lee-carter模型代码,所需数据文件内容
时间: 2023-12-04 09:03:44 浏览: 49
Lee-Carter模型需要一些人口统计数据,通常包括每年的死亡率矩阵。下面是一个简化的示例数据文件,包含了5个年龄组和10个年份的死亡率数据:
```
,Age 0-5,Age 6-10,Age 11-15,Age 16-20,Age 21-25
2000,0.001,0.002,0.003,0.004,0.005
2001,0.001,0.003,0.005,0.007,0.009
2002,0.002,0.004,0.006,0.008,0.010
2003,0.003,0.005,0.007,0.009,0.011
2004,0.004,0.006,0.008,0.010,0.012
2005,0.005,0.007,0.009,0.011,0.013
2006,0.006,0.008,0.010,0.012,0.014
2007,0.007,0.009,0.011,0.013,0.015
2008,0.008,0.010,0.012,0.014,0.016
2009,0.009,0.011,0.013,0.015,0.017
```
在这个示例数据文件中,每一行代表一个年份,每一列代表一个年龄组。数据文件的第一行是列名,第一列是索引。您可以将此数据保存为CSV文件,然后使用上一条回答中的Python代码读取并分析数据。
相关问题
lee-carter模型代码
Lee-Carter模型是一种经典的人口统计学模型,用于预测死亡率的变化趋势。以下是一个简单的Python代码实现Lee-Carter模型的示例:
```python
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.optimize import minimize
# 读取数据
data = pd.read_csv('mortality_data.csv', index_col=0)
# 提取年份和年龄
years = np.array(data.columns).astype(int)
ages = np.array(data.index).astype(int)
# 构建死亡率矩阵
mortality = np.array(data)
# 定义Lee-Carter模型函数
def lee_carter(t, k, a, b):
return np.exp(k * a + b * k * (t - 2000))
# 定义目标函数
def objective(params):
k, a, b = params
y_hat = np.zeros_like(mortality)
for i in range(len(years)):
y_hat[:, i] = lee_carter(years[i], k, a, b)
return np.sum((mortality - y_hat) ** 2)
# 最小化目标函数
result = minimize(objective, np.array([0.1, 0.1, 0.1]))
# 提取最优参数
k, a, b = result.x
# 绘制拟合曲线
plt.figure(figsize=(10, 5))
plt.plot(years, lee_carter(years, k, a, b))
plt.xlabel('Year')
plt.ylabel('Log Mortality Rate')
plt.show()
```
在上面的代码中,我们首先读取一些人口统计数据,并提取年份和年龄。然后,我们定义了Lee-Carter模型函数和目标函数,并使用Scipy库中的minimize函数来最小化目标函数,以获得最优参数。最后,我们使用最优参数绘制了拟合曲线。
请注意,实际使用Lee-Carter模型需要更多的数据预处理和模型评估。此代码示例仅用于演示Lee-Carter模型的基本实现。
Lee-Carter模型实现代码matlab
以下是Lee-Carter模型的Matlab代码:
```matlab
function [a, b, k] = lc(data)
% Lee-Carter model
% data: matrix with rows as years and columns as ages
% a, b, k: parameters of the Lee-Carter model
% compute the mean age at each year
mean_age = mean(data, 2);
% compute the log of the data
log_data = log(data);
% compute the deviation of the log data from the mean
deviation = log_data - mean_age;
% compute the singular value decomposition of the deviation matrix
[U, S, V] = svd(deviation);
% compute the principal component
pc = U(:, 1);
% compute the age and time effects
a = mean_age - mean(mean_age);
k = pc .* sqrt(S(1, 1));
b = log_data - repmat(mean_age, 1, size(data, 2)) - repmat(pc, 1, size(data, 2)) * repmat(k', size(data, 1), 1);
% compute the predicted log mortality rates
log_mortality = repmat(mean_age, 1, size(data, 2)) + repmat(a, size(data, 1), 1) + b * pinv(k);
% compute the predicted mortality rates
mortality = exp(log_mortality);
end
```
这个函数接受一个矩阵作为输入,其中每一行是一年的数据,每一列是一个年龄。函数输出Lee-Carter模型的三个参数a、b、k。其中,a是每一年的平均年龄与所有年龄的平均值的差,b是对数数据与年龄、时间效应和第一个主成分的乘积的差,k是第一个主成分乘以标准差。函数使用Matlab的`svd`函数来计算奇异值分解,并使用`pinv`函数来计算伪逆矩阵,因为矩阵k不一定是可逆的。函数最后使用指数函数计算预测的死亡率。