hola por favor podrias revisar el codigo en busca de errores y optimizaciones? namespace Accord.Statistics.Distributions.Univariate
{
    using Accord.Math;
    using Accord.Math.Optimization;
    using Accord.Statistics.Distributions.Fitting;
    using Accord.Statistics.Distributions.Multivariate;
    using System;

    [Serializable]
    public class CauchyDistribution : UnivariateContinuousDistribution,
        IFittableDistribution<double, CauchyOptions>,
        ISampleableDistribution<double>, IFormattable
    {

        // Distribution parameters
        private double location; // x0
        private double scale;    // γ (gamma)

        // Derived measures
        private double lnconstant;
        private double constant;

        private bool immutable;

        public CauchyDistribution()
            : this(0, 1)
        {
        }
        public CauchyDistribution([Real] double location, [Positive] double scale)
        {
            if (scale <= 0)
                throw new ArgumentOutOfRangeException("scale", "Scale must be greater than zero.");

            init(location, scale);
        }
        private void init(double location, double scale)
        {
            this.location = location;
            this.scale = scale;

            this.constant = 1.0 / (Math.PI * scale);
            this.lnconstant = -Math.Log(Math.PI * scale);
        }
        public double Location
        {
            get { return location; }
        }
        public double Scale
        {
            get { return scale; }
        }
        public override double Median
        {
            get
            {
                Accord.Diagnostics.Debug.Assert(location.IsEqual(base.Median, 1e-6));
                return location;
            }
        }
        public override DoubleRange Support
        {
            get { return new DoubleRange(Double.NegativeInfinity, Double.PositiveInfinity); }
        }
        public override double Mode
        {
            get { return location; }
        }
        public override double Mean
        {
            get { return Double.NaN; }
        }
        public override double Variance
        {
            get { return Double.NaN; }
        }
        public override double Entropy
        {
            get { return Math.Log(scale) + Math.Log(4.0 * Math.PI); }
        }
        public static double CDF(double x, double location, double scale) => 1.0 / Math.PI * Math.Atan2(x - location, scale) + 0.5;
        public double CDF(double x) => 1.0 / Math.PI * Math.Atan2(x - location, scale) + 0.5;

        protected internal override double InnerDistributionFunction(double x) => CDF(x);
        public static double PDF(double x, double location, double scale)
        {
            double constant = 1.0 / (Math.PI * scale);
            double z = (x - location) / scale;
            return constant / (1.0 + z * z);
        }
        public double PDF(double x)
        {
            double z = (x - location) / scale;
            return constant / (1.0 + z * z);
        }
        protected internal override double InnerProbabilityDensityFunction(double x) => PDF(x);
        protected internal override double InnerLogProbabilityDensityFunction(double x)
        {
            double z = (x - location) / scale;
            return lnconstant - Math.Log(1.0 + z * z);
        }
        public override void Fit(double[] observations, double[] weights, IFittingOptions options)
        {
            CauchyOptions cauchyOptions = options as CauchyOptions;
            if (options != null && cauchyOptions == null)
                throw new ArgumentException("The specified options' type is invalid.", "options");

            Fit(observations, weights, cauchyOptions);
        }
        public void Fit(double[] observations, double[] weights, CauchyOptions options)
        {
            if (immutable)
                throw new InvalidOperationException("This object can not be modified.");

            if (weights != null)
                throw new ArgumentException("This distribution does not support weighted samples.");

            bool useMLE = true;
            bool estimateT = true;
            bool estimateS = true;

            if (options != null)
            {
                useMLE = options.MaximumLikelihood;
                estimateT = options.EstimateLocation;
                estimateS = options.EstimateScale;
            }


            double t0 = location;
            double s0 = scale;

            int n = observations.Length;


