Collection of utility functions used in the KEHRA project (see http://www.brunel.ac.uk/ife/britishcouncil). It refers to the multidimensional analysis of air pollution, weather and health data.

Uses Bessel functions to calculate the
    fundamental and complementary analytic solutions to the
    Kelvin differential equation.

Computes the Kendall rank correlation and Mann-Kendall
        trend test. See documentation for use of block bootstrap when
        there is autocorrelation.

The computational complexity of the implemented algorithm for
    Kendall's correlation is O(n log(n)), which is faster than the base R
    implementation with a computational complexity of O(n^2). For small vectors
    (i.e., less than 100 observations), the time difference is negligible.
    However, for larger vectors, the speed difference can be substantial and the
    numerical difference is minimal. The references are
    Knight (1966) <doi:10.2307/2282833>,
    Abrevaya (1999) <doi:10.1016/S0165-1765(98)00255-9>,
    Christensen (2005) <doi:10.1007/BF02736122> and
    Emara (2024) <https://learningcpp.org/>.
    This implementation is described in
    Vargas Sepulveda (2025) <doi:10.1371/journal.pone.0326090>.

Kendall random walks are a continuous-space Markov chains generated
             by the Kendall generalized convolution. This package provides tools
             for simulating these random walks and studying distributions
             related to them. For more information about Kendall random walks see Jasiulis-Gołdyn (2014) <arXiv:1412.0220>.

Miscellaneous functions and data used in psychological research and teaching. Keng 
    currently has a built-in dataset depress, and could (1) scale a vector; (2) compute the cut-off 
    values of Pearson's r with known sample size; (3) test the significance and compute the post-hoc
    power for Pearson's r with known sample size; (4) conduct a priori power analysis and plan the 
    sample size for Pearson's r; (5) compare lm()'s fitted outputs using R-squared, f_squared, 
    post-hoc power, and PRE (Proportional Reduction in Error, also called partial R-squared or 
    partial Eta-squared); (6) calculate PRE from partial correlation, Cohen's f, or f_squared; 
    (7) conduct a priori power analysis and plan the sample size for one or a set of predictors in 
    regression analysis; (8) conduct post-hoc power analysis for one or a set of predictors in 
    regression analysis with known sample size; (9) randomly pick numbers for Chinese Super Lotto
    and Double Color Balls; (10) assess course objective achievement in Outcome-Based Education.