true_dist: True Distributions

In zhoucx1119/LogConcaveDESM: Log-Concave Density Estimation Using the Score Matching Loss Function

True Distributions

Description

Functions for drawing random samples from the specified distribution and evaluating the underlying density function and the first derivative of its logarithm.

Usage

truncated_normal(parent_mean, parent_sd, domain)

truncated_gamma(parent_shape, parent_rate, domain)

truncated_lognormal(parent_meanlog, parent_sdlog, domain)

beta_dist(shape1, shape2)

Arguments

parent_mean	A numeric of the mean parameter in the parent normal distribution.
parent_sd	A numeric of the standard deviation parameter in the parent normal distribution; must be strictly positive.
domain	A numeric vector of the domain over which the distribution is defined.
parent_shape	A numeric of the shape parameter in the parent gamma distribution; must be strictly positive.
parent_rate	A numeric of the rate parameter in the parent gamma distribution; must be strictly positive.
parent_meanlog	A numeric of the mean parameter in the parent log-normal distribution in the log scale.
parent_sdlog	A numeric of the standard deviation parameter in the parent log-normal distribution in the log scale.
shape1, shape2	Numeric values of the parameters in the parent beta distribution; must be strictly positive.

Value

An object of class "truncated_normal", "truncated_gamma", "truncated_lognormal", or "beta_dist", whose underlying structure is a list containing the following elements

sampling

function: generates random samples from the underlying distribution. The input is sample_size, the number of desired samples, and the output is a numeric vector of random samples.

evaluate_density

function: returns the underlying density values. The input is newx, the points at which the density function is to be evaluated, and the output is a data frame with the first column being the sorted newx and the second column being the corresponding density values.

evaluate_logderiv1

function: returns the first derivative values of the logarithm of the underlying density function. The input is newx, the points at which the first derivative is to be evaluated, and the output is a data frame with the first column being the sorted newx and the second column being the corresponding first derivative values.

domain

numeric: a numeric vector over which the density function is defined.

Examples

library(ggplot2)
######################################
# truncated normal
parent_mean <- 4
parent_sd <- 1
domain <- c(2, 5)
t_normal <- truncated_normal(parent_mean, parent_sd, domain)

# ------------------------------------
# sampling function
samples <- t_normal$sampling(10000)
df <- data.frame(x = samples)
x <- seq(domain[1], domain[2], by = 0.01)
y <- (dnorm(x, parent_mean, parent_sd) /
(pnorm(domain[2], parent_mean, parent_sd) -
pnorm(domain[1], parent_mean, parent_sd)))
density_df <- data.frame(x = x, y = y)
# use the Freedman-Diaconis rule for the binwidth
binwidth <- 2 * IQR(samples) / (length(samples) ** (1/3))
plot <- ggplot() +
geom_histogram(data = df, aes(x = x, y = ..density..),
binwidth = binwidth, color = "darkblue", fill = "lightblue") +
geom_line(data = density_df, aes(x = x, y = y), color = "black", size = 0.75) +
theme_bw()
plot

# ------------------------------------
# evaluate density
t_normal$evaluate_density(seq(-5, 10, by = 0.1))

# ------------------------------------
# evaluate derivative of log-density
t_normal$evaluate_logderiv1(seq(-5, 10, by = 0.1))

######################################
# truncated gamma
domain <- c(0, 10)
parent_shape <- 5
parent_rate <- 1
t_gamma <- truncated_gamma(parent_shape, parent_rate, domain)

# ------------------------------------
# sampling function
samples <- t_gamma$sampling(10000)
df <- data.frame(x = samples)
x <- seq(domain[1], domain[2], by = 0.01)
y <- (dgamma(x, parent_shape, parent_rate) /
(pgamma(domain[2], parent_shape, parent_rate) -
pgamma(domain[1], parent_shape, parent_rate)))
density_df <- data.frame(x = x, y = y)
# use the Freedman-Diaconis rule for the binwidth
binwidth <- 2 * IQR(samples) / (length(samples) ** (1/3))
plot <- ggplot() +
geom_histogram(data = df, aes(x = x, y = ..density..),
binwidth = binwidth, color = "darkblue", fill = "lightblue") +
geom_line(data = density_df, aes(x = x, y = y), color = "black", size = 0.75) +
theme_bw()
plot

# ------------------------------------
# evaluate density
t_gamma$evaluate_density(seq(-5, 10, by = 0.1))

# ------------------------------------
# evaluate derivative of log-density
t_gamma$evaluate_logderiv1(seq(-5, 10, by = 0.1))

######################################
# truncated lognormal
parent_meanlog <- 0
parent_sdlog <- 1/4
domain <- c(0, 5)
t_lognormal <- truncated_lognormal(parent_meanlog, parent_sdlog, domain)

# ------------------------------------
# sampling function
samples <- t_lognormal$sampling(10000)
df <- data.frame(x = samples)
x <- seq(domain[1], domain[2], by = 0.01)
y <- (dlnorm(x, parent_meanlog, parent_sdlog) /
(plnorm(domain[2], parent_meanlog, parent_sdlog) -
plnorm(domain[1], parent_meanlog, parent_sdlog)))
density_df <- data.frame(x = x, y = y)
# use the Freedman-Diaconis rule for the binwidth
binwidth <- 2 * IQR(samples) / (length(samples) ** (1/3))
plot <- ggplot() +
geom_histogram(data = df, aes(x = x, y = ..density..),
binwidth = binwidth, color = "darkblue", fill = "lightblue") +
geom_line(data = density_df, aes(x = x, y = y), color = "black", size = 0.75) +
theme_bw()
plot

# ------------------------------------
# evaluate density
t_lognormal$evaluate_density(seq(-5, 10, by = 0.1))

# ------------------------------------
# evaluate derivative of log-density
t_lognormal$evaluate_logderiv1(seq(-5, 10, by = 0.1))

######################################
# beta distribution
shape1 <- 4
shape2 <- 2
domain <- c(0, 1)
b <- beta_dist(shape1, shape2)

# ------------------------------------
# sampling function
samples <- b$sampling(10000)
df <- data.frame(x = samples)
x <- seq(domain[1], domain[2], by = 0.01)
y <- dbeta(x, shape1, shape2)
density_df <- data.frame(x = x, y = y)
# use the Freedman-Diaconis rule for the binwidth
binwidth <- 2 * IQR(samples) / (length(samples) ** (1/3))
plot <- ggplot() +
geom_histogram(data = df, aes(x = x, y = ..density..),
binwidth = binwidth, color = "darkblue", fill = "lightblue") +
geom_line(data = density_df, aes(x = x, y = y), color = "black", size = 0.75) +
theme_bw()
plot

# ------------------------------------
# evaluate density
b$evaluate_density(seq(0, 1, by = 0.1))

# ------------------------------------
# evaluate derivative of log-density
b$evaluate_logderiv1(seq(0, 1, by = 0.1))

zhoucx1119/LogConcaveDESM documentation built on Aug. 28, 2024, 3:25 p.m.