Norway. I would guess that their last name was originally their fathers last name, since people often started using their fathers last name instead of their patronymicon (Fathers first name + -sen or -datter) when they emigrated to US.

Another problem that I have found about information from records in United States, is that dates and other information might not always be correct.

I am from that area, so I might give it a try.

Are they in FS FamilyTree? Do you have their PID's?

@Bernard Girma

It appears that the above family search ID is likely correct. Josephine's family seemed to have traveled a bit and husband and wife are from different locations in Norway. She even went back to Norway for the birth of one son Arne where her full name was given as Elen Josefine Gustine Andersen.

https://www.familysearch.org/ark:/61903/3:1:3QHV-B3PP-KWP6?cc=4237104

So their records point to various locations. But this (entry 46) is almost certainly her birth record in Kvelde, Hedrum Parish, Vestfold.

https://media.digitalarkivet.no/en/view/5917/30301/98

She was in Rogaland in 1900 (it states she was born in Kvelde)

https://www.digitalarkivet.no/en/census/person/pf01037263000355

Her return from Norway to Chicago in 1911 with sons Arne born in Norway and Carl born in Chicago.

https://www.familysearch.org/ark:/61903/3:1:3Q9M-C9T4-SLHW?i=788&cc=1368704&personaUrl=%2Fark%3A%2F61903%2F1%3A1%3AJJG7-PQM

A sister born in Egersund, Rogaland. (the 1911 immigration erroneously says Josephine was born in Egersund but actually the family moved there later.

https://www.digitalarkivet.no/en/view/255/pd00000020949370

Here she is in a different location (Hordaland) in the 1891 census with her parents and siblings:

https://www.digitalarkivet.no/en/census/person/pf01052966004285

Here is her parents marriage in 1877 (entry 9) giving their birth dates and father's names

https://www.familysearch.org/ark:/61903/3:1:3QHK-93PP-YD6L?cc=4237104&personaUrl=%2Fark%3A%2F61903%2F1%3A1%3A68Q7-2MMD

Parents familysearch IDs (not linked yet to Josephine)

https://www.familysearch.org/tree/person/details/MFGM-CQ2

This may be her grandfather Anders Petter Johannesen in the Egersund 1875 census. It appears he is from Sweden

https://www.digitalarkivet.no/en/census/person/pf01052242000363

In some records he is from Elfsborg Sweden which is now apparently called Frölunda

https://geographic.org/geographic_names/name.php?uni=-3412401&fid=5901&c=sweden

Another Elfsborg Sweden

https://mapcarta.com/N5107847242

It might be that Elfsborg is Älvsborg Län Sweden.

I think this might be a Bråttensby, Älvsborg, Sverige census record of your Anders Petter Johannesen and his parents and siblings. The 21 August 1851 birthdate matches and the location is similar to the Bråthuberg, Elfsborg, Sverige location indexed in his marriage record. Looking at the actual image of the marriage record the location is likely Bråttensby.

https://www.familysearch.org/tree/person/sources/GDB5-VHY

a new familysearch ID for this one with his parents/siblings: GDB5-VHY