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