Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [mean-absolute-deviation]

Mean absolute deviation around the mean. Use [mad] for median absolute deviation around the median.

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Is mean absolute deviation smaller than standard deviation for $n\ge 3$?

I want to compare the mean absolute deviation with standard deviation in general case with this definition: $$MAD = \frac{1}{n-1}\sum_1^n|x_i - \mu|, \qquad SD = \sqrt{\frac{\sum_1^n(x_i-\mu)^2}{n-1}}$$ where $\mu =\frac{1}{n}\sum_1^n x_i$. Is it…
Lisbeth
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an upper bound of mean absolute difference?

Let $X$ be an integrable random variable with CDF $F$ and inverse CDF $F^*$. $Y$ is iid with $X$. Prove $$E|X-Y| \leq \frac{2}{\sqrt{3}}\sigma,$$ where $\sigma=\sqrt{Var(X)} = \sqrt{E[(X-\mu)^2]}$. I am looking for some hint for this proof. What…
Tan
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Relative Mean Deviation

The Mean Deviation, also referred to as Absolute Average Deviation, is sometimes preferred to the Standard Deviation (Cf. Gorard 2004). For a sample, it can be expressed as: $MD = \frac{1}{n} \sum\limits_{i=1}^n |x_i - \overline{x}|$ In order to…
Ismael Ghalimi
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Why not use modulus for variance?

I am trying to wrap my mind around the variance definition. Given a set of values S and n = #(S), the variance is defined as: $$ \operatorname{var}(S) = \frac{\sum_{i=1}^n( S_i - \operatorname{mean}(S) )^2} n $$ And the square root of that (standard…
Bitcoin Cash - ADA enthusiast
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Random variables $(X,Y)$ with $\text{Var}(X)<\text{Var}(Y)$ and $\mathbb{E}(|X-\mu_X|)>\mathbb{E}(|Y-\mu_Y|)$

I am looking for an example of a pair of random variables $(X,Y)$ with expected values $(\mu_X,\mu_Y)$ satisfying the following relationships: $$ \text{Var}(X)<\text{Var}(Y) $$ and $$ \mathbb{E}(|X-\mu_X|)>\mathbb{E}(|Y-\mu_Y|). $$
Richard Hardy
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Rephrasing Statistics using MAD

I just got done reading Gorard's "Revisiting a 90-year-old debate: the advantages of the mean deviation." (https://www.leeds.ac.uk/educol/documents/00003759.htm) I'm no expert at statistics; in fact, I'm quite aware of how much there is that I don't…
Somniad
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Mean Absolute Deviation of Student t distributions?

I could only find these two formulae, both apparently with some issues. Which is the correct one? Online references and derivation would be especially appreciated.
Quartz
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Why is there no improvement when training Xgboost with pseudo-Huber loss?

In this StackOverflow post I asked if there was something wrong with my syntax when training an XGboost model (in R) with the native pseudo-Huber loss reg:pseudohubererror, since nor training or test error improve (remain constant). There doesn't…
PaulG
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How to calculate the running mean absolute deviation

I wish to calculate the running mean absolute deviation (MAD) without storing the previous n data points. This calculation is for a continuous stream of data, i.e. infinite length. I am trying to calculated the running MAD for a window of samples of…
mr_js
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Is mean deviation the same as mean absolute difference?

Do both terms mean the same thing or are they different?
ankit
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Variance of Binomial total deviation

I have a Binomial random variable $X \sim B(n,p)$. Is there a closed form expression or an upper bound for the variance of the absolute deviation $|X-\mathbb{E}[X]|$ ?
K. Lakshmanan
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Mean Absolute Deviation for AR(1) process

Is there closed-form solution for mean absolute deviation (MAD) for AR(1) process? $X_t = c + \beta X_{t-1} + \epsilon_t $ $\epsilon_t \sim N(0,\sigma^{\epsilon})$ (Similar to the variance and the mean for AR(1): as we can derive mean as…
maril
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How do I calculate Correlation Coefficient using Mean Absolute Deviation?

I am trying to calculate Pearson's Correlation Coefficient using the product of the Mean Absolute Deviations (MADs) of my two lists as denominators instead of the Standard Deviations. Effectively, here's the formula I'm currently using: $$\frac{…
Adifyr
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Estimate the error bound of a histogram based mean absolute deviation approximation

Given a sequence of numbers $A = a_1, a_2, \cdots, a_n$. One way to calculate the mean absolute deviation of $A$ is by $G(A)= \sum_{i=0}^n |a_i - median(A)|$. yet, there can be an alternative, by first aggregating a histogram with $k$ bins. $A \to…
yupbank
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Ho do I determine the probability of price reversals using linear regression?

In the screenshot, you will see the daily prices of Nasdaq. Each candle has a High, Low, Open and Close price. I have drawn a regression line with a 2 standard deviation channel on either side. How would I go about determining the following…
Grantx
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