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Arithmetic Operations for Distributions

Source: R/Ops.R
Ops.dst.Rd

Apply arithmetic operators to probability distributions. These operations transform distributions in intuitive ways, treating them similarly to numeric values.

Usage

# S3 method for class 'dst'
Ops(e1, e2)

Arguments

e1

A probability distribution or numeric value.

e2

A probability distribution or numeric value.

Value

A transformed distribution object.

Details

These S3 methods extend arithmetic operators to work with distributions.

Supported Operators

d + a or a + d

Shifts the distribution by adding constant a. Equivalent to shift().

d - a

Shifts the distribution by subtracting constant a. Equivalent to shift(d, -a).

-d

Flips the distribution (negation). Equivalent to flip().

d * a or a * d

Scales the distribution by multiplying by constant a. Equivalent to multiply().

d / a

Scales the distribution by dividing by constant a. Equivalent to multiply(d, 1/a).

a / d

Returns the distribution of a / X (reciprocal scaling). For a = 1, equivalent to invert().

d ^ a

Raises the distribution to power a. For positive distributions only, computed as exp(a * log(d)).

a ^ d

Returns the distribution of a^X. Requires positive base a.

Power Operator Details

The power operator ^ deserves special attention:

  • When the base is a distribution (e.g., dst_beta(1, 1)^2), it computes the distribution of X^a using the transformation exp(a * log(X)). This requires all values in the distribution to be positive.

  • When the exponent is a distribution (e.g., 2^dst_norm(0, 1)), it computes the distribution of a^X using exp(X * log(a)). The base a must be positive.

These implementations internally use both Math.dst() methods log() and exp().

See also

Examples

d <- distionary::dst_beta(3, 2)

# Shifting and scaling
d + 10          # Shift right by 10
#> Shifted distribution (continuous) 
#> --Parameters--
#> $distribution
#> Beta distribution (continuous) 
#> --Parameters--
#> shape1 shape2 
#>      3      2 
#> 
#> $shift
#> [1] 10
#> 
d * 2           # Scale by 2
#> Scaled distribution (continuous) 
#> --Parameters--
#> $distribution
#> Beta distribution (continuous) 
#> --Parameters--
#> shape1 shape2 
#>      3      2 
#> 
#> $constant
#> [1] 2
#> 
3 * d - 5       # Scale then shift
#> Shifted distribution (continuous) 
#> --Parameters--
#> $distribution
#> Scaled distribution (continuous) 
#> --Parameters--
#> $distribution
#> Beta distribution (continuous) 
#> --Parameters--
#> shape1 shape2 
#>      3      2 
#> 
#> $constant
#> [1] 3
#> 
#> 
#> $shift
#> [1] -5
#> 

# Power operations
exp(d)          # e^X: exponential of Beta
#> Exponentiated distribution (continuous) 
#> --Parameters--
#> $distribution
#> Beta distribution (continuous) 
#> --Parameters--
#> shape1 shape2 
#>      3      2 
#> 
2^d             # 2^X: base 2 raised to Beta
#> Exponentiated distribution (continuous) 
#> --Parameters--
#> $distribution
#> Scaled distribution (continuous) 
#> --Parameters--
#> $distribution
#> Beta distribution (continuous) 
#> --Parameters--
#> shape1 shape2 
#>      3      2 
#> 
#> $constant
#> [1] 0.6931472
#> 
#> 

# With positive distributions
d_pos <- distionary::dst_unif(1, 2)
d_pos^2         # X^2: uniform squared
#> Exponentiated distribution (continuous) 
#> --Parameters--
#> $distribution
#> Scaled distribution (continuous) 
#> --Parameters--
#> $distribution
#> Logarithmic distribution (continuous) 
#> --Parameters--
#> $distribution
#> Uniform distribution (continuous) 
#> --Parameters--
#> min max 
#>   1   2 
#> 
#> 
#> $constant
#> [1] 2
#> 
#> 
d_pos^0.5       # sqrt(X): square root
#> Exponentiated distribution (continuous) 
#> --Parameters--
#> $distribution
#> Scaled distribution (continuous) 
#> --Parameters--
#> $distribution
#> Logarithmic distribution (continuous) 
#> --Parameters--
#> $distribution
#> Uniform distribution (continuous) 
#> --Parameters--
#> min max 
#>   1   2 
#> 
#> 
#> $constant
#> [1] 0.5
#> 
#> 
sqrt(d_pos)     # Equivalent to d_pos^0.5
#> Exponentiated distribution (continuous) 
#> --Parameters--
#> $distribution
#> Scaled distribution (continuous) 
#> --Parameters--
#> $distribution
#> Logarithmic distribution (continuous) 
#> --Parameters--
#> $distribution
#> Uniform distribution (continuous) 
#> --Parameters--
#> min max 
#>   1   2 
#> 
#> 
#> $constant
#> [1] 0.5
#> 
#>