statistics/normal_distribution.R

result <- dbSendQuery(conn, query_frames)
data <- fetch(result)

get_variance <- function(dataset = vector(), mean = 0) {
    sum <- 0
    for (item in dataset) {
        sum <- sum + ((item - mean) ^ 2)
    }

    variance <- sum / length(dataset)

    return(variance)
}

get_standard_deviation <- function(variance = 0) {
    return(round(sqrt(variance)))
}

dnorm_plot <- function(filename = "dnorm", dataset = vector(), title = "Title", xlab = "X Label") {
    mean <- round(mean(dataset))

    standard_deviation <- get_standard_deviation(get_variance(dataset, mean))

    possibility <- dnorm(dataset, mean, standard_deviation)

    png(file = filename)

    plot(dataset,
        possibility,
        xlab = xlab,
        ylab = "Probability Density",
        col = "blue",
        main = title)

    abline(v = c(mean, mean - standard_deviation, mean + standard_deviation),
        col = c("green", "red", "red"),
        lty = c(2, 2, 2))

    legend("topright",
        legend = c(round(mean, 2), standard_deviation),
        col = c("green", "red"),
        lty = 2,
        lwd = 1,
        box.lty = 1)
}

pnorm_less <- function(dataset = vector(), value = 0, word = "") {
    mean <- mean(dataset)

    standard_deviation <- get_standard_deviation(get_variance(dataset, mean))

    probability_text <- "The probability of getting less than"
    probability_text <- paste(probability_text, value)
    probability_text <- paste(probability_text, word)
    probability_text <- paste(probability_text, "is")
    probability_text <- paste(probability_text, round(pnorm(value, mean, standard_deviation) * 100, 2))
    probability_text <- paste(probability_text, "%", sep = "")

    print(probability_text)
}

pnorm_more <- function(dataset = vector(), value = 0, word = "") {
    mean <- mean(dataset)

    standard_deviation <- get_standard_deviation(get_variance(dataset, mean))

    probability_text <- "The probability of getting more than"
    probability_text <- paste(probability_text, value)
    probability_text <- paste(probability_text, word)
    probability_text <- paste(probability_text, "is")
    probability_text <- paste(probability_text, round(pnorm(value, mean, standard_deviation, lower.tail = FALSE) * 100, 2))
    probability_text <- paste(probability_text, "%", sep = "")

    print(probability_text)
}

pnorm_between <- function(dataset = vector(), min = 0, max = 0, word = "") {
    mean <- mean(dataset)

    standard_deviation <- get_standard_deviation(get_variance(dataset, mean))

    probability_text <- "The probability of getting between"
    probability_text <- paste(probability_text, min)
    probability_text <- paste(probability_text, "and")
    probability_text <- paste(probability_text, max)
    probability_text <- paste(probability_text, "coins is")
    probability_text <- paste(probability_text, round((pnorm(max, mean, standard_deviation) - pnorm(min, mean, standard_deviation)) * 100, 2))
    probability_text <- paste(probability_text, "%", sep = "")

    print(probability_text)
}

dnorm_plot("out/dnorm_coins.png", sort(data[, 1]), "Coins Normal Distribution", xlab = "Coins")
dnorm_plot("out/dnorm_time.png", sort(data[, 2]), "Time Normal Distribution", xlab = "Time (s)")

pnorm_less(sort(data[, 1]), 5, "coins")
pnorm_more(sort(data[, 1]), 5, "coins")
pnorm_between(sort(data[, 1]), 8, 10, "coins")