威布尔分布中的错误 [英] Error in Weibull distribution

问题描述

file.data具有以下值以适合Weibull分布

file.data has the following values to fit with Weibull distribution,

x       y 
2.53    0.00
0.70    0.99
0.60    2.45
0.49    5.36
0.40    9.31
0.31    18.53
0.22    30.24
0.11    42.23

在Weibull分布函数f(x)=1.0-exp(-lambda*x**n)之后，出现错误:

Following the Weibull distribution function f(x)=1.0-exp(-lambda*x**n), it is giving error:

fit f(x) 'data.dat' via lambda, n

最后绘制f(x)和xy图有很大差异.

and finally plotting f(x) and xy graph have large discrepancy.

任何反馈将不胜感激.谢谢！

Any feedback would be highly appreciated. Thanks!

推荐答案

几件事:

1. 您必须跳过第一行(如果它确实是x y).

您必须使用正确的功能(PDF而不是CDF，请参见 http://en.wikipedia.org/wiki/Weibull_distribution ，就像您在 https://stackoverflow.com/q/20336051中所做的一样/2604213 )

You must use the correct function (the pdf and not the CDF, see http://en.wikipedia.org/wiki/Weibull_distribution, like you did in https://stackoverflow.com/q/20336051/2604213)

您必须使用其他缩放参数，因为您的数据未标准化

You must use an additional scaling parameter, because your data are not normalized

您必须为拟合选择足够的初始值.

You must select adequate initial values for the fitting.

以下可以正常工作:

f(x) = (x < 0 ? 0 : a*(x/lambda)**(n-1)*exp(-(x/lambda)**n))
n = 0.5
a = 100
lambda = 0.15
fit f(x) 'data.dat' every ::1 via lambda, n, a

set encoding utf8
plot f(x) title sprintf('λ = %.2f, n = %.2f', lambda, n), 'data.dat' every ::1

给出(含4.6.4):

That gives (with 4.6.4):

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