# How to impute distribution by day based on per-week data

I have data from the CDC on the gestational length of pregnancies to the nearest week between 2007 and 2017. This is based on the "obstetric estimate" of gestation since it's rare that the mother knows the precise date of conception. I want to estimate these values down to the length in days based on the week-to-week estimates.

This is a thought experiment, not a medical project in which anyone's health rests on the outcome!

Here's the distribution by week. Data at the bottom.

The mean value is 38.5783 and the median is 39 (as is the mode, obviously). If I understand Wikipedia right, this is a normal distribution with a negative skew.

I think this is a pretty simple exercise, but how do I compute the distribution based on these landmark values (which we can consider Wednesday, or day 4 of the week), and then get the probability for the other six days in each interval?

I've seen example of researchers fitting a curve to the same data, such as in this paper, where the peak value of the model is not always aligned with the peak observation:

Thanks! Here's the data

weeks    births
28       74485
29       83165
30       111793
31       142432
32       215732
33       305938
34       559606
35       860860
36       1721195
37       3889454
38       7878585
39       15551230
40       9524099
41       2785017
42       175345
43       11835
44       3510
45       1214

• I don't understand, you have your distribution which is expressed in weeks (which looks like it is measured on a discrete scale, so not really normally distributed), and now you want to convert this distribution into days? If you have data only at a week level, there is no way to tell on which day it happened. Please edit your question with more details about your objective and data. Also your question has nothing to do with imputation. – user2974951 Feb 12 at 8:28
• I would convert to days, and then using maximum likelihood estimation with interval censoring. Then values for each day can be read off the estimated curve. – kjetil b halvorsen Mar 6 at 22:38