[R] changing distributions

[Markus Loecher]

Dear fellow R users,
I am struggling with the task of quantifying the statistical significance of changes in a discrete distribution over time.  If I was to measure e.g. the age distribution of people entering a building on a daily basis, I would naturally observe fluctuations in that distribution. Clearly, small variations would be interpreted as "sampling noise" whereas major shifts would indicate sth. more substantial. How would I quantify this ? 
Would a ChiSquare test be an appropriate test for testing overall stationarity ? Or a two-way ANOVA decomposition ?
Also, what if wanted to test specific days for significant deviation from my Null model instead of overall ?
I am familiar with univariate time series change point detection algorithms but am not clear on how to translate these tools to the constrained/multivariate distribution setting.

Thanking you!

Markus