static public StatisticSample ExponentialDistribution(ICollection <SampleRanking> valueSampleRanking, StatisticSample valueSample) { List <DistributionSamples> valueDistributionSample = new List <DistributionSamples> { }; ICollection <double> valueDoubleTemp = new List <double> { }; foreach (var el in valueSampleRanking) { valueDoubleTemp.Add(el.SampleData); } double ArithmeticMean = QuantitiveCharacteristicsService.ArithmeticalMean(valueDoubleTemp); double lambdaValue = 1 / ArithmeticMean; for (int i = 0; i < valueDoubleTemp.Count; i++) { valueDistributionSample.Add(new DistributionSamples { X = valueDoubleTemp.ElementAt(i), Y = valueDoubleTemp.ElementAt(i) < 0 ? 0 : valueSample.StepSize * lambdaValue * Math.Exp((-lambdaValue) * valueDoubleTemp.ElementAt(i)) }); } valueSample.DistributionSample = new ObservableCollection <DistributionSamples>(valueDistributionSample); return(valueSample); }
static public StatisticSample EvenDistribution(ICollection <SampleRanking> valueSampleRanking, StatisticSample valueSample) { List <DistributionSamples> valueDistributionSample = new List <DistributionSamples> { }; ICollection <double> valueDoubleTemp = new List <double> { }; foreach (var el in valueSampleRanking) { valueDoubleTemp.Add(el.SampleData); } double ArithmeticMean = QuantitiveCharacteristicsService.ArithmeticalMean(valueDoubleTemp); double RouteMean = QuantitiveCharacteristicsService.ArithmeticMeanDouble(valueDoubleTemp); double lambdaValue = 1 / ArithmeticMean; double aValue = ArithmeticMean - Math.Sqrt(3 * (RouteMean - Math.Pow(ArithmeticMean, 2.0))); double bValue = ArithmeticMean + Math.Sqrt(3 * (RouteMean - Math.Pow(ArithmeticMean, 2.0))); for (int i = 0; i < valueDoubleTemp.Count; i++) { valueDistributionSample.Add(new DistributionSamples { X = valueDoubleTemp.ElementAt(i), Y = valueDoubleTemp.ElementAt(i) < aValue || valueDoubleTemp.ElementAt(i) > bValue ? 0 : valueSample.StepSize * (1 / (bValue - aValue)) }); } valueSample.DistributionSample = new ObservableCollection <DistributionSamples>(valueDistributionSample); return(valueSample); }
static public StatisticSample VWeibullDistributionEmpirical(ICollection <SampleRanking> valueSampleRanking, StatisticSample valueSample) { List <DistributionSamples> valueDistributionSample = new List <DistributionSamples> { }; ICollection <double> valueDoubleTemp = new List <double> { }; foreach (var el in valueSampleRanking) { valueDoubleTemp.Add(el.SampleData); } double ArtiheticMean = QuantitiveCharacteristicsService.ArithmeticalMean(valueDoubleTemp); double AritheticMeanDouble = QuantitiveCharacteristicsService.ArithmeticMeanDouble(valueDoubleTemp); double LambdaValue = 1 / ArtiheticMean; double AValue = 1; double BValue = 1.5; for (int i = 0; i < valueDoubleTemp.Count; i++) { valueDistributionSample.Add(new DistributionSamples { X = valueDoubleTemp.ElementAt(i), Y = (1.0 - Math.Exp(-Math.Pow(valueDoubleTemp.ElementAt(i), BValue) / AValue)) }); } valueSample.DistributionSampleEmpirical = new ObservableCollection <DistributionSamples>(valueDistributionSample); return(valueSample); }