            DoubleRange range;
            double median = Measures.Quartiles(observations, out range, alreadySorted: false);

            if (estimateT)
                t0 = median;

            if (estimateS)
                s0 = range.Length;


            if (useMLE)
            {
                // Minimize the log-likelihood through numerical optimization
                var lbfgs = new BoundedBroydenFletcherGoldfarbShanno(2);

                lbfgs.LowerBounds[1] = 0; // scale must be positive

                // Define the negative log-likelihood function,
                // which is the objective we want to minimize:
                lbfgs.Function = (parameters) =>
                {
                    // Assume location is the first
                    // parameter, shape is the second
                    double t = (estimateT) ? parameters[0] : t0;
                    double s = (estimateS) ? parameters[1] : s0;

                    if (s < 0) s = -s;

                    double sum = 0;
                    for (int i = 0; i < observations.Length; i++)
                    {
                        double y = (observations[i] - t);
                        sum += Math.Log(s * s + y * y);
                    }

                    return -(n * Math.Log(s) - sum - n * Math.Log(Math.PI));
                };


                lbfgs.Gradient = (parameters) =>
                {
                    // Assume location is the first
                    // parameter, shape is the second
                    double t = (estimateT) ? parameters[0] : t0;
                    double s = (estimateS) ? parameters[1] : s0;

                    double sum1 = 0, sum2 = 0;
                    for (int i = 0; i < observations.Length; i++)
                    {
                        double y = (observations[i] - t);
                        sum1 += y / (s * s + y * y);
                        sum2 += s / (s * s + y * y);
                    }

                    double dt = -2.0 * sum1;
                    double ds = +2.0 * sum2 - n / s;

                    double[] g = new double[2];
                    g[0] = estimateT ? dt : 0;
                    g[1] = estimateS ? ds : 0;

                    return g;
                };


                // Initialize using the sample median as starting
                // value for location, and half interquartile range
                // for shape.

                double[] values = { t0, s0 };

                // Minimize
                lbfgs.Minimize(values);

                // Check solution
                t0 = lbfgs.Solution[0];
                s0 = lbfgs.Solution[1];
            }

            init(t0, s0); // Become the new distribution
        }
        public static CauchyDistribution Standard { get { return standard; } }
        private static readonly CauchyDistribution standard = new CauchyDistribution() { immutable = true };
        public override object Clone()
        {
            return new CauchyDistribution(location, scale);
        }
        #region ISamplableDistribution<double> Members
        public override double[] Generate(int samples, double[] result, Random source)
        {
            return Random(location, scale, samples, result, source);
        }
        public override double Generate(Random source)
        {
            return Random(location, scale, source);
        }
        public static double Random(double location, double scale)
        {
            return Random(location, scale, Accord.Math.Random.Generator.Random);
        }
        public static double[] Random(double location, double scale, int samples)
        {
            return Random(location, scale, samples, Accord.Math.Random.Generator.Random);
        }
        public static double[] Random(double location, double scale, int samples, double[] result)
        {
            return Random(location, scale, samples, result, Accord.Math.Random.Generator.Random);
        }
        public static double Random(double location, double scale, Random source)
        {
            // Generate uniform U on [-PI/2, +PI/2]
            double x = UniformContinuousDistribution.Random(-Math.PI / 2.0, +Math.PI / 2.0, source);
            return Math.Tan(x) * scale + location;
        }
        public static double[] Random(double location, double scale, int samples, Random source)
        {
            return Random(location, scale, samples, new double[samples], source);
        }
        public static double[] Random(double location, double scale, int samples, double[] result, Random source)
        {
            // Generate uniform U on [-PI/2, +PI/2]
            UniformContinuousDistribution.Random(-Math.PI / 2.0, +Math.PI / 2.0, samples, result, source);
            for (int i = 0; i < result.Length; i++)
                result[i] = Math.Tan(result[i]) * scale + location;
            return result;
        }
        #endregion
        public override string ToString(string format, IFormatProvider formatProvider)
        {
            return String.Format(formatProvider, "Cauchy(x; x0 = {0}, γ = {1})",
                location.ToString(format, formatProvider),
                scale.ToString(format, formatProvider));
        }
        public MultivariateCauchyDistribution ToMultivariateDistribution()
        {
            return new MultivariateCauchyDistribution(new double[] { this.Location }, new double[,] { { this.Scale } });
        }
        public static double[] Random(int samples, double[] result, Random source, double location, double scale)
        {
            for (int i = 0; i < samples; i++)
            {
                result[i] = Random(location, scale, source);
            }

            return result;
        }
        public static double[] Random(int samples, double[] result, Random source) => Random(samples, result, source, 0.0, 1.0);
    }
}