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FRM®一级风险管理基础备考公式（4）
文章来源：网络
发布时间：2022-01-04 10:31
阅读：424次
本文继续为大家介绍FRM®一级风险管理基础的备考公式，以下是定量分析备考公式（4），一起来看吧。
Population and Sample Mean
The population mean sums all observed values in the population and divides by the number of observations in the population, N.
The sample mean is the sum of all values in a sample of a population, ΣX, divided by the number of observations in the sample, n. It is used to make inferences about the population mean.
Population and Sample Variance
The population variance is defined as the average of the squared deviations from the mean. The population standard deviation is the square root of the population variance.
The sample variance, s 2 , is the measure of dispersion that applies when we are evaluating a sample of n observations from a population. Using n – 1 instead of n in the denominator improves the statistical properties of s2 as an estimator of σ2.【点击免费下载>>>更多FRM学习相关资料】
Sample Covariance
Desirable Properties of an Estimator
A point estimate should be a linear estimator when it can be used as a linear function of sample data.
An unbiased estimator is one for which the expected value of the estimator is equal to the parameter you are trying to estimate.
A consistent estimator is one for which the accuracy of the parameter estimate increases as the sample size increases. Central Limit Theorem When selecting simple random samples of size n from a population with mean μ and finite
variance σ2, the sampling distribution of sample means approaches the normal probability distribution with mean μ and variance equal to σ2 /n as the sample size becomes large.
Skewness and Kurtosis
Skewness, or skew, refers to the extent to which a distribution is not symmetrical. The skewness of a normal distribution is equal to zero.
A positively skewed distribution is characterized by many outliers in the upper region, or right tail.
A negatively skewed distribution has a disproportionately large amount of outliers that fall within its lower (left) tail.
Kurtosis is a measure of the degree to which a distribution is spread out compared to a normal distribution. Excess kurtosis = kurtosis – 3.
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