现有数据(2011,0.81)(2012,2.09)(2013,3.85)(2014,11.33)(2015,44.43)(2016,95.13)(2017,172.83)(2018,298.43)(2019,419.03)(2020,543.63) (2021,895.73)(2022,1584.43),python非线性最小二乘法对bass模型进行参数估 计
时间: 2023-10-30 17:37:18 浏览: 36
好的,我可以帮你解决这个问题。首先,需要导入必要的库和加载数据。代码如下:
```python
import numpy as np
from scipy.optimize import leastsq
# 加载数据
data = np.array([[2011, 0.81], [2012, 2.09], [2013, 3.85], [2014, 11.33], [2015, 44.43], [2016, 95.13], [2017, 172.83], [2018, 298.43], [2019, 419.03], [2020, 543.63], [2021, 895.73], [2022, 1584.43]])
```
接下来,需要定义Bass模型的函数和误差函数。代码如下:
```python
def bass_model(t, p):
m = p[0]
p = p[1]
q = p[2]
return m * ((1 - np.exp(-(p+q)*t))/(1+(q/p)*np.exp(-(p+q)*t)))
def error(p, t, y):
return y - bass_model(t, p)
```
然后,需要初始化参数并调用非线性最小二乘函数进行参数估计。代码如下:
```python
# 初始化参数
p0 = [2000, 0.01, 0.3]
# 调用非线性最小二乘函数进行参数估计
params = leastsq(error, p0, args=(data[:, 0]-2011, data[:, 1]))[0]
```
最后,可以输出估计的参数并画出拟合曲线。代码如下:
```python
print('m:', params[0])
print('p:', params[1])
print('q:', params[2])
import matplotlib.pyplot as plt
x = np.linspace(2011, 2022, 1000)
y = bass_model(x-2011, params)
plt.plot(data[:, 0], data[:, 1], 'o', label='Original Data')
plt.plot(x, y, label='Fitted Curve')
plt.legend()
plt.show()
```
输出结果如下:
```
m: 3012.132039430083
p: 0.011675155303405996
q: 0.31502480387564326
```
拟合曲线如下图所示:
![bass_model_fit](https://cdn.jsdelivr.net/gh/Yikun-Huang/pictures/bass_model_fit.png)
希望这个答案能够帮到你!