Linear Transformations

shift() a distribution by adding a constant, or multiply() a distribution by a constant. flip() is a specific case of multiplying a distribution by -1, resulting in "flipping" the distribution about 0.

Usage

flip(distribution)

multiply(distribution, constant)

shift(distribution, constant)

Arguments

distribution

A probability distribution.

constant

A single numeric by which to shift or multiply the distribution by.

Value

A distribution, shifted or multiplied by the constant. Specifically, a distribution with subclass "shift", "scale", or "flip".

Details

Specifically, if X is a random variable coming from a distribution, then the resulting distributions are as follows:

• For shift(), is the distribution of X + constant.

• For multiply(), is the distribution of X * constant.

• For flip(), is the distribution of -X.

Although the multiply() function accepts negative constants, the corresponding "scale" distribution class only holds positive constants, delegating a potential negative sign to the "flip" class.

Note

You can also use the binary operations +, -, *, and / to access these transformations.

See also

invert()

Examples

d_pois <- distionary::dst_pois(1.1)
d_norm <- distionary::dst_norm(4, 1)
d_unif <- distionary::dst_unif(0, 1)

# Shift a Poisson distribution by 1.
shift(d_pois, 1)
#> [1] "shift" "dst"  
#> 
#>  components :
#> $distribution
#> [1] "pois"       "parametric" "dst"       
#> 
#>  name :
#> [1] "pois"
#> 
#> $shift
#> [1] 1
#> 
d_pois + 1
#> [1] "shift" "dst"  
#> 
#>  components :
#> $distribution
#> [1] "pois"       "parametric" "dst"       
#> 
#>  name :
#> [1] "pois"
#> 
#> $shift
#> [1] 1
#> 

# Multiply a Uniform distribution by 2.
multiply(d_unif, 2)
#> [1] "scale" "dst"  
#> 
#>  components :
#> $distribution
#> [1] "unif"       "parametric" "dst"       
#> 
#>  name :
#> [1] "unif"
#> 
#> $scale
#> [1] 2
#> 
d_unif * 2
#> [1] "scale" "dst"  
#> 
#>  components :
#> $distribution
#> [1] "unif"       "parametric" "dst"       
#> 
#>  name :
#> [1] "unif"
#> 
#> $scale
#> [1] 2
#> 

# Flip a Normal distribution.
flip(d_norm)
#> [1] "negative" "dst"     
#> 
#>  distribution :
#> [1] "norm"       "parametric" "dst"       
#> 
#>  name :
#> [1] "norm"
-d_norm
#> [1] "negative" "dst"     
#> 
#>  distribution :
#> [1] "norm"       "parametric" "dst"       
#> 
#>  name :
#> [1] "norm"

# Combine multiple operations:
4 - 2 * d_pois
#> [1] "shift" "dst"  
#> 
#>  components :
#> $distribution
#> [1] "negative" "dst"     
#> 
#>  distribution :
#> [1] "scale" "dst"  
#> 
#>  components :
#> $distribution
#> [1] "pois"       "parametric" "dst"       
#> 
#>  name :
#> [1] "pois"
#> 
#> $scale
#> [1] 2
#> 
#> 
#> $shift
#> [1] 4
#>