How can I compare two variables when one has lots of zeros? Specifically, I want to understand the contributions to insurance premiums and claims. In this case, everyone pays a premium, but only some people make claims. I want to understand whether the insurance company is over or undercharging for specific risk attributes. In the example below, the insurance company is properly charging for the additional risk of driving a BMW. I have about 15 variables like 'car' - some nominal, some interval. I'd like to compare the ratio of claim to premium across groups, but I'm struggling to conceptualize how to do this. 
I've tried anova/regression to identify mispriced variables, but I have to perform two - one for claim and one for premium and this is hard to compare. I can't even make a box plot because it doesn't make sense with so many claims as 0.
customer----car----claim-----premium
1--------------bmw-----0-----------200
2--------------bmw-----0-----------200
3--------------bmw-----0-----------200
4--------------bmw-----800--------200
5--------------gmc-----0-----------100
6--------------gmc-----0-----------100
7--------------gmc-----0-----------100
8--------------gmc-----400---------100
 A: Depending on the structure of your data you can either use a regression or descriptive statistics or hypothesis testing. In any case visualising the data will be very useful.
Regressions:
COUNT DATA


*

*Zero-inflated poisson

*Hurdle Poisson

*Zero-inflated NegBin

*Hurdle NegBin
CONTINUOUS DATA


*

*Tobit Regression

*Heckman selection model
Descriptive Statistics:
In terms of descriptive statistics try to look at quantiles instead of the mean. One quantile which is of particular interest is the median.  The mean of claim will be very low because of the zeros.It is the 50th percentile. However if >50 % of the data will be zeros the median will also be zero which makes interpretation difficult. 
Data visualisation:
Note that there are alternatives to boxplots. There are other one-dimensional data visualisations such as violin plots. The violin plot shows more information than the boxplot as it shows the density of the variable. This is especially helpful when you have heavily non-normal data as in your case.  You can also adjust the percentiles of the boxplot manually. 
In any case you can also use a transformed scale. If you want to transform the data you should take into account that 0s have no logarithm. You can use log(x+1) or the inverse hyperbolic sine (asinh() in R) instead.
Hypothesis testing:
You can also use statistical tests in order to compare for the zeros. In this case a t-test might not be optimal as you are violating the assumption of normality. You can try a wilcoxon test instead. 
Concluding recommendation:
I recommend you to use a Heckman selection model. The dependent variable will be the claims and the other variables will be the independent variables in your regression. It is a non-random process which defines which defines whether the claim will be zero, e.g. women may drive more carefully than men and 40 years old drivers may cause less accidents than 20 years old drivers. The two-stage regression will prevent this bias.
