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Spacekime Analytics (Time Complexity and Inferential Uncertainty)

Chapter 6: Circular Kime-Phase and Electron Orbit Densities (Circular Distributions)

# install.packages("circular")
# library(crosstalk)
# crosstalkLibs()
library(htmlwidgets)
library(circular)
library(animation)
library(ggplot2)
library(tidyr)
library(plotly)

In this TCIU/Spacekime section, we show some of the parallels between circular kime-phase densities and electron orbital densities depicted as 2D circular or 3D spherical distributions.

1 Random sampling from a given probability distribution

By definition, experimental science and confirmatory evidence decision-making are based on observations, which are typically assumed to be identically-distributed and independent (IID) random samples from an unknown distribution. Observable phenomena (or processes) may be modeled by simple primary distributions, or by composite superpositions (or mixtures) of several primary (base) distributions.

The animation below illustrates the process of drawing a random sample from any univariate distribution. Analogous IID sampling applies for drawing random observations from multiple (multivariate) distributions, see SOCR bivariate and trivariate distribution webapp.