# 统计代写|抽样理论作业代写sampling theory代考|STAT41020

## 统计代写|抽样理论作业代写sampling theory代考|Definitions and Basic Relationships

In a complex subject such as heterogeneity, it does not take long before the reader encounters notation difficulties; for quick and easy reference we conveniently summarized all notations pertaining to this chapter in Table 6.1.

We would like to mention again that in this chapter, all units make up a population in which their order is not taken into consideration, which means that all units within the lot are strictly considered as a random population. On the contrary, in Chapter 7 the order of the units is taken into account, and the lot is considered as a chronological series.

Now let us consider $L$ as a given lot of material made of discrete units, $N_u$ as the number of these units, and $U_m$ as the current unit of $L$ with $m=1,2, \ldots, N_u$. By definition, in a zero-dimensional lot, these units constitute a population in which there is no obvious order. These units can be made of fragments of particulate material (e.g., particles of minerals or solid chemicals, grains of a cereal, fruits, seeds, etc.), or groups of neighboring fragments, or transportation units (e.g., railroad cars, trucks, barrels, bags, jars, shovels, etc.). In all of these cases, as far as the heterogeneity carried out by one component of interest is concerned, the material making up one unit $U_m$ is completely defined by three parameters that can be called its descriptors:
$M_{m r}$ : the total weight of the active components in $U_m$
$A_m$ : the weight of the component of interest (also called critical component) in $U_m$ $a_m$ : the component of interest content (also called critical content) in $U_m$

These three descriptors are related as follows:
$$A_m=a_m M_m$$
The three parameters $A, a$, and $M$ are related by one equality, and only two of them are sufficient to completely define the unit under consideration. Often, we choose the total weight $M$ and the critical content $a$; thus, we define units with two descriptors.
Now, let us suppose that one of these two parameters is practically constant in all the units of the population; therefore, only one descriptor is necessary to completely define the unit under consideration. Thus, we define units with one descriptor. In the same manner, a lot $\mathrm{L}$ is completely defined by the three descriptors $M_L A_L$, and $a_L$, which are themselves defined by the following relations:
$$\begin{gathered} M_L=\sum_m M_m \ A_L=\sum_m A_m \ a_L=\frac{A_L}{M_L} \end{gathered}$$

## 统计代写|抽样理论作业代写sampling theory代考|The Intrinsic Heterogeneity of the Fragments Making Up the Lot

As defined by equation (6.18). the Constitution Heterogeneity $\mathrm{CH}_L$ is not easy to calculate in most of the real cases in which we are interested. Part of the reason is the difficulty or impossibility in estimating $N_F$, which is usually very large.

In practice, we need to be able to calculate in all cases, and at the cost of some approximations if necessary, the characteristic of the material making up the lot, and this characteristic shall be independent of the size of the lot (i.e., suppressing the need to estimate $N_F$ ).

This can be done by multiplying $\mathrm{CH}_L$ by the term $\mathrm{M}_L / N_F$ which is nothing more than the average weight $\bar{M}_i$ of a fragment. Therefore, we may define the Intrinsic Heterogeneity $I_L$ by the following extremely important relation:
$$I H_L=\frac{C H_L M_L}{N_F}=C H_L \overline{M_i}=\sum_i \frac{\left(a_i-a_L\right)^2}{a_L^2} \cdot \frac{M_i^2}{M_L}$$
The larger font used for this critically important equation is to emphasize its importance for all the work we are going to do for the Fundamental Sampling Error FSE and for the Grouping and Segregation Error GSE. Many practitioners refer to Gy’s formula by using the wrong formula. If there is such a thing as a Gy’s formula, equation (6.20) is the one, and no one describes it as such.

Because $\mathrm{CH}{\mathrm{L}}$ is dimensionless, $\mathrm{IH}{\mathrm{L}}$ has the dimension of a weight. Now we are going to find out why $I H_L$ deserves the name of Intrinsic Heterogeneity.

# 抽样理论代考

## 统计代写|抽样理论作业代写采样理论代考|定义和基本关系

.

$M_{m r}$: $U_m$中活性组分的总权重
$A_m$: $U_m$$a_m中感兴趣的组分(也称为临界组分)的权重:U_m中兴趣内容(也称为关键内容)的组成部分 这三个描述符的关系如下:$$ A_m=a_m M_m $$A, a和M这三个参数之间有一个相等的关系，只有其中两个参数足以完全定义所考虑的单位。通常，我们选择总权重M和关键内容a;因此，我们用两个描述符来定义单元。现在，让我们假设这两个参数中的一个在总体的所有单位中实际上是恒定的;因此，只需要一个描述符就可以完全定义考虑中的单元。因此，我们用一个描述符来定义单元。以同样的方式，很多\mathrm{L}完全由三个描述符M_L A_L和a_L定义，它们本身由以下关系定义:$$ \begin{gathered} M_L=\sum_m M_m \ A_L=\sum_m A_m \ a_L=\frac{A_L}{M_L} \end{gathered} $$## 统计代写|抽样理论作业代写采样理论代考|组成批次的碎片的内在异质性 由式(6.18)定义。宪法异质性\mathrm{CH}_L在我们感兴趣的大多数实际案例中并不容易计算。部分原因是很难或不可能估计N_F，这通常是非常大的 在实践中，我们需要能够在所有情况下计算，并在必要时以一些近似为代价，计算组成批量的材料的特性，而该特性应与批量的大小无关(即抑制估计N_F的需要) 这可以通过将\mathrm{CH}_L乘以术语\mathrm{M}_L / N_F来实现，这仅仅是一个片段的平均权重\bar{M}_i。因此，我们可以通过以下极其重要的关系来定义内在异质性I_L:$$ I H_L=\frac{C H_L M_L}{N_F}=C H_L \overline{M_i}=\sum_i \frac{\left(a_i-a_L\right)^2}{a_L^2} \cdot \frac{M_i^2}{M_L}$$这个极其重要的方程使用较大的字体是为了强调它对于我们将要进行的基本抽样误差FSE和分组和分离误差GSE的所有工作的重要性。许多实践者用错误的公式引用Gy的公式。如果存在一个Gy公式，那么(6.20)式就是其中之一，而且没有人这样描述它 因为$\mathrm{CH}{\mathrm{L}}$是无量纲的，所以$\mathrm{IH}{\mathrm{L}}$有一个权重的量纲。现在我们来看看为什么$I H_L\$值得被称为内在异质性。

myassignments-help数学代考价格说明

1、客户需提供物理代考的网址，相关账户，以及课程名称，Textbook等相关资料~客服会根据作业数量和持续时间给您定价~使收费透明，让您清楚的知道您的钱花在什么地方。

2、数学代写一般每篇报价约为600—1000rmb，费用根据持续时间、周作业量、成绩要求有所浮动(持续时间越长约便宜、周作业量越多约贵、成绩要求越高越贵)，报价后价格觉得合适，可以先付一周的款，我们帮你试做，满意后再继续，遇到Fail全额退款。

3、myassignments-help公司所有MATH作业代写服务支持付半款，全款，周付款，周付款一方面方便大家查阅自己的分数，一方面也方便大家资金周转，注意:每周固定周一时先预付下周的定金，不付定金不予继续做。物理代写一次性付清打9.5折。

Math作业代写、数学代写常见问题

myassignments-help擅长领域包含但不是全部: