高校数学の質問スレ（医者・東大卒専用） Part438

高校数学の質問スレ（医者・東大卒専用） Part438 (991ﾚｽ)
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849: 05/25(日)06:42 ID:P4nhnL8B(3/6) AA×
>>847

849:  [sage] 2025/05/25(日) 06:42:27.34 ID:P4nhnL8B

>>847
このプロトタイプをAIに与えて描画機能やコメントをつけてもらった。

beta.parameter <- function(lower, upper, credMass = 0.95, verbose = FALSE) {

# Helper function to convert decimal numbers to fraction strings using MASS::fractions
fractionStr <- function(x) {
as.character(MASS::fractions(x))
}

# Function to compute beta parameter (beta) based on alpha,
# derived from the condition on the shape of the distribution between lower and upper
f <- function(alpha) {
1 + ((alpha - 1) * log(upper / lower)) / log((1 - lower) / (1 - upper))
}

# Root-finding function: difference between desired credible mass
# and the Beta CDF probability between lower and upper with parameters (alpha, f(alpha))
g <- function(alpha) {
pbeta(upper, alpha, f(alpha)) - pbeta(lower, alpha, f(alpha)) - credMass
}

# Find the root of g(alpha) = 0 over the interval [1, 1e5]
# to find the alpha value that satisfies the credible mass condition
re <- uniroot(g, c(1, 1e5))
alpha <- re$root
beta <- f(alpha)

# Calculate the mean of the Beta distribution
mean <- alpha / (alpha + beta)

# Calculate the mode if defined (alpha > 1 and beta > 1),
# otherwise set mode to NA as it is undefined
mode <- if (alpha > 1 && beta > 1) {
(alpha - 1) / (alpha + beta - 2)
} else {
NA
}

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