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Jason S
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Oh wait -- I just thought of something:

  • generate $u$ from a uniform distribution $\in [-1,1]$
  • calculate $x = |u|^p \operatorname{sgn} u$ for $0 < p \leq1$ (also include $p=0$ by defining $x=1$ if $u=0$), which yields a uniform distribution for $p=1$ and a point distribution for $p=0$.

Not sure of its variance, but the general behavior is what I'm looking for.

cdf here for p=0, 0.2, 0.4, 0.6, 0.8, 1.0

enter image description here

Oh wait -- I just thought of something:

  • generate $u$ from a uniform distribution $\in [-1,1]$
  • calculate $x = |u|^p \operatorname{sgn} u$ for $0 < p \leq1$ (also include $p=0$ by defining $x=1$ if $u=0$), which yields a uniform distribution for $p=1$ and a point distribution for $p=0$.

Not sure of its variance, but the general behavior is what I'm looking for.

Oh wait -- I just thought of something:

  • generate $u$ from a uniform distribution $\in [-1,1]$
  • calculate $x = |u|^p \operatorname{sgn} u$ for $0 < p \leq1$ (also include $p=0$ by defining $x=1$ if $u=0$), which yields a uniform distribution for $p=1$ and a point distribution for $p=0$.

Not sure of its variance, but the general behavior is what I'm looking for.

cdf here for p=0, 0.2, 0.4, 0.6, 0.8, 1.0

enter image description here

Source Link
Jason S
  • 255
  • 1
  • 8

Oh wait -- I just thought of something:

  • generate $u$ from a uniform distribution $\in [-1,1]$
  • calculate $x = |u|^p \operatorname{sgn} u$ for $0 < p \leq1$ (also include $p=0$ by defining $x=1$ if $u=0$), which yields a uniform distribution for $p=1$ and a point distribution for $p=0$.

Not sure of its variance, but the general behavior is what I'm looking for.