code snippets for inverse chi-square distribution

inverschi.py

from scipy.stats.distributions import chi2
chi2.ppf(0.95, df=5)     # 11.07

inversechi.py

function mean_of_inversechi(v) {
    if (v > 2) {
    return 1/(v-2);
    }else{
     return 0;
    }

}




function variance_of_inversechi(v) {
    if (v > 2) {
    return 2/(Math.pow(v-2,2) * (v-4));
    }else{
     return 0;
    }

}



function inverseChiSquarePDF(x, v) {
    if (x <= 0 || v <= 0) {
        throw new Error("Both x and degrees of freedom (v) must be greater than 0");
    }

    const numerator = Math.pow(2, -v / 2);
    const denominator = jStat.gammafn(v / 2);
    const exponent = -1 / (2 * x);

    const pdfValue = (numerator / denominator) * Math.pow(x, -(v / 2) - 1) * Math.exp(exponent);

    return pdfValue;
}

inversechi.R

library(VGAMextra)
xx    <- seq(0, 3.0, len = 301)
yy    <- dinv.chisq(xx, df = df)
qtl   <- seq(0.1, 0.9, by = 0.1)
d.qtl <- qinv.chisq(qtl, df = df)
plot(xx, yy, type = "l", col = "orange", 
     main = "Orange is density, blue is cumulative distribution function",
     sub  = "Brown dashed lines represent the 10th, ... 90th percentiles",
     las = 1, xlab = "x", ylab = "", ylim = c(0, 1))
abline(h = 0, col= "navy", lty = 2)
lines(xx, pinv.chisq(xx, df = df), col = "blue")
lines(d.qtl, dinv.chisq(d.qtl, df = df), type ="h", col = "brown", lty = 3)