Evaluates moments of ratios (and products) of quadratic forms
    in normal variables, specifically using recursive algorithms developed by
    Bao and Kan (2013) <doi:10.1016/j.jmva.2013.03.002> and Hillier et al.
    (2014) <doi:10.1017/S0266466613000364>. Also provides distribution,
    quantile, and probability density functions of simple ratios of quadratic
    forms in normal variables with several algorithms. Originally developed as
    a supplement to Watanabe (2023) <doi:10.1007/s00285-023-01930-8> for
    evaluating average evolvability measures in evolutionary quantitative
    genetics, but can be used for a broader class of statistics. Generating 
    functions for these moments are also closely related to the top-order zonal
    and invariant polynomials of matrix arguments.

Option pricing (financial derivatives) techniques mainly following textbook 'Options, Futures and Other Derivatives', 9ed by John C.Hull, 2014. Prentice Hall. Implementations are via binomial tree option model (BOPM), Black-Scholes model, Monte Carlo simulations, etc. 
  This package is a result of Quantitative Financial Risk Management course (STAT 449 and STAT 649) at Rice University, Houston, TX, USA, taught by Oleg Melnikov, statistics PhD student, as of Spring 2015.

Function that implements the Quantum Genetic Algorithm, first proposed by Han and Kim in 2000. This is an R implementation of the 'python' application developed by Lahoz-Beltra  (<https://github.com/ResearchCodesHub/QuantumGeneticAlgorithms>). Each optimization problem is represented as a maximization one, where each solution is a sequence of (qu)bits. Following the quantum paradigm, these qubits are in a superposition state: when measuring them, they collapse in a 0 or 1 state. After measurement, the fitness of the solution is calculated as in usual genetic algorithms. The evolution at each iteration is oriented by the application of two quantum gates to the amplitudes of the qubits: (1) a rotation gate (always); (2) a Pauli-X gate (optionally). The rotation is based on the theta angle values: higher values allow a quicker evolution, and lower values avoid local maxima. The Pauli-X gate is equivalent to the classical mutation operator and determines the swap between alfa and beta amplitudes of a given qubit. The package has been developed in such a way as to permit a complete separation between the engine, and the particular problem subject to combinatorial optimization.