chi2comb

Cumulative density function of linear combinations of independent chi-square random variables and a standard Normal distribution.

As of now, this is basically a repackaging of the davies function implemented in the CompQuadForm library for R.

Requirements

It requires an C compiler toolchain that supports the C11 standard and the cmake software for orchestrating the building process.

Install

You can install it via conda:

conda install -c conda-forge chi2comb

A second installation option would be to download the latest source and to build it by yourself. On Linux or macOS systems it can be as simple as:

bash <(curl -fsSL https://raw.githubusercontent.com/limix/chi2comb/master/install)

Similarly, on Windows you can install by entering in the terminal:

powershell -Command "(New-Object Net.WebClient).DownloadFile('https://raw.githubusercontent.com/limix/chi2comb/master/install.bat', 'install.bat')" && install.bat

Documentation

This library exports a single function:

/** Cumulative distribution function of non-central chi-squared distributions.
 *
 * Computes P[Q<q] where Q=λ₁X₁ + ... + λₙXₙ + σ X₀. Xᵢ is an independent random variable
 * having a non-central chi-squared distribution with nᵢ degrees of freedom and
 * non-centrality parameter δ²ⱼ. X₀ is an independent random variable having a standard
 * Gaussian distribution.
 *
 * Parameters
 * ----------
 * q : double
 *     Value point at which distribution function is to be evaluated.
 * chi2s : struct chi2comb_chisquareds
 *     Chi-squared distributions.
 * gcoef : double
 *     Coefficient of the standard Normal distribution.
 * lim : int
 *     Maximum number of integration terms.
 * abstol : double
 *     Absolute error tolerance.
 * info : struct chi2comb_info*
 *     Algorithm information.
 * result : double *
 *     Estimated c.d.f. evaluated at `q`.
 *
 * Returns
 * -------
 * error : int
 *     0: completed successfully
 *     1: required accuracy not achieved
 *     2: round-off error possibly significant
 *     3: invalid parameters
 *     4: unable to locate integration parameters
 *     5: out of memory
 */
CHI2COMB_API int chi2comb_cdf(double q, struct chi2comb_chisquareds *chi2s, double gcoef,
                              int lim, double abstol, struct chi2comb_info *info,
                              double *result);

The structure

struct chi2comb_chisquareds {
    const double *coefs;  /* chi-squared coefficients */
    const double *ncents; /* noncentrality parameters */
    const int *dofs;      /* degree of freedoms */
    int n;                /* number of terms */
};

represents a list of Noncentral chi-squared distributions and their coefficients.

The structure

struct chi2comb_info {
    double emag; /* error magnitude */
    int niterms; /* total number of integration terms */
    int nints;   /* number of integrations */
    double intv; /* integration interval in final integration */
    double truc; /* truncation point in initial integration */
    double sd;   /* s.d. of initial convergence factor */
    int ncycles; /* cycles to locate integration parameters */
};

stores information about the optimisation method for estimating the c.d.f.

Acknowledgments

• P. Lafaye de Micheaux for creating the amazing CompQuadForm library for R.

Authors

• Danilo Horta

License

This project is licensed under the MIT License.