What Does the Prime Symbol Mean in Statistical Moments?

In summary, the prime notation (') in statistics signifies a differentiation of variable names while maintaining a general meaning. For example, t and t' may both represent "time" but for different objects or purposes. It is commonly used to distinguish a "moment about the origin" from a "moment about the mean" in a distribution.
  • #1
freedominator
5
0
sometimes in statistics there is a prime ( ' ) after the variable for moment ( u sub r ) what does that mean?
 
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  • #2
Please provide an example.
The prime notation is used to differentiate the variable name while keeping a general meaning ... so t and t' are both "time" but may be for different objects or have different uses as in a place-holder variable.
 
  • #3
As Simon says. ( I had to day that!)
In particular, the prime notation is often used to distinguish a "moment about the origin" from a "moment about the mean" of a distribution as in https://en.wikipedia.org/wiki/Central_moment
 
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  • #4
tyvm
 
  • #5


The prime symbol (') after the variable for moment (u sub r) indicates that the moment being referred to is a derivative of a higher order. In other words, it is a higher degree of the original moment. This is commonly used in statistics to represent a specific moment in a distribution, such as the second moment (u sub 2) or the third moment (u sub 3). The prime symbol is often used in mathematical notation to denote differentiation, so in this case, it is used to indicate a higher order moment.
 

FAQ: What Does the Prime Symbol Mean in Statistical Moments?

What is a moment prime in statistics?

A moment prime in statistics is a type of statistical moment that measures the shape of a probability distribution. It is the average of the deviations from the mean raised to a power, typically the second power.

2. How is a moment prime calculated?

To calculate a moment prime, you first need to calculate the mean of the data set. Then, for each data point, you subtract the mean and raise it to the desired power. Finally, you take the average of these values to get the moment prime.

3. What is the significance of moment prime in statistics?

Moment prime is significant because it helps to quantify the shape of a probability distribution. It is used in various statistical analyses, such as calculating moments of inertia in physics or determining the skewness of a distribution in finance.

4. Can moment prime be negative?

Yes, moment prime can be negative. This typically occurs when the data points are spread out more to the left of the mean, resulting in negative deviations from the mean.

5. How does moment prime differ from other statistical moments?

Moment prime differs from other statistical moments, such as the mean or variance, in that it considers the deviations from the mean raised to a power, rather than just the deviations themselves. This allows it to capture the shape of the distribution more accurately.

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