Package {ierd}

Pipe operator

Description

See magrittr::%>% for details.

Usage

lhs %>% rhs

Arguments

Value

The result of calling rhs(lhs).

Density of the Inverted Exponentiated Rayleigh Distribution

Description

This function computes the probability density function (PDF) of the Inverted Exponentiated Rayleigh distribution.

Usage

dierd(x, shape, scale)

Arguments

Details

The probability density function is mathematically defined as:

f(x) = 2 \alpha \beta x^{-3} \exp(-\beta / x^2) (1 - \exp(-\beta / x^2))^{\alpha - 1}

for x > 0, where \alpha is the shape parameter and \beta is the scale parameter.

Value

A numeric vector of density values evaluated at x.

Examples

# Compute the density at various values of x
dierd(x = c(0.5, 1, 1.5, 2), shape = 2, scale = 1)

Cumulative Distribution Function of the Inverted Exponentiated Rayleigh Distribution

Description

This function computes the Cumulative Distribution Function (CDF) of the Inverted Exponentiated Rayleigh distribution.

Usage

pierd(t, shape, scale)

Arguments

Details

The cumulative distribution function is mathematically defined as:

F(t) = 1 - (1 - \exp(-\beta / t^2))^\alpha

for t > 0, where \alpha is the shape parameter and \beta is the scale parameter.

Value

A numeric vector of cumulative probabilities evaluated at t.

Examples

# Compute the cumulative probabilities at various values of t
pierd(t = c(0.5, 1, 1.5, 2), shape = 2, scale = 1)

Plot Multiple Inverted Exponentiated Rayleigh Densities

Description

This function creates a ggplot2 visualization comparing the dierd PDF across combinations of shape and scale parameters.

Usage

plot_dierd(shape, scale, lower = 0.01, upper = 5, paired = FALSE)

Arguments

Value

A ggplot object showing the density curves.

Examples

# Full grid: 2 shapes * 2 scales = 4 curves
plot_dierd(shape = c(1, 2), scale = c(1, 2))

# Paired: 2 specific combinations = 2 curves
plot_dierd(shape = c(1, 2), scale = c(1, 2), paired = TRUE)

Plot Multiple Inverted Exponentiated Rayleigh CDFs

Description

This function creates a ggplot2 visualization of the pierd CDF across combinations of shape and scale parameters.

Usage

plot_pierd(shape, scale, lower = 0.01, upper = 7.5, paired = FALSE)

Arguments

Value

A ggplot object showing the cumulative distribution curves.

Examples

# Full grid: 2 shapes * 2 scales = 4 curves
plot_pierd(shape = c(1, 2), scale = c(1, 2))

# Paired: 2 specific combinations = 2 curves
plot_pierd(shape = c(1, 2), scale = c(1, 2), paired = TRUE)

Quantile Function of the Inverted Exponentiated Rayleigh Distribution

Description

This function computes the quantile function (inverse CDF) of the Inverted Exponentiated Rayleigh distribution.

Usage

qierd(p, shape, scale)

Arguments

Details

The quantile function is mathematically defined as:

Q(p) = \sqrt{\frac{-\beta}{\log(1 - (1 - p)^{1/\alpha})}}

for 0 \le p \le 1, where \alpha is the shape parameter and \beta is the scale parameter.

Value

A numeric vector of quantiles evaluated at p.

Examples

# Compute the quantiles at various probability values (e.g., quartiles)
qierd(p = c(0.25, 0.5, 0.75), shape = 2, scale = 1)

Random Numbers from the Inverted Exponentiated Rayleigh Distribution

Description

This function generates random numbers from an Inverted Exponentiated Rayleigh distribution using inverse transform sampling.

Usage

rierd(n, shape, scale)

Arguments

Value

A numeric vector of length n containing the generated random numbers.

Examples

# Generate 10 random numbers with shape = 2 and scale = 1
rierd(n = 10, shape = 2, scale = 1)