Simulation and Moment Computation for Order Statistics

Provides a comprehensive set of tools for working with order statistics, including functions for simulating order statistics, censored samples (Type I and Type II), and record values from various continuous distributions. Additionally, it offers functions to compute moments (mean, variance, skewness, kurtosis) of order statistics for several continuous distributions. These tools assist researchers and statisticians in understanding and analyzing the properties of order statistics and related data. The methods and algorithms implemented in this package are based on several published works, including Ahsanullah et al (2013, ISBN:9789491216831), Arnold and Balakrishnan (2012, ISBN:1461236444), Harter and Balakrishnan (1996, ISBN:9780849394522), Balakrishnan and Sandhu (1995) , Genç (2012) , Makouei et al (2021) and Nagaraja (2013) .

mos: Simulation and Moments Computation for Order Statistics

The mos package provides tools for simulating order statistics, censored samples (Type I and Type II), and record values from various continuous distributions. It also includes functions to compute the moments (mean, variance, skewness, and kurtosis) of order statistics using exact or simulation-based methods.

Installation

You can install the package from CRAN with:

install.packages("mos")

Features

• Simulation of order statistics from known or user-defined distributions via ros().
• Generation of censored samples: rcens() and rpcens2().
• Generation of upper and lower k-records: rkrec().
• Moment computations for order statistics using closed-form or Monte Carlo methods:
  • Exact: mo_unif(), mo_exp(), mo_weibull(), etc.
  • Simulated: mo_norm(), mo_gamma(), mo_beta(), etc.

Example

Compute the first and second moments of the 2nd order statistic from an exponential distribution:

mo_exp(r = 2, n = 10, k = 1)  # First moment
mo_exp(r = 2, n = 10, k = 2)  # Second moment

Simulate order statistics from the normal distribution:

ros(size = 5, r = 2, n = 10, dist = "norm", mean = 0, sd = 1)

License

GPL-3