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Obtaining simple characterizations of the shape of a distribution was the purpose of Galtung's AJUS system proposed in Galtung (1969) and implemented, for instance, in the R agrmt package. As summariz …

If your assumptions regarding the normality of $X$ and $Y$ are correct, then you have two normally distributed random variables $X\sim\mathcal{N}(\mu_X, \sigma_X^2)$ and $Y\sim\mathcal{N}(\mu_Y, \sigm …

Mathematically, it sounds like you have the following piecewise linear function for $P(A=1~|~B=t)$: $$P(A=1~|~B = t) = \left\{\begin{array}{ll} 0 & \text{if}~t < T^- \\ \frac{t-T^-}{2(T-T^-)} & \tex …

Of course many distributions would fit. …

Let's assume $r_i$, the rank of list element $i$, has a value in $\{0, 1, \ldots, n-1\}$ for a list with $n$ elements (ties can be broken randomly). Then we could define the probability of selecting $ …

Consider the following example: $$ X\sim\text{Unif}(0, 1) \\ Y = 1-X $$ $X$ and $Y$ are identically distributed as the standard uniform distribution, and $X-Y = 2X-1$, so $X-Y\sim\text{Unif}(-1, 1)$ …

A good example of this is provided by Glen_b -Reinstate Monica at https://stats.stackexchange.com/a/189633/40036 . The question there was slightly different -- asking if normally distributed $X$ and $ …