Wikipedia:Reference desk/Archives/Science/2019 December 16
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December 16
editStatistics: What causes what distribution?
editI get that if you throw a handful of dice, you'll end up with a normal distribution. Could someone suggest literature matching process/phenomenon to expected distribution? (not only how to statistically analyze the resulting distribution) --C est moi anton (talk) 06:20, 16 December 2019 (UTC)
- A book that will give you lots of real world examples of distributions is "Statistical Procedures for Engineering, Management, and Science" by Leland Blank. It has a section called "Level Two: Distributions and Their Uses". The section contains several chapters, each on a different distribution, and several examples within each chapter. The examples are fairly specific, rather than general phenomena, so it might not be exactly what you are looking for.--Wikimedes (talk) 07:46, 16 December 2019 (UTC)
- A fair traditional die thrown once provides a Univariate distribution of its 6 discrete settling positions, each with probability 1/6 = 0.166... . A true normal or Gaussian distribution can only be approximated by dice throws due to the Central limit theorem that states that the average of many throws with finite mean and variance is itself a random variable whose distribution converges to a normal distribution as the number of throws increases. DroneB (talk) 15:43, 16 December 2019 (UTC)
- If every throw is done precisely the same way, wouldn't the same face of the die turn up nearly all if not all the time? ←Baseball Bugs What's up, Doc? carrots→ 16:03, 16 December 2019 (UTC)
- No, because the system is highly sensitive to initial conditions. A rolled die is not a perfect random system (studies have shown that there is are small effects that skew statistics ever so slightly one way or the other over many rolls) but insofar as it is a random system, a rolled die and the results of rolling thereof is akin to the double pendulum problem, in the sense that the tolerances for resetting the system are much larger than the differences in outcomes based on those differences. In other words, it isn't physically possible to recreate the initial conditions given that your level of uncertainty over those initial conditions is large enough that variations within those unknowables produces unpredictably different results. This is the basis for studies like chaos theory, which is a powerful tool making meaningful conclusions about such systems without resorting to the clockwork universe requirements of Newtonian physics. --Jayron32 21:06, 16 December 2019 (UTC)
- Presumably, using some sort of machine to roll a die or toss a coin would negate the presumed "randomness" of it - and we also assume those objects are "fair", i.e. that they are weight-balanced. ←Baseball Bugs What's up, Doc? carrots→ 22:10, 16 December 2019 (UTC)
- If presumption could make things work then a Brownian ratchet sort-of-machine promises free power. DroneB (talk)
- Refs to Coin_flipping#Physics say coin flip probabilities can be derandomized in real conditions (e.g. an illusionist performing a trick). Dice rolls is not in our article, a bit of searching finds [1] and it's more complicated: basically, if you can limit the die to a few bounces it falls on the initially-up face way more often, but if not, it's pretty much "random" (chaotic). TigraanClick here to contact me 15:50, 17 December 2019 (UTC)
- Presumably, using some sort of machine to roll a die or toss a coin would negate the presumed "randomness" of it - and we also assume those objects are "fair", i.e. that they are weight-balanced. ←Baseball Bugs What's up, Doc? carrots→ 22:10, 16 December 2019 (UTC)
- No, because the system is highly sensitive to initial conditions. A rolled die is not a perfect random system (studies have shown that there is are small effects that skew statistics ever so slightly one way or the other over many rolls) but insofar as it is a random system, a rolled die and the results of rolling thereof is akin to the double pendulum problem, in the sense that the tolerances for resetting the system are much larger than the differences in outcomes based on those differences. In other words, it isn't physically possible to recreate the initial conditions given that your level of uncertainty over those initial conditions is large enough that variations within those unknowables produces unpredictably different results. This is the basis for studies like chaos theory, which is a powerful tool making meaningful conclusions about such systems without resorting to the clockwork universe requirements of Newtonian physics. --Jayron32 21:06, 16 December 2019 (UTC)
- If every throw is done precisely the same way, wouldn't the same face of the die turn up nearly all if not all the time? ←Baseball Bugs What's up, Doc? carrots→ 16:03, 16 December 2019 (UTC)
- A fair traditional die thrown once provides a Univariate distribution of its 6 discrete settling positions, each with probability 1/6 = 0.166... . A true normal or Gaussian distribution can only be approximated by dice throws due to the Central limit theorem that states that the average of many throws with finite mean and variance is itself a random variable whose distribution converges to a normal distribution as the number of throws increases. DroneB (talk) 15:43, 16 December 2019 (UTC)
- If you're interested in the applications to physics: Wikipedia has compiled a list of textbooks in thermodynamics and statistical mechanics. Of these, I can personally recommend Landau and Lifshitz; Kittel; Stowe.
- It is fair to say that the whole art of modern physics is the qualitative process of matching a physical phenomenon to the statistical distribution that accurately models it. The more unexplored parts of modern physics are those phenomena for which scientists still debate which model is appropriate - or even if any statistical model is appropriate at all.
- Nimur (talk) 16:04, 16 December 2019 (UTC)