Skip to main content
MathOverflow

Return to Question

replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
Source Link
Community Bot
Community Bot
  • 1
  • 2
  • 3

This is a cross-post of the unanswered question (the given answer turned out to be incorrect) http://math.stackexchange.com/questions/245591/period-of-linear-congruential-generatorhttps://math.stackexchange.com/questions/245591/period-of-linear-congruential-generator .

How can you calculate the probability distribution of the period length of a linear congruential generator? This is $X_{n+1} = (aX_n + c) \bmod m$ where $a$ and $c$ are chosen uniformly from $\{0,\dots, m-1\}$ and $m$ is a fixed prime. Take $X_0$ to be an arbitrary integer from $\{0,\dots,m-1\}$.

If it is hard to do exactly, is it possible to give good bounds for the cdf?

This is a cross-post of the unanswered question (the given answer turned out to be incorrect) http://math.stackexchange.com/questions/245591/period-of-linear-congruential-generator .

How can you calculate the probability distribution of the period length of a linear congruential generator? This is $X_{n+1} = (aX_n + c) \bmod m$ where $a$ and $c$ are chosen uniformly from $\{0,\dots, m-1\}$ and $m$ is a fixed prime. Take $X_0$ to be an arbitrary integer from $\{0,\dots,m-1\}$.

If it is hard to do exactly, is it possible to give good bounds for the cdf?

This is a cross-post of the unanswered question (the given answer turned out to be incorrect) https://math.stackexchange.com/questions/245591/period-of-linear-congruential-generator .

How can you calculate the probability distribution of the period length of a linear congruential generator? This is $X_{n+1} = (aX_n + c) \bmod m$ where $a$ and $c$ are chosen uniformly from $\{0,\dots, m-1\}$ and $m$ is a fixed prime. Take $X_0$ to be an arbitrary integer from $\{0,\dots,m-1\}$.

If it is hard to do exactly, is it possible to give good bounds for the cdf?

added 46 characters in body
Source Link
ArtM
ArtM
  • 21
  • 2

This is a cross-post of the unanswered question (the given answer turned out to be incorrect) http://math.stackexchange.com/questions/245591/period-of-linear-congruential-generator .

How can you calculate the probability distribution of the period length of a linear congruential generator? This is $X_{n+1} = (aX_n + c) \bmod m$ where $a$ and $c$ are chosen uniformly from $\{0,\dots, m-1\}$ and $m$ is a fixed prime. Take $X_0$ to be an arbitrary integer from $\{0,\dots,m-1\}$.

If it is hard to do exactly, is it possible to give good bounds for the cdf?

This is a cross-post of the unanswered question http://math.stackexchange.com/questions/245591/period-of-linear-congruential-generator .

How can you calculate the probability distribution of the period length of a linear congruential generator? This is $X_{n+1} = (aX_n + c) \bmod m$ where $a$ and $c$ are chosen uniformly from $\{0,\dots, m-1\}$ and $m$ is a fixed prime. Take $X_0$ to be an arbitrary integer from $\{0,\dots,m-1\}$.

If it is hard to do exactly, is it possible to give good bounds for the cdf?

This is a cross-post of the unanswered question (the given answer turned out to be incorrect) http://math.stackexchange.com/questions/245591/period-of-linear-congruential-generator .

How can you calculate the probability distribution of the period length of a linear congruential generator? This is $X_{n+1} = (aX_n + c) \bmod m$ where $a$ and $c$ are chosen uniformly from $\{0,\dots, m-1\}$ and $m$ is a fixed prime. Take $X_0$ to be an arbitrary integer from $\{0,\dots,m-1\}$.

If it is hard to do exactly, is it possible to give good bounds for the cdf?

Source Link
ArtM
ArtM
  • 21
  • 2

Period of linear congruential generator

This is a cross-post of the unanswered question http://math.stackexchange.com/questions/245591/period-of-linear-congruential-generator .

How can you calculate the probability distribution of the period length of a linear congruential generator? This is $X_{n+1} = (aX_n + c) \bmod m$ where $a$ and $c$ are chosen uniformly from $\{0,\dots, m-1\}$ and $m$ is a fixed prime. Take $X_0$ to be an arbitrary integer from $\{0,\dots,m-1\}$.

If it is hard to do exactly, is it possible to give good bounds for the cdf?