Chapter04 {DanielBiostatistics10th}

Chapter 4: Probability Distributions

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

Functions binomBar and poisBar generate bar plots of binomial and Poisson distributions.

Value

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

See Also

dbinom dpois

Examples

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

library(DanielBiostatistics10th)

# Example 4.2.1-4.2.7; Page 93-97 (10th ed), Page 81-85 (11th ed)
d421 = rep(1:8, times = c(62L, 47L, 39L, 39L, 58L, 37L, 4L, 11L))
print_freqs(d421) # Table 4.2.1, 4.2.2, 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)

# Example 4.2.8; Page 98 (10th ed), Page 85 (11th ed)
mean(d421)
sd(d421)
var(d421)

# Example 4.3.1; Page 99 (10th ed)
dbinom(x = 3L, size = 5L, prob = .858)
# Example 4.3.1; Page 87 (11th ed) 
dbinom(x = 3L, size = 5L, prob = .899)

# Example 4.3.2; Page 103 (10th ed), Page 90 (11th ed)
dbinom(x = 4L, size = 10L, prob = .14)

# Example 4.3.3; Page 103 (10th ed), Page 91 (11th ed)
(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 # = 1

# Example 4.3.4; Page 105 (10th ed), Page 92 (11th ed) 
dbinom(x = 7L, size = 12L, prob = .55)
pbinom(q = 5L, size = 12L, prob = .55)
pbinom(q = 7L, size = 12L, prob = .55, lower.tail = FALSE)

# Example 4.4.1; Page 110 (10th ed), Page 97 (11th ed) 
dpois(x = 3L, lambda = 12) 

# Example 4.4.2; Page 110 (10th ed), Page 98 (11th ed) 
ppois(2L, lambda = 12, lower.tail = FALSE)

# Example 4.4.3; Page 110 (10th ed), Page 98 (11th ed) 
ppois(1L, lambda = 2) 

# Example 4.4.4; Page 111 (10th ed), Page 98 (11th ed) 
dpois(3L, lambda = 2)

# Example 4.4.5; Page 112 (10th ed), Page 98 (11th ed) 
ppois(5L, lambda = 2, lower.tail = FALSE)

# Example 4.6.1; Page 119 (10th ed), Page 106 (11th ed) 
pnorm(2)

# Example 4.6.2; Page 120 (10th ed), Page 106 (11th ed) 
pnorm(2.55) - pnorm(-2.55)
1 - 2 * pnorm(-2.55) # alternative solution

# Example 4.6.3; Page 121 (10th ed), Page 107 (11th ed) 
pnorm(1.53) - pnorm(-2.74)

# Example 4.6.4; Page 121 (10th ed), Page 107 (11th ed) 
pnorm(2.71, lower.tail = FALSE)

# Example 4.6.5; Page 122 (10th ed), Page 107 (11th ed) 
pnorm(2.45) - pnorm(.84)

# Example 4.7.1; Page 122 (10th ed), Page 109 (11th ed) 
pnorm(q = 3, mean = 5.4, sd = 1.3)
pnorm(q = (3-5.4)/1.3) # manual solution

# Example 4.7.2; Page 125 (10th ed), Page 111 (11th ed) 
pnorm(649, mean = 491, sd = 119) - pnorm(292, mean = 491, sd = 119)

# Example 4.7.3; Page 122 (10th ed), Page 111 (11th ed) 
1e4L * pnorm(8.5, mean = 5.4, sd = 1.3, lower.tail = FALSE)