Perlin noise value range

I used perlin noise to generate a 2D height map. At first i tried some parameters manually and found a good combination of amplitude, persistence,... for my job.

Now that i'm developing the program, i added the feature for user to change the map parameters and make a new map for himself but now i see that for certain parameters (Mostly octaves and frequency) the values are not in the range i used to see. I thought that if a set Amplitude = 20, the values(heights) i get from it will be in e.g [0,20] or [-10,10] or [-20,20] ranges but now i see that Amplitude is not the only parameter that controls output range.

My question is: Is there an exact mathematical formula (a function of Amplitude, Octaves, Frequency and persistence) to compute the range or i should take a lot of samples (like 100,000) and check minimum and maximum values of them to guess the aproximate range?

Note: The following code is an implementation of perlin noise that one of stackoverflow guys worte it in C and i ported it to java.

PerlinNoiseParameters.java

public class PerlinNoiseParameters {

    public double persistence;
    public double frequency;
    public double amplitude;
    public int octaves;
    public int randomseed;

    public PerlinNoiseParameters(double persistence, double frequency, double amplitude, int octaves, int randomseed) {
        this.ChangeParameters(persistence, frequency, amplitude, octaves, randomseed);
    }

    public void ChangeParameters(double persistence, double frequency, double amplitude, int octaves, int randomseed) {
        this.persistence = persistence;
        this.frequency = frequency;
        this.amplitude = amplitude;
        this.octaves = octaves;
        this.randomseed = 2 + randomseed * randomseed;
    }
}

PerlinNoiseGenerator.java

public class PerlinNoiseGenerator {

    PerlinNoiseParameters parameters;

    public PerlinNoiseGenerator() {
    }

    public PerlinNoiseGenerator(PerlinNoiseParameters parameters) {
        this.parameters = parameters;
    }

    public void ChangeParameters(double persistence, double frequency, double amplitude, int octaves, int randomseed) {
        parameters.ChangeParameters(persistence, frequency, amplitude, octaves, randomseed);
    }

    public void ChangeParameters(PerlinNoiseParameters newParams) {
        parameters = newParams;
    }

    public double get(double x, double y) {
        return parameters.amplitude * Total(x, y);
    }

    private double Total(double i, double j) {
        double t = 0.0f;
        double _amplitude = 1;
        double freq = parameters.frequency;

        for (int k = 0; k < parameters.octaves; k++) {
            t += GetValue(j * freq + parameters.randomseed, i * freq + parameters.randomseed)
                    * _amplitude;
            _amplitude *= parameters.persistence;
            freq *= 2;
        }

        return t;
    }

    private double GetValue(double x, double y) {
        int Xint = (int) x;
        int Yint = (int) y;

        double Xfrac = x - Xint;
        double Yfrac = y - Yint;

        double n01 = Noise(Xint - 1, Yint - 1);
        double n02 = Noise(Xint + 1, Yint - 1);
        double n03 = Noise(Xint - 1, Yint + 1);
        double n04 = Noise(Xint + 1, Yint + 1);
        double n05 = Noise(Xint - 1, Yint);
        double n06 = Noise(Xint + 1, Yint);
        double n07 = Noise(Xint, Yint - 1);
        double n08 = Noise(Xint, Yint + 1);
        double n09 = Noise(Xint, Yint);
        double n12 = Noise(Xint + 2, Yint - 1);
        double n14 = Noise(Xint + 2, Yint + 1);
        double n16 = Noise(Xint + 2, Yint);
        double n23 = Noise(Xint - 1, Yint + 2);
        double n24 = Noise(Xint + 1, Yint + 2);
        double n28 = Noise(Xint, Yint + 2);
        double n34 = Noise(Xint + 2, Yint + 2);

        double x0y0 = 0.0625 * (n01 + n02 + n03 + n04) + 0.1250
                * (n05 + n06 + n07 + n08) + 0.2500 * n09;

        double x1y0 = 0.0625 * (n07 + n12 + n08 + n14) + 0.1250
                * (n09 + n16 + n02 + n04) + 0.2500 * n06;

        double x0y1 = 0.0625 * (n05 + n06 + n23 + n24) + 0.1250
                * (n03 + n04 + n09 + n28) + 0.2500 * n08;

        double x1y1 = 0.0625 * (n09 + n16 + n28 + n34) + 0.1250
                * (n08 + n14 + n06 + n24) + 0.2500 * n04;

        double v1 = Interpolate(x0y0, x1y0, Xfrac);
        double v2 = Interpolate(x0y1, x1y1, Xfrac);

        double fin = Interpolate(v1, v2, Yfrac);

        return fin;
    }

    private double Interpolate(double x, double y, double a) {
        double negA = 1.0 - a;
        double negASqr = negA * negA;
        double fac1 = 3.0 * (negASqr) - 2.0 * (negASqr * negA);
        double aSqr = a * a;
        double fac2 = 3.0 * aSqr - 2.0 * (aSqr * a);

        return x * fac1 + y * fac2;
    }

    private double Noise(int x, int y) {
        int n = x + y * 57;
        n = (n << 13) ^ n;
        int t = (n * (n * n * 15731 + 789221) + 1376312589) & 0x7fffffff;
        return 1.0 - (double) t * 0.931322574615478515625e-9;
    }
}

The range of a single perlin noise step is: http://digitalfreepen.com/2017/06/20/range-perlin-noise.html

-sqrt(N/4), sqrt(N/4)

With N being the amount of dimensions. 2 in your case.

Octaves, persistence and amplitude add on top of that:

double range = 0.0;
double _amplitude = parameters.;
for (int k = 0; k < parameters.octaves; k++) {
    range += sqrt(N/4) * _amplitude;
    _amplitude *= parameters.persistence;
}
return range;

There might be some way to do this as a single mathematical expression. Involving pow(), but by brain fails me right now.