Mathematical Transformations for Distributions

Apply mathematical functions like log() and exp() to probability distributions. If X is a random variable following a distribution, these functions return the distribution of the transformed variable.

Usage

# S3 method for class 'dst'
Math(x, ...)

Arguments

x

A probability distribution object.

...

Additional arguments passed to specific methods. For log(), you can specify base (defaults to exp(1) for natural log).

Value

A transformed distribution object.

Details

These S3 methods extend base R functions to work with distributions.

Supported Functions

log(x, base = exp(1))

Returns the distribution of log(X). The base can be specified (defaults to natural log). An error is returned if the distribution has non-positive values as possible outcomes.

log10(x)

Returns the distribution of log10(X). Equivalent to log(x, base = 10).

exp(x)

Returns the distribution of exp(X).

sqrt(x)

Returns the distribution of sqrt(X). Equivalent to x^0.5. Requires all values to be non-negative.

Power Operator

The power operator ^ also works with distributions (see Ops.dst()). When raising a distribution to a numeric power (e.g., dst^2), it uses the relationship X^a = exp(a * log(X)), combining both exponential and logarithmic transformations.

See also

• Ops.dst() for the ^ operator and other arithmetic operations

• shift(), multiply(), flip(), invert() for linear transformations

Examples

# Logarithmic transformations
d <- distionary::dst_unif(1, 10)
log(d)              # Natural log
#> Logarithmic distribution (continuous) 
#> --Parameters--
#> $distribution
#> Uniform distribution (continuous) 
#> --Parameters--
#> min max 
#>   1  10 
#> 
log(d, base = 10)   # Log base 10
#> Scaled distribution (continuous) 
#> --Parameters--
#> $distribution
#> Logarithmic distribution (continuous) 
#> --Parameters--
#> $distribution
#> Uniform distribution (continuous) 
#> --Parameters--
#> min max 
#>   1  10 
#> 
#> 
#> $constant
#> [1] 0.4342945
#> 
log10(d)            # Also log base 10
#> Scaled distribution (continuous) 
#> --Parameters--
#> $distribution
#> Logarithmic distribution (continuous) 
#> --Parameters--
#> $distribution
#> Uniform distribution (continuous) 
#> --Parameters--
#> min max 
#>   1  10 
#> 
#> 
#> $constant
#> [1] 0.4342945
#> 
sqrt(d)             # Square root of uniform
#> Exponentiated distribution (continuous) 
#> --Parameters--
#> $distribution
#> Scaled distribution (continuous) 
#> --Parameters--
#> $distribution
#> Logarithmic distribution (continuous) 
#> --Parameters--
#> $distribution
#> Uniform distribution (continuous) 
#> --Parameters--
#> min max 
#>   1  10 
#> 
#> 
#> $constant
#> [1] 0.5
#> 
#> 

# Exponential transformation
d2 <- distionary::dst_norm(0, 1)
d3 <- distionary::dst_beta(5, 4)
exp(d2)             # Log-normal distribution
#> Log Normal distribution (continuous) 
#> --Parameters--
#> meanlog   sdlog 
#>       0       1 
exp(d3)             # No simplification
#> Exponentiated distribution (continuous) 
#> --Parameters--
#> $distribution
#> Beta distribution (continuous) 
#> --Parameters--
#> shape1 shape2 
#>      5      4 
#> 

# These can be combined
log(exp(d2))        # Returns back to normal distribution
#> Normal distribution (continuous) 
#> --Parameters--
#> mean   sd 
#>    0    1 
log(exp(d3))        # Still returns d3.
#> Beta distribution (continuous) 
#> --Parameters--
#> shape1 shape2 
#>      5      4 
5^(log(d3, base = 5)) # Still returns d3.
#> Beta distribution (continuous) 
#> --Parameters--
#> shape1 shape2 
#>      5      4