I am working on a dataset on time devoted to domestic work by individuals I have grouped the data based on the day of the week the information has been collected. This was done to examine the relation between mean and variance for the variable. So, we have 7 points, 1 for each day of the week. My finding is that mean and variance is not independent and has a relation with each other. But the relation is appearing negative, meaning as mean is rising for a group, variance is falling. While days like Monday, Tuesday and Wednesday have low mean and high variance, days like Sunday have high mean and low variance. Can you please give some suggestions whether this corresponds to any known distributions?
2
-
$\begingroup$ The question is missing a lot of information so I cannot provide you with a known distribution that might have this property. But here are some things to think about/add to your question: - What's the variable that you are measuring? If this variable has some upper bound, and the groups are grouped based on this variable, it can be that the groups with the highest mean are just approaching the upper bound, hence the variance within these groups falls. - If the first is not the case, a probability distribution is more than just a mean and variance. Examine the relationship of the higher moments $\endgroup$– ImotVoksimCommented Jun 9, 2022 at 18:20
-
$\begingroup$ I have made the changes in my question as suggested by you. Kindly suggest me what I should do in order to determine the underlying distribution. It doesn't follow Normal distribution since there is over-dispersion in the variable and also mean-variance are not independent. $\endgroup$– Deb B.Commented Jun 10, 2022 at 8:36
Add a comment
|