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# Questions tagged [mean-absolute-deviation]

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

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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, ...
12 views

### How would the MAE of a set of predictions affect further predictions made with that set of predictions

Suppose I have a model (Model_A) that can predict the net weights of products from an arbitrary input X. Weight = Model_A(X) Model_A has a mean absolute error of <...
40 views

The calculation the MAD (Mean Absolute Deviation)/Mean ratio is this, according to the title: $$\frac{\overline{\left | Forecast - Demand \right |}}{\overline{Demand}}$$ However, the calculation is ...
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### Count the fraction of trials for which the absolute deviation from the mean is larger than the standard deviation?

So, I have a data set containing 99 elements each with their own associated value. I have computed the standard deviation and the mean, but I am a little stumped with how exactly I should proceed with ...
58 views

### Deducing $L^1$ Boundary from Mahalanobis Boundary

Assume maximum likelihood estimators $a,b$ of size $p$, with corresponding estimated covariance matrices $V^a,V^b$. In fact $a,b$ are two regression coefficient vectors. Denote $q=a-b$ the vector of ...
179 views

### Standard Deviations of Detrended Data vs Original Data

I'am interested to know the opinion on this matter. I have Data of a Financial Security. The goal is to view the Standard Deviations levels of the data to possibly see patterns of behavior of the ...
88 views

### measure for deviation/error that is guarantueed to be smaller than the mean

I am presenting some non-negative values by using a mean value with error bars, basically something like this: So the mean values are shown as dots and the error bars are displayed vertically, ...
1 vote
43 views

### 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 ...
1 vote
808 views

### Best way to describe changes in performance through time.

I'm wondering how to explain changes in production/performance metrics quarter to quarter. In the example below, one can see that the average processing time for "widgets" has decreased substantially ...
89 views

### Least Absolute Values Regression

I have the data: x <- c(0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0) y <- c(2.06, 2.12, 2.32, 2.02, 2.76, 3.04, 2.83, 3.15, 3.36, 3.68, 3.96) I ...
1 vote
256 views

### 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, ...
1 vote
62 views

### 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 ...
789 views

### 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 ...
934 views

### 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 ...
398 views

318 views

### Difference between absolute deviation to population median and sample mean

I have independent variables $X_i\in[0;1]$ and suppose they are uniformly distributed. If you want to minimize the total absolute deviation to a fixed number, how much can you gain from using the ...
539 views

4k views

### Why not use modulus for variance? [duplicate]

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}(...
1 vote
191 views

### An efficient algorithm for sliding mean deviation

I'm searching for a computationally efficient algorithm to calculate the sliding mean deviation from sample $x_a$ to sample $x_b$ belonging to a large set $x_0, x_1 ... x_n$ with the condition that $a$...
1k views

### Is mean deviation the same as mean absolute difference?

Do both terms mean the same thing or are they different?
1k views

### 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.
1 vote
459 views

### Why don't dispersions like median deviation and mode deviation exists on the lines of mean deviation?

Or to say in the formula MD=$\frac{1}{N}\sum_{i=1}^{N}|x_i-\overline{x}|$ why can't we have median or mode instead of mean($\overline{x}$) and as a result speak about additional possible measures of ...
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 $|X-\mathbb{E}[X]|$ ?