Posted a blog entry on my current work, which is looking at how similar the stable distributions are to each other. The upshot is that translating a stable distribution along the axis has the minimal effect for α=1 (e.g.,the Cauchy distribution), and the maximal effect for very small α.
#math #mathematics #probability #statistics
https://www.skewray.com/articles/distance-between-stable-distributions-location-parameter
I've updated my dice problem collection with a new problem (#29 of the now 83 problems).
The question is: how many times, on average, do we need to roll a die, multiplying the results, until we reach a perfect square? So we might roll a 1 or 4 and be immediately square. Or we might roll 2-6-5-4-3-5 to reach the square 3600.
It turns out that the expected number of rolls needed is 2^pi(s) where s is the number of sides of the die, and pi(x) is the number of primes less than or equal to x.
So, curiously, a five-sided and a six-sided die both have 8 as the expected number of rolls.
Also, it doesn't matter whether the die is fair. As long as, for example, all sides are possible (have positive probability), the expected number of rolls is the same as a fair die.
Fun stuff!
https://www.madandmoonly.com/doctormatt/mathematics/dice1.pdf
For two centuries, the credential system gave intelligence a route to heritable capital. Artificial intelligence is closing that route. This essay builds the argument from first principles - with probability theory, interactive simulations, and a prediction specific enough to be falsifiable - and puts a number on the window that remains.
"It's extremely important to realise that a p-value is the probability of observing data like thas observed or more extreme, assuming the hypothesis is correct. It is not the probability of the hypothesis being true, given the data." - Lyons, arXiv:1301.1273
#Science #Physics #Hypothesis #PValue #Probability #Statistics
About metrics for measuring agreement on regression on continuous datasets:
Reasons to avoid R² and use RMSE instead: https://feat.engineering/03-Review_of_the_Modeling_Process.html#sec-reg-metrics
From Max Kuhn @topepo, Kjell Johnson (2026), "Feature Engineering and Selection: A Practical Approach for Predictive Models"
#prediction #dataDev #modelEvaluation #regression #modelling #linearRegression #modeling #probability #probabilities #statistics #stats #gotcha
This 👇🏽 doesn’t actually try to explain the Central Limit Theorem – bummer:
“The Math That Explains Why Bell Curves Are Everywhere”, Quanta (https://www.quantamagazine.org/the-math-that-explains-why-bell-curves-are-everywhere-20260316/).
Have you ever wondered just how quickly the chances of success add up if you can make a check repeatedly without consequence? This post looks at #d20 #checks and how the #probability ramps up, and uses this to make suggestions for applying them at your #DnD or #TTRPG table.
https://melestrua.net/2026/03/22/dice-probabilities-with-multiple-rolls/
Have you ever wondered just how quickly the chances of success add up if you can make a check repeatedly without consequence? This post looks at d20 checks, including with advantage or disadvantage, and how this changes if there is a chance of instant failure.
Skewray Research (ZF¬C)
Space Feed
Matthew Conroy
N-gated Hacker News
QCCEクリス
Eric Maugendre about data
रञ्जित (Ranjit Mathew)
Melestrua (he/him)
DiodioGlow — Sénégal