public void When_Solve_Integral_With_SimpsonEstimate()
{
VariableEntity x = "x";
var function = MathEntity.Sqrt(x);
var estimate = new SimpsonEstimate();
var estimation = estimate.Estimate(function, x, 4, 0, 8);
Assert.Equal(14.855493563580854, estimation);
}
public double ComputeLowerCumulative(double tStat, double degreeOfFreedom)
{
VariableEntity x = _variableName;
VariableEntity v = _degreeOfFreedomName;
var betaFunction = new BetaFunction();
var betaResult = betaFunction.Evaluate(0.5, degreeOfFreedom / 2);
var firstEntity = MathEntity.Pow(Number.Create(1) + (MathEntity.Pow(x, Number.Create(2)) / v), Number.Create(-1) * ((v + Number.Create(1)) / Number.Create(2)));
var secondEntity = MathEntity.Sqrt(v) * Number.Create(betaResult);
var result = (firstEntity / secondEntity);
result.Assign(v, (NumberEntity)Number.Create(degreeOfFreedom));
var simpsonEstimate = new SimpsonEstimate();
return(simpsonEstimate.Estimate(result, x, _n, _a, tStat));
}
public double ComputeLowerCumulative(double average, double standardDeviation, double value)
{
VariableEntity µ = _avgVariableName;
VariableEntity σ = _standardDeviationVariableName;
VariableEntity x = _variableName;
var exponent = Number.Create(-0.5) * MathEntity.Pow((x - µ) / σ, Number.Create(2));
var integralEquation = MathEntity.Pow(Number.Create(System.Math.E), exponent);
integralEquation.Assign(µ, new NumberEntity(Number.Create(average)));
integralEquation.Assign(σ, new NumberEntity(Number.Create(standardDeviation)));
var estimate = new SimpsonEstimate();
var estimation = estimate.Estimate(integralEquation, x, _n, _a, value);
var equation = (Number.Create(1) / (σ * MathEntity.Sqrt(Number.Create(2) * Number.Create(System.Math.PI)))) * Number.Create(estimation);
equation.Assign(σ, new NumberEntity(Number.Create(standardDeviation)));
return((equation.Eval() as NumberEntity).Number.Value);
}