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### Absolute continuity of distributions --- why do we need this? [duplicate]

Why do we define continuous probability distribution as those with absolutely continuous CDF, instead of just continuous CDF?
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### How to prove some statistical model to be dominated? [duplicate]

I have a model following the PDF $$f_\theta(x) = \theta^2 x \exp(-\theta x)\delta_{[0, +\infty)}(x)$$ where $\theta > 0$ is the parameter and $\delta_\mathcal{S}$ denotes the indicator function of ...
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60 views

### Sufficient Statistic for Absolutely Continuous Distribution [duplicate]

The following is a homework problem. Please tell me if my solution is correct and if not please point out my mistakes. Let $x_{1}, x_{2},...,x_{M}$ be i.i.d. samples from the absolute continuous ...
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1 vote
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### Are there really many continous distributions without the PDF [duplicate]

This is one interesting question I take some time to search if there is any distribution function that is continuous but without the PDF. After some search I found Cantor distribution, sometimes ...
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