# Moving Average/Basic Approach

## Generic Approach to Moving Average

[edit | edit source]An element moves in an additive Group (mathematics) or Vector Space *V*.
In a generic approach, we have a moving probability distribution that defines how the values in the environment of have an impact on the moving average.

### Discrete/continuous Moving Average

[edit | edit source]According to probability distributions we have to distinguish between a

**discrete**(probability mass function ) and**continuous**(probability density function )

moving average. The terminology refers to probability distributions and the semantics of probability mass/density function describes the distrubtion of weights around the value . In the discrete setting the means that has a 20% impact on the moving average for .

### Moving/Shift Distributions

[edit | edit source]If the probility distribution are shifted by in . This means that the probability mass functions resp. probability density functions are generated by a probability distribution at the zero element of the additive group resp. zero vector of the vector space. Due to nature of the collected data *f(x)* exists for a subset . In many cases *T* are the points in time for which data is collected. The and the shift of a distribution is defined by the following property:

**discrete:**For all the probability mass function fulfills for**continuous:**For all probability density function fulfills

The moving average is defined by:

**discrete**: (probability mass function )

Remark: for a countable subset of

**continuous**probability density function

It is important for the definition of probability mass functions resp. probability density functions that the support (measure theory) of is a subset of *T*. This assures that 100% of the probability mass is assigned to collected data. The support is defined as: