两种可能结果的离散随机变量概率分布 ,失败是0,成功是1,p是成功的概率。
dbinorm() :提供任何有效x的概率质量函数
pbinom() :提供累积概率分布,求结果成功q次及q次以下的累积概率,给定分位数值q,输出累积概率p
qbinom() :累积概率分布的逆( pbinom() 的逆),给定累积概率p,输出分位数值q
rbinom() :产生n个服从二项分布的随机数
3. dpois() , ppois() , qpois() , rpois()
dt() , pt() , qt() , rt()
1、RMSE(均方根误差)即标准误差:假如数据在A1:Z1
标准方差用函数=STDEV(A1:Z1)
方差用函数=VARA(A1:Z1)
2、MRE(平均相对误差)
Excel/函数/统计/STDEV(Sd)
计算出标准偏差Sd值,然后除以平均数再×100%就可以了。
为了找到均方根误差,我们首先需要找到残差(也称为误差,我们需要对这些值均方根),然后需要计算这些残差的均方根。因此,如果我们有一个线性回归模型对象说M,则均方根误差可以找到为sqrt(mean(M $residuals ^ 2))。
x1<-rnorm(500,50,5)
y1<-rnorm(500,50,2)
M1<-lm(y1~x1)
summary(M1)
输出结果
Call:
lm(formula = y1 ~ x1)
Residuals:
Min 1QMedian3QMax
-5.6621 -1.2257 -0.0272 1.4151 6.6421
Coefficients:
EstimateStd.Errort value Pr(>|t|)
(Intercept) 50.178943 0.915473 54.812 <2e-16 ***
x1 -0.002153 0.018241 -0.118 0.906
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.966 on 498 degrees of freedom
Multiple R-squared: 2.798e-05, Adjusted R-squared: -0.00198
F-statistic: 0.01393 on 1 and 498 DF, p-value: 0.9061
从模型M1中找到均方根误差-
示例
sqrt(mean(M1$residuals^2))
输出结果
[1] 1.961622
示例
x2<-rnorm(5000,125,21)
y2<-rnorm(5000,137,10)
M2<-lm(y2~x2)
summary(M2)
输出结果
Call:
lm(formula = y2 ~ x2)
Residuals:
Min 1QMedian3QMax
-37.425 -7.005 -0.231 6.836 36.627
Coefficients:
Estimate Std.Error t value Pr(>|t|)
(Intercept) 138.683501 0.851247 162.918 <2e-16 ***
x2 -0.014386 0.006735 -2.136 0.0327 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 10.06 on 4998 degrees of freedom
Multiple R-squared: 0.0009121, Adjusted R-squared: 0.0007122
F-statistic: 4.563 on 1 and 4998 DF, p-value: 0.03272
从模型M2中找到均方根误差:
示例
sqrt(mean(M2$residuals^2))
输出结果
[1] 10.05584
示例
x37<-rpois(500,5)
y3<-rpois(500,10)
M3<-lm(y3~x3)
summary(M3)
输出结果
Call:
lm(formula = y3 ~ x3)
Residuals:
Min 1QMedian3QMax
-7.9004 -1.9928 -0.2155 2.1921 9.3770
Coefficients:
EstimateStd.Error t value Pr(>|t|)
(Intercept) 10.17770 0.3233031.481<2e-16 ***
x3 -0.09244 0.06145-1.5040.133
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.027 on 498 degrees of freedom
Multiple R-squared: 0.004524, Adjusted R-squared: 0.002525
F-statistic: 2.263 on 1 and 498 DF, p-value: 0.1331
从模型M3查找均方根误差-
示例
sqrt(mean(M3$residuals^2))
输出结果
[1] 3.020734
示例
x4<-runif(50000,5,10)
y4<-runif(50000,2,10)
M4<-lm(y4~x4)
summary(M4)
输出结果
Call:
lm(formula = y4 ~ x4)
Residuals:
Min1Q Median 3QMax
-4.0007 -1.9934 -0.0063 1.9956 3.9995
Coefficients:
EstimateStd.Error t value Pr(>|t|)
(Intercept) 5.9994268 0.0546751 109.729 <2e-16 ***
x40.0001572 0.0071579 0.0220.982
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 2.309 on 49998 degrees of freedom
Multiple R-squared: 9.646e-09, Adjusted R-squared: -1.999e-05
F-statistic: 0.0004823 on 1 and 49998 DF, p-value: 0.9825
从模型M4找到均方根误差-
示例
sqrt(mean(M4$residuals^2))
输出结果
[1] 2.308586
示例
x5<-sample(5001:9999,100000,replace=TRUE)
y5<-sample(1000:9999,100000,replace=TRUE)
M5<-lm(y5~x5)
summary(M5)
输出结果
Call:
lm(formula = y5 ~ x5)
Residuals:
Min 1QMedian 3Q Max
-4495 -2242-42230 4512
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.504e+03 4.342e+01 126.765 <2e-16 ***
x5-1.891e-03 5.688e-03 -0.333 0.74
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 2594 on 99998 degrees of freedom
Multiple R-squared: 1.106e-06, Adjusted R-squared: -8.895e-06
F-statistic: 0.1106 on 1 and 99998 DF, p-value: 0.7395
从模型M5中找到均方根误差<
示例
sqrt(mean(M5$residuals^2))
输出结果
[1] 2593.709
function 是定义一个函数,这个函数的名字是poissonproc,感脚上是个泊松过程吧;rpois是按照泊松分布生成随机数rpois(n, lambda),生成n个;
runif是按照均匀分布生成随机数runif(n, min=0, max=10), 生成n个,这个n是之前的结果,最大值是10,最小值默认为0;
返回的 均匀分布的随机数中,[4, 5]之间的个数;
最后一句:上述过程重复10000次;