static public String ExponentialDistributionInterval(ICollection <SampleRanking> valueSampleRanking, StatisticSample valueSample) { List <DistributionSamples> valueDistributionSample = new List <DistributionSamples> { }; ICollection <double> valueDoubleTemp = new List <double> { }; foreach (var el in valueSampleRanking) { valueDoubleTemp.Add(el.SampleData); } double ArithmeticMean = QuantitiveCharacteristicsService.ArithmeticalMean(valueDoubleTemp); double lambdaValue = 1 / ArithmeticMean; double ourDLambda = Math.Pow(lambdaValue, 2) / valueDoubleTemp.Count; lambdaValue = Math.Round(lambdaValue, valueSample.RoundValue); ourDLambda = Math.Round(ourDLambda, valueSample.RoundValue); String returnValue = $"\n##############################################" + $"\nДовірче оцінювання: LambdaValue" + $"\nОцінка: {Math.Round(lambdaValue, valueSample.RoundValue)}" + $"\nДисперсія: {Math.Round(ourDLambda, valueSample.RoundValue)}" + $"\nВерхня межа: {lambdaValue + Math.Round(Math.Sqrt(ourDLambda), valueSample.RoundValue)}" + $"\nНижня межа: {lambdaValue - Math.Round(Math.Sqrt(ourDLambda), valueSample.RoundValue)}" + $"\n##############################################"; return(returnValue); }
static public StatisticSample ArcSinDistribution(ICollection <SampleRanking> valueSampleRanking, StatisticSample valueSample) { List <DistributionSamples> valueDistributionSample = new List <DistributionSamples> { }; ICollection <double> valueDoubleTemp = new List <double> { }; foreach (var el in valueSampleRanking) { valueDoubleTemp.Add(el.SampleData); } double ArtiheticMean = QuantitiveCharacteristicsService.ArithmeticalMean(valueDoubleTemp); double AritheticMeanDouble = QuantitiveCharacteristicsService.ArithmeticMeanDouble(valueDoubleTemp); double AValue = Math.Sqrt(2) * Math.Sqrt((AritheticMeanDouble - Math.Pow(ArtiheticMean, 2.0))); for (int i = 0; i < valueDoubleTemp.Count; i++) { if (valueDoubleTemp.ElementAt(i) > -AValue && valueDoubleTemp.ElementAt(i) < AValue) { valueDistributionSample.Add(new DistributionSamples { X = valueDoubleTemp.ElementAt(i), Y = 1 / (3.14 * Math.Sqrt(AValue * AValue - valueDoubleTemp.ElementAt(i) * valueDoubleTemp.ElementAt(i))) * valueSample.StepSize }); } } valueSample.DistributionSample = new ObservableCollection <DistributionSamples>(valueDistributionSample); return(valueSample); }
static public StatisticSample ArcSinDistributionEmpirical(ICollection <SampleRanking> valueSampleRanking, StatisticSample valueSample) { List <DistributionSamples> valueDistributionSample = new List <DistributionSamples> { }; ICollection <double> valueDoubleTemp = new List <double> { }; foreach (var el in valueSampleRanking) { valueDoubleTemp.Add(el.SampleData); } double ArtiheticMean = QuantitiveCharacteristicsService.ArithmeticalMean(valueDoubleTemp); double AritheticMeanDouble = QuantitiveCharacteristicsService.ArithmeticMeanDouble(valueDoubleTemp); double AValue = Math.Sqrt(2) * Math.Sqrt((AritheticMeanDouble - Math.Pow(ArtiheticMean, 2.0))); for (int i = 0; i < valueDoubleTemp.Count; i++) { if (valueDoubleTemp.ElementAt(i) < -AValue) { valueDistributionSample.Add(new DistributionSamples { X = valueDoubleTemp.ElementAt(i), Y = 0 }); } else if (valueDoubleTemp.ElementAt(i) > -AValue && valueDoubleTemp.ElementAt(i) < AValue) { double temp = 0.5; temp += (0.5 * Math.Asin(valueDoubleTemp.ElementAt(i) / AValue)); if (temp > 1) { temp = 1; } else if (temp < 0) { temp = 0; } valueDistributionSample.Add(new DistributionSamples { X = valueDoubleTemp.ElementAt(i), Y = temp }); } else { valueDistributionSample.Add(new DistributionSamples { X = valueDoubleTemp.ElementAt(i), Y = 1 }); } } valueSample.DistributionSampleEmpirical = new ObservableCollection <DistributionSamples>(valueDistributionSample); return(valueSample); }
static public StatisticSample ExponentialDistributionEmpirical(ICollection <SampleRanking> valueSampleRanking, StatisticSample valueSample) { List <DistributionSamples> valueDistributionSample = new List <DistributionSamples> { }; ICollection <double> valueDoubleTemp = new List <double> { }; foreach (var el in valueSampleRanking) { valueDoubleTemp.Add(el.SampleData); } double ArtiheticMean = QuantitiveCharacteristicsService.ArithmeticalMean(valueDoubleTemp); double LambdaValue = 1 / ArtiheticMean; for (int i = 0; i < valueDoubleTemp.Count; i++) { valueDistributionSample.Add(new DistributionSamples { X = valueDoubleTemp.ElementAt(i), Y = valueDoubleTemp.ElementAt(i) < 0 ? 0 : 1 - Math.Exp((-LambdaValue) * valueDoubleTemp.ElementAt(i)) }); } valueSample.DistributionSampleEmpirical = new ObservableCollection <DistributionSamples>(valueDistributionSample); valueSample.HistogramLowerLimit = new ObservableCollection <Models.Histograma.DataValueHistogram> { }; valueSample.HistogramUpperLimit = new ObservableCollection <Models.Histograma.DataValueHistogram> { }; double UA = 1.9 + 0.04; foreach (var el in valueSample.DistributionSampleEmpirical) { double S_Variance = Math.Pow(el.X, 2.0) * Math.Exp(-2 * LambdaValue * el.X) * Math.Pow(LambdaValue, 2.0) / valueDoubleTemp.Count; double f1 = el.Y + UA * Math.Sqrt(S_Variance), f2 = el.Y - UA * Math.Sqrt(S_Variance); f1 = f1 < 0 ? 0 : f1 > 1 ? 1 : f1; f2 = f2 < 0 ? 0 : f2 > 1 ? 1 : f2; valueSample.HistogramUpperLimit.Add(new Models.Histograma.DataValueHistogram { x = el.X, p = f1 }); valueSample.HistogramLowerLimit.Add(new Models.Histograma.DataValueHistogram { x = el.X, p = f2 }); } return(valueSample); }
static public StatisticSample VWeibullDistribution(ICollection <SampleRanking> valueSampleRanking, StatisticSample valueSample) { List <DistributionSamples> valueDistributionSample = new List <DistributionSamples> { }; ICollection <double> valueDoubleTemp = new List <double> { }; foreach (var el in valueSampleRanking) { valueDoubleTemp.Add(el.SampleData); } double ArtiheticMean = QuantitiveCharacteristicsService.ArithmeticalMean(valueDoubleTemp); double AritheticMeanDouble = QuantitiveCharacteristicsService.ArithmeticMeanDouble(valueDoubleTemp); double NSize = valueDoubleTemp.Count; double aValue = 1; double bValue = 1.5; NSize = NSize / (NSize - 1); double ourO = NSize * Math.Sqrt((AritheticMeanDouble - Math.Pow(ArtiheticMean, 2.0))); for (int i = 0; i < valueDoubleTemp.Count; i++) { double ourT = bValue / aValue; double ourT2 = Math.Pow(valueDoubleTemp.ElementAt(i), bValue - 1.0); ourT *= ourT2; ourT2 = Math.Exp(-(Math.Pow(valueDoubleTemp.ElementAt(i), bValue) / aValue)); ourT *= ourT2; ourT *= valueSample.StepSize; valueDistributionSample.Add(new DistributionSamples { X = valueDoubleTemp.ElementAt(i), Y = ourT }); } valueSample.DistributionSample = new ObservableCollection <DistributionSamples>(valueDistributionSample); return(valueSample); }
