好吧，我自己算出来了。@Nelfeal关于只需要当前计算所基于的值的数量的评论是我所遗漏的。下面是使其工作的两个函数：
首先是循环缓冲区：

double append(double in) {
    double poppedValue = 0;
    if (out.elements == wnd_sz) {
        poppedValue = out.arr[out.count];
    } else {
        out.elements++;
    }
        out.arr[out.count] = in;
        out.count = (out.count+1) % wnd_sz;
        return poppedValue;
}

其次是实际的统计工作。这需要分为三个状态：
1.缓冲区中无数据的启动
1.缓冲区有数据但未满
1.缓冲区已满

void stats(double in)
{
    //append element to circular buffer
    double poppedValue = append(in); //append process should return popped value or null if not full, also update out->count

    if (emptyBuffer) { //Buffer not full yet
        // initialize when the first value is added
        out.mean = in;
        out.dSquared = 0;
        emptyBuffer = false;
        out.std_dev = sqrt(out.dSquared/out.count);
        out.max = out.mean + out.std_dev;
        out.min = out.mean - out.std_dev; 
    } 
    
    if (!emptyBuffer && out.elements < wnd_sz) {
        // if the buffer is not full yet, use standard Welford method
        double meanIncrement = (in - out.mean) / out.count;
        double newMean = out.mean + meanIncrement;
        double dSquaredIncrement = (in - newMean);
        dSquaredIncrement *= (in - out.mean);
        double newDSquared = out.dSquared + dSquaredIncrement;
        out.mean = newMean;
        out.dSquared = newDSquared;
        out.std_dev = sqrt(out.dSquared/out.count);
        out.max = out.mean + out.std_dev;
        out.min = out.mean - out.std_dev; 
    } else {
        // once the buffer is full, adjust Welford Method for window size
        double meanIncrement = (in - poppedValue);
        meanIncrement /= 100.0;
        double newMean = out.mean + meanIncrement;
        double dSquaredIncrement = (in - poppedValue);
        dSquaredIncrement *= (in - newMean + poppedValue - out.mean);
        double newDSquared = out.dSquared + dSquaredIncrement;
        out.mean = newMean;
        out.dSquared = newDSquared;
        out.std_dev = sqrt(out.dSquared/wnd_sz);
        out.max = out.mean + out.std_dev;
        out.min = out.mean - out.std_dev; 
    }
}