How to find the parameters for a skewed normal distribution?

According to this website: https://datayze.com/labor-probability-calculator

One can model the probability distribution function of spontaneous labour given two pieces of information.

a) the due date of the pregnant women b) the current date

I have a set of information that provides the due date of labour, and actual date of labour for hundred's of women. It looks like this:

Est. Due Date Actual Labour Date
11th Sep 9th Sep
12th Oct 18th Oct
... ...
15th Aug 26th July

I would like to be able to generate a model similar to the above linked website that allows me to make predictions similar to the website. I.e. I can make a statement like

Your due date is 14th November 2022, given you haven't already given birth there is a x% chance you will give birth today.

or more generally a function that takes a due date as input and outputs the probability of the labour happening over the next number of days (until that probability hits 0 or close enough)

I.e. if the due date is 14th Nov and labour hasn't occurred yet it might produce:

Date Probability of labour
11th Nov 3.1%
12th Nov 3.6%
... ...
15th Dec 0.00003%

The website suggests a skewed normal distribution, but I am not sure how to generate these given the data I have.

Does anyone know how to model such a distribution given what I have and how to use that to make predictions?