static public double lambdaValueExponential(ICollection <SampleRanking> valueSampleRanking) { ICollection <double> valueDoubleTemp = new List <double> { }; foreach (var el in valueSampleRanking) { valueDoubleTemp.Add(el.SampleData); } double ArithmeticMean = QuantitiveCharacteristicsService.ArithmeticalMean(valueDoubleTemp); double lambdaValue = 1 / ArithmeticMean; return(lambdaValue); }
static public StatisticSample Standartization(StatisticSample valueSample) { double MED = QuantitiveCharacteristicsService.MEDFind(valueSample.Sample); double MAD = QuantitiveCharacteristicsService.MADFind(valueSample.Sample); ObservableCollection <double> ourXi = new ObservableCollection <double> { }; foreach (var el in valueSample.Sample) { double ourNum = (el - MED); ourNum /= MAD; ourXi.Add(ourNum); } valueSample.Sample = ourXi; return(valueSample); }
//Довірчі інтервали static public String NormalDistributionInterval(ICollection <SampleRanking> valueSampleRanking, StatisticSample valueSample) { List <DistributionSamples> valueDistributionSample = new List <DistributionSamples> { }; ICollection <double> valueDoubleTemp = new List <double> { }; foreach (var el in valueSampleRanking) { valueDoubleTemp.Add(el.SampleData); } double ArtiheticMean = Math.Round(QuantitiveCharacteristicsService.ArithmeticalMean(valueDoubleTemp), valueSample.RoundValue); //Мат сподівання double AritheticMeanDouble = Math.Round(QuantitiveCharacteristicsService.ArithmeticMeanDouble(valueDoubleTemp), valueSample.RoundValue); double NSize = valueDoubleTemp.Count; NSize = NSize / (NSize - 1); double ourO = Math.Round(NSize * Math.Sqrt((AritheticMeanDouble - Math.Pow(ArtiheticMean, 2.0))), valueSample.RoundValue); double ourDArithmeticMean = Math.Round(Math.Pow(ourO, 2) / valueDoubleTemp.Count, valueSample.RoundValue); double ourDO = Math.Round(Math.Pow(ourO, 2) / (2 * valueDoubleTemp.Count), valueSample.RoundValue); ourO = Math.Round(ourO, valueSample.RoundValue); ourDArithmeticMean = Math.Round(ourDArithmeticMean, valueSample.RoundValue); ourDO = Math.Round(ourDO, valueSample.RoundValue); String returnValue = $"\n##############################################" + $"\nДовірче оцінювання: m | Sigma" + $"\nОцінка: {ArtiheticMean} | {ourO}" + $"\nДисперсія: {ourDArithmeticMean} | {ourDO}" + $"\nВерхня межа: {ArtiheticMean + Math.Round(Math.Sqrt(ourDArithmeticMean), valueSample.RoundValue)} | {ourO + Math.Round(Math.Sqrt(ourDO), valueSample.RoundValue)}" + $"\nНижня межа: {ArtiheticMean - Math.Round(Math.Sqrt(ourDArithmeticMean), valueSample.RoundValue)} | {ourO - Math.Round(Math.Sqrt(ourDO), valueSample.RoundValue)}" + $"\n##############################################"; return(returnValue); }
static public String EvenDistributionInterval(ICollection <SampleRanking> valueSampleRanking, StatisticSample valueSample) { List <DistributionSamples> valueDistributionSample = new List <DistributionSamples> { }; ICollection <double> valueDoubleTemp = new List <double> { }; foreach (var el in valueSampleRanking) { valueDoubleTemp.Add(el.SampleData); } double ArithmeticMean = QuantitiveCharacteristicsService.ArithmeticalMean(valueDoubleTemp); double RouteMean = QuantitiveCharacteristicsService.ArithmeticMeanDouble(valueDoubleTemp); double lambdaValue = 1 / ArithmeticMean; double aValue = ArithmeticMean - Math.Sqrt(3 * (RouteMean - Math.Pow(ArithmeticMean, 2.0))); double bValue = ArithmeticMean + Math.Sqrt(3 * (RouteMean - Math.Pow(ArithmeticMean, 2.0))); double ourDAValue = Math.Pow((bValue - aValue), 2) / (12.0 * valueDoubleTemp.Count); double ourDBValue = (Math.Pow((bValue - aValue), 4) + 15.0 * Math.Pow(aValue + bValue, 2) * Math.Pow(bValue - aValue, 2)) / (180.0 * valueDoubleTemp.Count); double cov = (aValue + bValue) * Math.Pow(bValue - aValue, 2) / (12 * valueDoubleTemp.Count); aValue = Math.Round(aValue, valueSample.RoundValue); bValue = Math.Round(bValue, valueSample.RoundValue); String returnValue = $"\n##############################################" + $"\nДовірче оцінювання: a | b" + $"\nОцінка: {aValue} | {bValue}" + $"\nДисперсія: {Math.Round(ourDAValue, valueSample.RoundValue)} | {Math.Round(ourDBValue,valueSample.RoundValue)}" + $"\nВерхня межа: {aValue + Math.Round(Math.Sqrt(ourDAValue), valueSample.RoundValue)} | {bValue + Math.Round(Math.Sqrt(ourDBValue), valueSample.RoundValue)}" + $"\nНижня межа: {aValue - Math.Round(Math.Sqrt(ourDAValue), valueSample.RoundValue)} | {bValue - Math.Round(Math.Sqrt(ourDBValue), valueSample.RoundValue)}" + $"\n##############################################"; return(returnValue); }
static public StatisticSample EvenDistributionEmpirical(ICollection <SampleRanking> valueSampleRanking, StatisticSample valueSample) { List <DistributionSamples> valueDistributionSample = new List <DistributionSamples> { }; ICollection <double> valueDoubleTemp = new List <double> { }; foreach (var el in valueSampleRanking) { valueDoubleTemp.Add(el.SampleData); } double ArtiheticMean = QuantitiveCharacteristicsService.ArithmeticalMean(valueDoubleTemp); double AritheticMeanDouble = QuantitiveCharacteristicsService.ArithmeticMeanDouble(valueDoubleTemp); double LambdaValue = 1 / ArtiheticMean; double AValue = ArtiheticMean - Math.Sqrt(3 * (AritheticMeanDouble - Math.Pow(ArtiheticMean, 2.0))); double BValue = ArtiheticMean + Math.Sqrt(3 * (AritheticMeanDouble - Math.Pow(ArtiheticMean, 2.0))); for (int i = 0; i < valueDoubleTemp.Count; i++) { valueDistributionSample.Add(new DistributionSamples { X = valueDoubleTemp.ElementAt(i), Y = valueDoubleTemp.ElementAt(i) < AValue ? 0 : valueDoubleTemp.ElementAt(i) >= AValue && valueDoubleTemp.ElementAt(i) < BValue ? (valueDoubleTemp.ElementAt(i) - AValue) / (BValue - AValue) : 1 }); } valueSample.DistributionSampleEmpirical = new ObservableCollection <DistributionSamples>(valueDistributionSample); valueSample.HistogramLowerLimit = new ObservableCollection <Models.Histograma.DataValueHistogram> { }; valueSample.HistogramUpperLimit = new ObservableCollection <Models.Histograma.DataValueHistogram> { }; double UA = 1.9 + 0.04; double ourDAValue = Math.Pow((BValue - AValue), 2) / (12.0 * valueDoubleTemp.Count); double ourDBValue = (Math.Pow((BValue - AValue), 4) + 15.0 * Math.Pow(AValue + BValue, 2) * Math.Pow(BValue - AValue, 2)) / (180.0 * valueDoubleTemp.Count); double cov = (AValue + BValue) * Math.Pow(BValue - AValue, 2) / (12 * valueDoubleTemp.Count); foreach (var el in valueSample.DistributionSampleEmpirical) { double S_Variance = (Math.Pow(el.X - BValue, 2.0) / Math.Pow(BValue - AValue, 4.0)) * ourDAValue + (Math.Pow(el.X - AValue, 2.0) / Math.Pow(BValue - AValue, 4.0)) * ourDBValue + ((el.X - AValue) * (el.X - BValue) / Math.Pow(BValue - AValue, 4.0)) * cov; double f1 = el.Y + UA * Math.Sqrt(S_Variance), f2 = el.Y - UA * Math.Sqrt(S_Variance); f1 = f1 < 0 ? 0 : f1 > 1 ? 1 : f1; f2 = f2 < 0 ? 0 : f2 > 1 ? 1 : f2; valueSample.HistogramUpperLimit.Add(new Models.Histograma.DataValueHistogram { x = el.X, p = f1 }); valueSample.HistogramLowerLimit.Add(new Models.Histograma.DataValueHistogram { x = el.X, p = f2 }); } return(valueSample); }
//Функція розподілу ймовірностей static public StatisticSample NormalDistributionEmpirical(ICollection <SampleRanking> valueSampleRanking, StatisticSample valueSample) { List <DistributionSamples> valueDistributionSample = new List <DistributionSamples> { }; ICollection <double> valueDoubleTemp = new List <double> { }; foreach (var el in valueSampleRanking) { valueDoubleTemp.Add(el.SampleData); } double ArtiheticMean = QuantitiveCharacteristicsService.ArithmeticalMean(valueDoubleTemp); double AritheticMeanDouble = QuantitiveCharacteristicsService.ArithmeticMeanDouble(valueDoubleTemp); double NSize = valueDoubleTemp.Count; NSize = NSize / (NSize - 1); double ourO = NSize * Math.Sqrt((AritheticMeanDouble - Math.Pow(ArtiheticMean, 2.0))); for (int i = 0; i < valueDoubleTemp.Count; i++) { valueDistributionSample.Add(new DistributionSamples { X = valueDoubleTemp.ElementAt(i), Y = ourFFind((valueDoubleTemp.ElementAt(i) - ArtiheticMean) / ourO) }); } valueSample.DistributionSampleEmpirical = new ObservableCollection <DistributionSamples>(valueDistributionSample); double DM = Math.Pow(ourO, 2.0) / valueDoubleTemp.Count; double DO = Math.Pow(ourO, 2.0) / (valueDoubleTemp.Count * 2.0); double UA = 1.9 + 0.04; valueSample.HistogramLowerLimit = new ObservableCollection <Models.Histograma.DataValueHistogram> { }; valueSample.HistogramUpperLimit = new ObservableCollection <Models.Histograma.DataValueHistogram> { }; foreach (var el in valueSample.DistributionSampleEmpirical) { double dFdM = (1.0 / (ourO * Math.Sqrt(2.0 * Math.PI))) * Math.Exp(-(Math.Pow(el.X - ArtiheticMean, 2.0) / (2.0 * Math.Pow(ourO, 2.0)))); double dFdO = ((el.X - ArtiheticMean) / (Math.Pow(ourO, 2.0) * Math.Sqrt(2.0 * Math.PI))) * Math.Exp(-(Math.Pow(el.X - ArtiheticMean, 2.0) / (2.0 * Math.Pow(ourO, 2.0)))); double S_Variance = Math.Pow(dFdM, 2.0) * DM + Math.Pow(dFdO, 2.0) * DO; double f1 = el.Y + UA * Math.Sqrt(S_Variance), f2 = el.Y - UA * Math.Sqrt(S_Variance); f1 = f1 < 0 ? 0 : f1 > 1 ? 1 : f1; f2 = f2 < 0 ? 0 : f2 > 1 ? 1 : f2; valueSample.HistogramUpperLimit.Add(new Models.Histograma.DataValueHistogram { x = el.X, p = f1 }); valueSample.HistogramLowerLimit.Add(new Models.Histograma.DataValueHistogram { x = el.X, p = f2 }); } return(valueSample); }