Chapter04 {DanielBiostatistics10th}

R Documentation

Chapter 4

Description

Functions for Chapter 4, Probability Distributions.

Usage

binomBar(size, prob, xlim = size, title)

poisBar(lambda, xlim, title)

Arguments

size	non-negative integer scalar, number of trials for binomial distribution
prob	numeric scalar between 0 and 1, probability of success on each trial for binomial distribution
xlim	length-two numeric vector, horizontal limit of the figure
title	character scalar, title of the figure
lambda	positive numeric scalar, mean of Poisson distribution

Details

binomBar() and poisBar() generate bar plots of binomial and Poisson distributions.

Value

binomBar() and poisBar() returns a 'discreteDistBar' object, for which a print method, an autolayer and an autoplot method are defined.

References

Wayne W. Daniel, Biostatistics: A Foundation for Analysis in the Health Sciences, Tenth Edition. Wiley, ISBN: 978-1-119-62550-6.

See Also

dbinom dpois

Examples

binomBar(size = 25L, prob = .1)
poisBar(lambda = 12, xlim = 30L)

library(DanielBiostatistics10th)

# Page 93-97, Example 4.2.1 - Example 4.2.7
d421 = rep(1:8, times = c(62L, 47L, 39L, 39L, 58L, 37L, 4L, 11L))
(fq421 = print_freqs(factor(d421))) # Page 94, Table 4.2.1 and 4.2.2; Page 96, Table 4.2.3

# ?dbinom # 'd' for binomial 'density'; calculate Prob(X = x)
# ?pbinom # 'p' for binomial 'probability' 
# `lower.tail = TRUE` (default), calculate Prob(X <= x)
# `lower.tail = FALSE`, calculate Prob(X > x)

# Page 99, Example 4.3.1
dbinom(x = 3L, size = 5L, prob = .858)
# Page 103, Example 4.3.2
dbinom(x = 4L, size = 10L, prob = .14)
# Page 103, Example 4.3.3
(pL = pbinom(q = 5L, size = 25L, prob = .1, lower.tail = TRUE)) # (a) including!
(pU = pbinom(q = 5L, size = 25L, prob = .1, lower.tail = FALSE)) # (b) excluding!
pL + pU # R makes sure they add up to 1
# Page 105, Example 4.3.4
dbinom(x = 7L, size = 12L, prob = .55)
pbinom(q = 5L, size = 12L, prob = .55)
pbinom(q = 7L, size = 12L, prob = .55, lower.tail = FALSE)

# Page 110, Example 4.4.1
dpois(x = 3L, lambda = 12) 
# Page 110, Example 4.4.2
ppois(2L, lambda = 12, lower.tail = FALSE)
# Page 110, Example 4.4.3
ppois(1L, lambda = 2) 
# Page 111, Example 4.4.4
dpois(3L, lambda = 2)
# Page 112, Example 4.4.5
ppois(5L, lambda = 2, lower.tail = FALSE)

# Page 119. Example 4.6.1
pnorm(2)
# Page 120. Example 4.6.2
pnorm(2.55) - pnorm(-2.55)
1 - 2 * pnorm(-2.55) # alternative solution
# Page 121. Example 4.6.3
pnorm(1.53) - pnorm(-2.74)
# Page 121. Example 4.6.4
pnorm(2.71, lower.tail = FALSE)
# Page 122. Example 4.6.5
pnorm(2.45) - pnorm(.84)

# Page 122. Example 4.7.1
pnorm(q = 3, mean = 5.4, sd = 1.3)
pnorm(q = (3-5.4)/1.3) # manual solution
# Page 125. Example 4.7.2
pnorm(649, mean = 491, sd = 119) - pnorm(292, mean = 491, sd = 119)
# Page 122. Example 4.7.3
1e4L * pnorm(8.5, mean = 5.4, sd = 1.3, lower.tail = FALSE)

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