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5 votes
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Does CDF must have value 0 at lowest possible input?

Consider the following probability function as an example: $$f(x) = \left\{ \begin{array}{@{}ll@{}} 0.2, & \text{if}\ x=0, \\ 0.8 \cdot \beta(x;\alpha,\beta), & 0 < x < 1 \...
jbowman's user avatar
  • 40.5k
4 votes

How to show that many functions (a hundred, a thousand) have the same shape an distribution of values over an interval?

To show that several functions are more or less the same you could just superimpose them graphically. I don't think quantile plots of any flavour are directly relevant or likely to be helpful. The ...
Nick Cox's user avatar
  • 58.6k
3 votes

Exercise on finding probability density function

It is simpler to do this with a single integral. For all $u>0$ we can write the distribution function as: $$\begin{align} F_U(u) &\equiv \mathbb{P}(U \leqslant u) \\[12pt] &= \mathbb{P}(...
Ben's user avatar
  • 129k

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