| Title: | Inverted Exponentiated Rayleigh Distribution Tools |
| Version: | 0.1.1 |
| Description: | Provides the density, distribution function, quantile function, random generation, and visualization tools for the Inverted Exponentiated Rayleigh Distribution. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| RoxygenNote: | 8.0.0 |
| Imports: | dplyr, ggplot2, magrittr, tidyr |
| URL: | https://github.com/SudiptaPal0709/ierd |
| BugReports: | https://github.com/SudiptaPal0709/ierd/issues |
| Language: | en-US |
| NeedsCompilation: | no |
| Packaged: | 2026-06-08 22:59:39 UTC; sudip |
| Author: | Sudipta Pal [aut, cre] |
| Maintainer: | Sudipta Pal <sudiptapal0709@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2026-06-16 20:10:02 UTC |
Pipe operator
Description
See magrittr::%>% for details.
Usage
lhs %>% rhs
Arguments
lhs |
A value or the magrittr placeholder. |
rhs |
A function call using the magrittr semantics. |
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
x |
A numeric vector of quantiles. |
shape |
A strictly positive numeric value for the shape parameter ( |
scale |
A strictly positive numeric value for the scale parameter ( |
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
t |
A numeric vector of quantiles. |
shape |
A strictly positive numeric value for the shape parameter ( |
scale |
A strictly positive numeric value for the scale parameter ( |
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
shape |
A numeric vector of strictly positive shape parameters. |
scale |
A numeric vector of strictly positive scale parameters. |
lower |
A numeric value for the lower bound of the x-axis (default is 0.01). |
upper |
A numeric value for the upper bound of the x-axis (default is 5). |
paired |
Logical. If FALSE (default), creates a full grid of all possible shape and scale combinations. If TRUE, pairs the shape and scale vectors element-by-element (vectors must be the same length). |
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
shape |
A numeric vector of strictly positive shape parameters. |
scale |
A numeric vector of strictly positive scale parameters. |
lower |
A numeric value for the lower bound of the x-axis (default is 0.01). |
upper |
A numeric value for the upper bound of the x-axis (default is 7.5). |
paired |
Logical. If FALSE (default), creates a full grid of all possible shape and scale combinations. If TRUE, pairs the shape and scale vectors element-by-element (vectors must be the same length). |
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
p |
A numeric vector of probabilities. |
shape |
A strictly positive numeric value for the shape parameter ( |
scale |
A strictly positive numeric value for the scale parameter ( |
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
n |
An integer specifying the number of random values to return. |
shape |
A strictly positive numeric value for the shape parameter. |
scale |
A strictly positive numeric value for the scale parameter. |
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)