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这里是LearingYard学苑！
今天小编为大家带来《随机需求下生鲜电商供应链物流合作与运营决策》
数值分析部分知识介绍。
欢迎您的用心访问！
本期推文阅读时长大约5分钟，请您耐心阅读。
Share interest, spread happiness,
increase knowledge, and leave beautiful.
Dear you,
this is the LearningYard Academy!
Today I bring you "Fresh produce e-commerce supply chain logistics cooperation and operational decisions under stochastic demand
Numerical analysis part of knowledge introduction.
Welcome your visit!
The reading time of this tweet is about 5 minutes, please read it with patience.
内容摘要
本期推文将通过思维导图，复刻论文内容，知识补充三个板块，复刻来自于中国管理科学期刊的期刊论文《随机需求下生鲜电商供应链物流合作与运营决策》数值分析部分知识介绍。
In this issue, the tweet will reproduce the numerical analysis part of the knowledge introduction of the journal paper "Cooperation and operational decisions in fresh produce e-commerce supply chain logistics under stochastic demand" from the Chinese Journal of Management Science through three sections: mind map, reproduction of the paper content and knowledge supplement.
思维导图
关于数值分析部分知识介绍的思维导图如下：
A mind map of the knowledge presented in the section on numerical analysis is as follows:
精读内容
上期推文介绍了不同模式下的决策和收益情况对比，本期推文将介绍数值分析部分知识介绍，由于作者考虑了需求量是随机的，而且涉及到了概率密度函数和分布函数，均匀分布等内容，那么小编带大家回顾一下这些内容！
首先是概率密度函数的定义：
The last tweet introduced a comparison of the decision and benefit situation under different models, this tweet will introduce the numerical analysis part of the knowledge introduction, as the author considered the demand is random, and involves the probability density function and distribution function, uniform distribution, etc., then I take you to review these contents!
First is the definition of the probability density function:
对于概率密度函数的理解，可以总结为自变量落在a到b区间的概率。
其特点有概率密度函数大于等于0，负无穷到正无穷的概率密度积分为1。
然后是分布函数的定义：
The understanding of the probability density function can be summarised as the probability of the independent variable falling in the interval a to b.
It is characterised by a probability density function greater than or equal to 0 and a probability density integral of 1 for negative infinity to positive infinity.
Then comes the definition of the distribution function:
可以看到分布函数就是负无穷到自变量这个范围的概率密度函数的积分，分布函数的性质如下：
It can be seen that the distribution function is the integral of the probability density function over the range from negative infinity to the independent variable, and the properties of the distribution function are as follows:
根据上述图片可以看到分布函数数值范围在0-1、是x的不减函数、负无穷的分布函数为0，正无穷的分布函数为1，分布函数与概率密度函数的关系、在x点如果连续，分布函数求导后的结果就是概率密度函数。
最后是均匀分布的定义：
According to the above picture, we can see that the value of the distribution function ranges from 0 to 1, it is a non-decreasing function of x, the distribution function of negative infinity is 0, the distribution function of positive infinity is 1, the relationship between the distribution function and the probability density function, at the point x if continuous, the result of the derivative of the distribution function is the probability density function.
Finally, the definition of a uniform distribution:
回到文章中，可以看到f(u)=1/2的原因就是处于均匀分布的概率密度函数了，并根据分布函数的计算方法，得到正偏差和负偏差的具体公式。
Returning to the article, it can be seen that the reason for f(u) = 1/2 is that the probability density function is now in a uniform distribution, and the specific formulas for positive and negative deviations are obtained according to the calculation of the distribution function.
知识补充
本文的均匀分布考虑的是连续型随机变量，那么还有哪些常见的连续型随机变量的分布呢？
正态分布：
The uniform distribution in this paper considers continuous random variables, so what other common distributions of continuous random variables are there?
Normal distribution:
指数分布：
Index distribution:
今天的分享就到这里了。
如果您对今天的文章有独特的想法，
欢迎给我们留言，
让我们相约明天。
祝您今天过得开心快乐！
That's it for today's sharing.
If you have a unique idea about today’s article,
welcome to leave us a message,
let us meet tomorrow.
I wish you a nice day !!
参考资料：DeepL翻译，知乎，百度
参考文献：崔鑫,李春发,周驰,米新新,沈瑶.随机需求下生鲜电商供应链物流合作与运营决策[J/OL].中国管理科学:1-15[2023-02-05].
本文由LearningYard学苑整理发出，如有侵权请在后台留言！
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