Help for package StatDeriveR

Title:

Step-by-Step Derivation and Simulation Verification in Mathematical Statistics

Version:

0.1.0

Description:

Provides step-by-step derivations of key results in mathematical statistics, including transformations of random variables, order statistics, and sampling distributions. The package combines analytical derivation with Monte Carlo simulation to compare theoretical and empirical results, facilitating deeper understanding of statistical theory and its computational implementation. The methods are motivated by standard treatments in mathematical statistics (Hogg, McKean, and Craig, 2019, ISBN: 9780134686991).

License:

MIT + file LICENSE

Encoding:

UTF-8

Language:

en-US

Depends:

R (≥ 4.0.0)

Imports:

grDevices, graphics, stats

Suggests:

knitr, rmarkdown, testthat (≥ 3.0.0)

RoxygenNote:

7.3.3

URL:

https://github.com/Jokhrof042/StatDeriveR

BugReports:

https://github.com/Jokhrof042/StatDeriveR/issues

NeedsCompilation:

Packaged:

2026-04-06 16:12:14 UTC; lenovo

Author:

Jokhrof Ahmed Doha [aut, cre]

Maintainer:

Jokhrof Ahmed Doha <s-2021711817@isrt.du.ac.bd>

Repository:

CRAN

Date/Publication:

2026-04-10 14:00:02 UTC

Get CDF function for a distribution

Description

Get CDF function for a distribution

Usage

.cdf_eval(dist, params)

Arguments

dist

Character name of distribution

params

List of distribution parameters

Value

A function that evaluates the cdf

Compute theoretical mean of order statistic

Description

Compute theoretical mean of order statistic

Usage

.compute_orderstat_mean(dist, params, n, r)

Compute theoretical variance of order statistic

Description

Compute theoretical variance of order statistic

Usage

.compute_orderstat_var(dist, params, n, r)

Default parameters for distribution

Description

Default parameters for distribution

Usage

.default_params(dist)

Arguments

dist

Distribution name

Value

List of default parameters

Derive Y = exp(X)

Description

Derive Y = exp(X)

Usage

.derive_exp_x(dist, params, support)

Derive Y = 1/X

Description

Derive Y = 1/X

Usage

.derive_inv_x(dist, params, support)

Derive Y = log(X)

Description

Derive Y = log(X)

Usage

.derive_log_x(dist, params, support)

Derive Y = sqrt(X)

Description

Derive Y = sqrt(X)

Usage

.derive_sqrt_x(dist, params, support)

Derive Y = X^2

Description

Derive Y = X^2

Usage

.derive_x_squared(dist, params, support)

Format distribution for printing

Description

Format distribution for printing

Usage

.format_dist(dist, params)

Arguments

dist

Distribution name

params

Parameters

Value

Formatted string

Get PDF function for a distribution

Description

Get PDF function for a distribution

Usage

.pdf_eval(dist, params)

Arguments

dist

Character name of distribution

params

List of distribution parameters

Value

A function that evaluates the pdf

Plot order statistic with theory vs simulation

Description

Plot order statistic with theory vs simulation

Usage

.plot_orderstat(x)

Plot transformation with theory vs simulation

Description

Plot transformation with theory vs simulation

Usage

.plot_transform(x)

Print order statistic derivation

Description

Print order statistic derivation

Usage

.print_orderstat(x)

Print simulation results

Description

Print simulation results

Usage

.print_simulation(x)

Print transformation derivation

Description

Print transformation derivation

Usage

.print_transform(x)

Get random number generator

Description

Get random number generator

Usage

.rng_eval(dist, params, n)

Arguments

dist

Character name of distribution

params

List of distribution parameters

n

Number of observations

Value

Vector of random values

Simulate order statistic

Description

Simulate order statistic

Usage

.simulate_orderstat(object, n_sim)

Simulate transformed variable

Description

Simulate transformed variable

Usage

.simulate_transform(object, n_sim)

Get support of a distribution

Description

Get support of a distribution

Usage

.support_eval(dist, params)

Arguments

dist

Character name of distribution

params

List of distribution parameters

Value

List with lower and upper bounds

Derive the distribution of an order statistic

Description

Derive the distribution of an order statistic

Usage

derive_orderstat(dist, params, n, r)

Arguments

dist

Character: base distribution name

params

List: distribution parameters

n

Integer: sample size

r

Integer: order (1 = min, n = max)

Value

Object of class "statderive" with order statistic derivation

Examples

# Minimum of 5 exponential(rate=2) samples
obj <- derive_orderstat(
  dist = "exponential",
  params = list(rate = 2),
  n = 5,
  r = 1
)

Derive the distribution of a transformed random variable

Description

Derive the distribution of a transformed random variable

Usage

derive_transform(dist, params, transform, support = NULL)

Arguments

dist

Character: base distribution name

params

List: distribution parameters

transform

Character: transformation (e.g., "x^2", "sqrt(x)", "1/x")

support

Optional vector c(lower, upper) for original support

Value

Object of class "statderive" with derivation steps

Examples

# Transform Y = X^2 where X ~ Uniform(0,1)
obj <- derive_transform(
  dist = "uniform",
  params = list(min = 0, max = 1),
  transform = "x^2"
)

Imported functions

Description

Internal imports required for package checks.

Plot method for statderive objects

Description

Plot method for statderive objects

Usage

## S3 method for class 'statderive'
plot(x, y = NULL, ...)

Arguments

x

Object of class "statderive"

y

Unused (required for S3 plot method)

...

Additional arguments

Value

Invisibly returns the input object x (of class statderive). This function is called primarily for its side effect of producing plots that compare simulated data with theoretical probability density functions.

Print method for statderive objects

Description

Print method for statderive objects

Usage

## S3 method for class 'statderive'
print(x, ...)

Arguments

x

Object of class "statderive"

...

Additional arguments

Value

Invisibly returns the input object x (of class statderive). This function is called primarily for its side effect of printing a formatted summary of the statistical derivation and optional simulation results.

Run Monte Carlo simulation and compare with theory

Description

Run Monte Carlo simulation and compare with theory

Usage

simulate_check(object, n_sim = 10000, seed = 123)

Arguments

object

Object of class "statderive" from derive_transform or derive_orderstat

n_sim

Integer: number of simulations (default 10000)

seed

Integer: random seed for reproducibility

Value

Updated object with simulation results added

Examples

obj <- derive_transform("uniform", list(min = 0, max = 1), "x^2")
obj_sim <- simulate_check(obj, n_sim = 5000)