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hyginn 2020-09-23 00:32:36 +10:00
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FND-STA-Probability_distribution.R
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@ -1,20 +1,16 @@
# tocID <- "FND-STA-Probability_distribution.R" # tocID <- "FND-STA-Probability_distribution.R"
# #
# ---------------------------------------------------------------------------- #
# PATIENCE ... #
# Do not yet work wih this code. Updates in progress. Thank you. #
# boris.steipe@utoronto.ca #
# ---------------------------------------------------------------------------- #
# #
# Purpose: A Bioinformatics Course: # Purpose: A Bioinformatics Course:
# R code accompanying the FND-STA-Probability_distribution unit. # R code accompanying the FND-STA-Probability_distribution unit.
# #
# Version: 1.3 # Version: 1.4
# #
# Date: 2017 10 - 2019 01 # Date: 2017-10 - 2020-09
# Author: Boris Steipe (boris.steipe@utoronto.ca) # Author: Boris Steipe (boris.steipe@utoronto.ca)
# #
# Versions: # Versions:
# 1.4 2020 Maintenance
# 1.3 Change from require() to requireNamespace(), # 1.3 Change from require() to requireNamespace(),
# use <package>::<function>() idiom throughout, # use <package>::<function>() idiom throughout,
# 1.2 Update set.seed() usage # 1.2 Update set.seed() usage
@ -34,24 +30,24 @@
#TOC> ========================================================================== #TOC> ==========================================================================
#TOC> #TOC>
#TOC> Section Title Line #TOC> Section Title Line
#TOC> ----------------------------------------------------------------------------- #TOC> -----------------------------------------------------------------------------
#TOC> 1 Introduction 52 #TOC> 1 Introduction 54
#TOC> 2 Three fundamental distributions 115 #TOC> 2 Three fundamental distributions 117
#TOC> 2.1 The Poisson Distribution 118 #TOC> 2.1 The Poisson Distribution 120
#TOC> 2.2 The uniform distribution 172 #TOC> 2.2 The uniform distribution 174
#TOC> 2.3 The Normal Distribution 192 #TOC> 2.3 The Normal Distribution 194
#TOC> 3 quantile-quantile comparison 233 #TOC> 3 quantile-quantile comparison 235
#TOC> 3.1 qqnorm() 243 #TOC> 3.1 qqnorm() 245
#TOC> 3.2 qqplot() 309 #TOC> 3.2 qqplot() 311
#TOC> 4 Quantifying the difference 326 #TOC> 4 Quantifying the difference 328
#TOC> 4.1 Chi2 test for discrete distributions 361 #TOC> 4.1 Chi2 test for discrete distributions 363
#TOC> 4.2 Kullback-Leibler divergence 452 #TOC> 4.2 Kullback-Leibler divergence 454
#TOC> 4.2.1 An example from tossing dice 463 #TOC> 4.2.1 An example from tossing dice 465
#TOC> 4.2.2 An example from lognormal distributions 586 #TOC> 4.2.2 An example from lognormal distributions 588
#TOC> 4.3 Kolmogorov-Smirnov test for continuous distributions 629 #TOC> 4.3 Kolmogorov-Smirnov test for continuous distributions 631
#TOC> #TOC>
#TOC> ========================================================================== #TOC> ==========================================================================
@ -167,10 +163,10 @@ set.seed(NULL)
# Add these values to the plot # Add these values to the plot
y <- numeric(26) # initialize vector with 26 slots y <- numeric(26) # initialize vector with 26 slots
y[as.numeric(names(t)) + 1] <- t # put the tabled values there (index + 1) y[as.numeric(names(t)) + 1] <- t # put the tabled values there (index + 1)
points(midPoints, y, pch = 21, cex = 0.7, bg = "firebrick") points(midPoints - 0.55, y, type = "s", col = "firebrick")
legend("topright", legend("topright",
legend = c("poisson distribution", "samples"), legend = c("theoretical", "simulated"),
pch = c(22, 21), pch = c(22, 22),
pt.bg = c("#E6FFF6", "firebrick"), pt.bg = c("#E6FFF6", "firebrick"),
bty = "n") bty = "n")
@ -230,7 +226,7 @@ for (i in 1:length(v)) {
v[i] <- mean(sample(x, 77)) v[i] <- mean(sample(x, 77))
} }
hist(v, breaks = 20, col = "#F8DDFF") hist(v, breaks = 20, col = "#F8DDFF", freq = FALSE)
# The outcomes all give normal distributions, regardless what the details of our # The outcomes all give normal distributions, regardless what the details of our
# original distribution were! # original distribution were!
@ -466,7 +462,7 @@ chisq.test(countsL1, countsG1.9, simulate.p.value = TRUE, B = 10000)
# be applied to discrete distributions. But we need to talk a bit about # be applied to discrete distributions. But we need to talk a bit about
# converting counts to p.m.f.'s. # converting counts to p.m.f.'s.
# === 4.2.1 An example from tossing dice # === 4.2.1 An example from tossing dice
# The p.m.f of an honest die is (1:1/6, 2:1/6, 3:1/6, 4:1/6, 5:1/6, 6:1/6). But # The p.m.f of an honest die is (1:1/6, 2:1/6, 3:1/6, 4:1/6, 5:1/6, 6:1/6). But
# there is an issue when we convert sampled counts to frequencies, and estimate # there is an issue when we convert sampled counts to frequencies, and estimate
@ -589,7 +585,7 @@ abline(v = KLdiv(rep(1/6, 6), pmfPC(counts, 1:6)), col="firebrick")
# somewhat but not drastically atypical. # somewhat but not drastically atypical.
# === 4.2.2 An example from lognormal distributions # === 4.2.2 An example from lognormal distributions
# We had compared a set of lognormal and gamma distributions above, now we # We had compared a set of lognormal and gamma distributions above, now we
# can use KL-divergence to quantify their similarity: # can use KL-divergence to quantify their similarity: