C++で2つの系列の平均と分散の組み合わせを見つける

コンセプト

サイズbおよびaの2つの異なるシリーズarr1[b]およびarr2[a]が与えられた2つに関して。私たちのタスクは、結合された系列の平均と分散を決定することです。

入力

Arr1[] = { 24, 46, 35, 79, 13, 77, 35 };
Arr2[] = { 66, 68, 35, 24, 46 };

出力

Mean1: 44.1429
Mean2: 47.8
StandardDeviation1: 548.694
StandardDeviation2: 294.56
Combined Mean: 45.6667
d1 square: 2.322
d2_square: 4.5511
Combined Variance: 446.056

メソッド

さて、

n1=「リージョン1」の観測数

n2=「リージョン1」の観測数

X1=領域1の平均。

X2=リージョン2の平均。

S ₁ =領域1の標準偏差。

S ₂ =領域2の標準偏差。

S ₁ ² =領域1の分散。

S ₂ ² =領域2の分散。

X=グループ全体の平均

したがって、d ₁ =X – X1

およびd₂ =X – X2

グループX全体の平均を次のように計算します

（n1 * X1 + n2 * X2）/（n1 + n2）

グループ全体の分散を次のように計算します

n1 *（S ₁ ² + d ₁ ² ）+ n2 *（S ₂ ² + d ₂ ² ）/（n1 + n2）

例

// C++ program to find combined mean
// and variance of two series.
#include <bits/stdc++.h>
using namespace std;
// Shows function to find mean of series.
float mean(int Arr[], int b){
   int sum1 = 0;
   for (int i = 0; i < b; i++)
      sum1 = sum1 + Arr[i];
   float mean = (float)sum1 / b;
   return mean;
}
// Shows function to find the standard
// deviation of series.
float sd(int Arr[], int b){
   float sum1 = 0;
   for (int i = 0; i < b; i++)
      sum1 = sum1 + (Arr[i] - mean(Arr, b)) *
   (Arr[i] - mean(Arr, b));
   float sdd = sum1 / b;
   return sdd;
}
//Shows function to find combined variance
// of two different series.
float combinedVariance(int Arr1[], int Arr2[],
int b, int a){
   // Here, mean1 and mean2 are the mean
   // of two arrays.
   float mean1 = mean(Arr1, b);
   float mean2 = mean(Arr2, a);
   cout << "Mean1: " << mean1
   << " mean2: " << mean2 << endl;
   // Here, sd1 and sd2 are the standard
   // deviation of two array.
   float sd1 = sd(Arr1, b);
   float sd2 = sd(Arr2, a);
   cout << "StandardDeviation1: " << sd1
   << " StandardDeviation2: " << sd2
   << endl;
   // Here, combinedMean is variable to store
   // the combined mean of both array.
   float combinedMean = (float)(b * mean1 +
   a * mean2) / (b + a);
   cout << "Combined Mean: " << combinedMean
   << endl;
   // Here, d1_square and d2_square are
   // the combined mean deviation.
   float d1_square = (mean1 - combinedMean) *(mean1 - combinedMean);
   float d2_square = (mean2 - combinedMean) *(mean2 - combinedMean);
   cout << "d1 square: " << d1_square<< " d2_square: " << d2_square
   << endl;
   // Here, combinedVar is variable to store
   // combined variance of both array.
   float combinedVar = (b * (sd1 + d1_square) + a *(sd2 + d2_square)) / (b + a);
   cout << "Combined Variance: " << combinedVar;
}
// Driver function.
int main(){
   int Arr1[] = { 24, 46, 35, 79, 13, 77, 35 };
   int Arr2[] = { 66, 68, 35, 24, 46 };
   int b = sizeof(Arr1) / sizeof(Arr1[0]);
   int a = sizeof(Arr2) / sizeof(Arr2[0]);
   // Shows function call to combined mean.
   combinedVariance(Arr1, Arr2, b, a);
   return 0;
}

出力

Mean1: 44.1429 mean2: 47.8
StandardDeviation1: 548.694 StandardDeviation2: 294.56
Combined Mean: 45.6667
d1 square: 2.322 d2_square: 4.5511
Combined Variance: 446.056