NormalDistribution dist = new(mu: 1, sigma: 3);

// PDF
for (ddouble x = -4; x <= 4; x += 0.125) {
    ddouble pdf = dist.PDF(x);

    Console.WriteLine($"pdf({x})={pdf}");
}

// CDF
for (ddouble x = -4; x <= 4; x += 0.125) {
    ddouble ccdf = dist.CDF(x, Interval.Upper);

    Console.WriteLine($"ccdf({x})={ccdf}");
}

// Quantile
for (int i = 0; i <= 10; i++) {
    ddouble p = (ddouble)i / 10;
    ddouble x = dist.Quantile(p, Interval.Upper);

    Console.WriteLine($"cquantile({p})={x}");
}

// Statistic
Console.WriteLine($"Support={dist.Support}");
Console.WriteLine($"Mu={dist.Mu}");
Console.WriteLine($"Sigma={dist.Sigma}");
Console.WriteLine($"Mean={dist.Mean}");
Console.WriteLine($"Median={dist.Median}");
Console.WriteLine($"Mode={dist.Mode}");
Console.WriteLine($"Variance={dist.Variance}");
Console.WriteLine($"Skewness={dist.Skewness}");
Console.WriteLine($"Kurtosis={dist.Kurtosis}");
Console.WriteLine($"Entropy={dist.Entropy}");

// Random Sampling
Random random = new(1234);
double[] xs = dist.Sample(random, 100000).ToArray();

// Fitting
// note: The distribution that minimizes the squared error 
//       of the quantile function over the specified interval is return.
(NormalDistribution? dist_fit, ddouble error) = 
    NormalDistribution.Fit(xs, fitting_quantile_range: (0.1, 0.9));