What is population skew?

Question

BlackTom AI · Accepted Answer

To analyze the concept of population skew, we should recall what skewness measures in a distribution. 
Option 1: E[((x-μ)/σ)^4] - 3. This expression is related to kurtosis, specifically the excess kurtosis measure, which characterizes the tails and peakedness rather than skewness. Subtracting 3 is a common normalization for excess kurtosis, so this option is about kurtosis, not skewness. 
Option 2: E[((x-μ)/σ)^3]. This is the third standardized moment of the distribution. It captures asymmetry: if it is zero, the distribution is symmetric about its mean; if positive or negative, there is a right or left skew. This aligns with the conventional definition of population skew (the skewness). 
Option 3: E[((x-μ)/σ)^2]. This is the second standardized moment, which equals 1 for any distribution (since it is the variance normalized by σ^2). It measures dispersion but does not convey asymmetry, so it does not represent skewness. 
Option 4: E[((x-μ)/σ)^4]. This is the fourth standardized moment, which relates to kurtosis, not skewness. While it informs about tail heaviness and peakedness, it does not describe asymmetry. 
In summary, only the expression in Option 2 directly corresponds to the concept of population skew as the third standardized moment; the other options pertain to kurtosis or dispersion and do not quantify skewness.

ERMCPS5350_006_2025_3 - INTRO TO QUANTITATIVE RISK MANAGEMENT 5. Quiz for Class 5

What is population skew?

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ERMCPS5350_006_2025_3 - INTRO TO QUANTITATIVE RISK MANAGEMENT 5. Quiz for Class 5

What is population skew?

查看解析

登录即可查看完整答案

类似问题

偏度衡量数值分布的对称性，不对称的分布称为偏斜分布。给定一个变量的直方图，下列哪种偏度类型最能描述该分布？

In a right-skewed distribution

Histograms (1 mark)Which of the following statements about the following histogram of data points in 'y' is true:[Fill in the blank]

If the shape of a distribution is skewed, with a long tail projecting longer to the left than to the right, how would the distribution be skewed?​

A sample of people who have attended a football game at the U has a mean = 3.2 members in their family. The mode number of family members is 2 and the median number is 2.0. Based on this information:

The shape of the data distribution displayed by this dot plot is best described as:

What is considered severe skew in a data distribution?

The shape of the data distribution displayed by this dot plot is best described as:

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If the shape of a distribution is skewed, with a long tail projecting longer to the left than to the right, how would the distribution be skewed?