Linear and Reciprocal Transformations

Transform distributions using location shifts, scaling, negation, and reciprocals. If X is a random variable following a distribution, these functions return the distribution of the transformed variable.

Usage

flip(distribution)

invert(distribution)

multiply(distribution, constant)

shift(distribution, constant)

Arguments

distribution

A probability distribution.

constant

A numeric value for shifting or scaling.

Value

A transformed distribution.

Functions vs Operators

These transformations can be applied using named functions or arithmetic operators:

• shift(d, a) or d + a - Returns distribution of X + a

• multiply(d, a) or d * a - Returns distribution of X * a

• flip(d) or -d - Returns distribution of -X

• invert(d) or 1 / d - Returns distribution of 1 / X

For complete documentation of operator usage, see Ops.dst().

Special Cases

Negation in multiplication: When multiply() receives a negative constant, it internally calls flip() on the result of multiplying by the absolute value.

Inversion constraint: invert() requires that the distribution has no mass at zero (i.e., P(X = 0) = 0). An error is returned if this condition is violated.

Simplifications

These functions apply automatic simplifications when possible. For example:

• Shifting a Normal distribution returns another Normal distribution

• Multiplying a Uniform distribution returns another Uniform distribution

• Flipping a symmetric distribution may preserve its form

More simplifications will be added in future versions of distplyr.

See also

Ops.dst() for arithmetic operators including +, -, *, /.

Examples

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

# Shifting
shift(d_pois, 1)
#> Shifted distribution (discrete) 
#> --Parameters--
#> $distribution
#> Poisson distribution (discrete) 
#> --Parameters--
#> lambda 
#>    1.1 
#> 
#> $shift
#> [1] 1
#> 
d_pois + 1           # Equivalent using operator
#> Shifted distribution (discrete) 
#> --Parameters--
#> $distribution
#> Poisson distribution (discrete) 
#> --Parameters--
#> lambda 
#>    1.1 
#> 
#> $shift
#> [1] 1
#> 

# Scaling
multiply(d_unif, 2)
#> Uniform distribution (continuous) 
#> --Parameters--
#> min max 
#>   0   2 
d_unif * 2           # Equivalent using operator
#> Uniform distribution (continuous) 
#> --Parameters--
#> min max 
#>   0   2 

# Negation
flip(d_norm)
#> Normal distribution (continuous) 
#> --Parameters--
#> mean   sd 
#>   -4    1 
-d_norm              # Equivalent using operator
#> Normal distribution (continuous) 
#> --Parameters--
#> mean   sd 
#>   -4    1 

# Inversion
d_positive <- distionary::dst_unif(1, 2)
invert(d_positive)
#> Inverse distribution (continuous) 
#> --Parameters--
#> $distribution
#> Uniform distribution (continuous) 
#> --Parameters--
#> min max 
#>   1   2 
#> 
1 / d_positive       # Equivalent using operator
#> Inverse distribution (continuous) 
#> --Parameters--
#> $distribution
#> Uniform distribution (continuous) 
#> --Parameters--
#> min max 
#>   1   2 
#> 

# Combine multiple operations
4 - 2 * d_pois
#> Shifted distribution (discrete) 
#> --Parameters--
#> $distribution
#> Negated distribution (discrete) 
#> --Parameters--
#> $distribution
#> Scaled distribution (discrete) 
#> --Parameters--
#> $distribution
#> Poisson distribution (discrete) 
#> --Parameters--
#> lambda 
#>    1.1 
#> 
#> $constant
#> [1] 2
#> 
#> 
#> 
#> $shift
#> [1] 4
#> 
multiply(flip(multiply(d_pois, 2)), -1) + 4  # Equivalent
#> Shifted distribution (discrete) 
#> --Parameters--
#> $distribution
#> Scaled distribution (discrete) 
#> --Parameters--
#> $distribution
#> Poisson distribution (discrete) 
#> --Parameters--
#> lambda 
#>    1.1 
#> 
#> $constant
#> [1] 2
#> 
#> 
#> $shift
#> [1] 4
#>