Surveys show 74 % of people believe they are above average drivers.
This claim motivates my question, but some clarification is needed. I am not asking for someone to source out the statistic nor to address the empirical claim. Rather, I would like a concrete and simple example of my intuition that it is mathematically possible. I've put together a wish list of additional criteria:
- Has a 'clean' algebraic expression for its probability density function or probability mass function (i.e. not just a constructed dataset or a 'tortured piecewise function')
- Support is single-variable
- Support is continuous or contiguous
- If support is discrete, each bin with nonzero probability mass must have one or two adjacent bins with nonzero probability mass
- Distribution is unimodal