Distribution_transformation {mistr}

Transformation of a Distribution Object

Description

The methods for arithmetic operators +, -, *, /, ^, log, exp, sqrt, which perform a transformation of a given random variable.

Usage

## S3 method for class 'univdist'
e1 + e2 = NULL

## S3 method for class 'trans_univdist'
e1 + e2 = NULL

## S3 method for class 'univdist'
e1 * e2

## S3 method for class 'trans_univdist'
e1 * e2

## S3 method for class 'dist'
e1 / e2

## S3 method for class 'dist'
e1 - e2 = NULL

## S3 method for class 'dist'
sqrt(x)

## S3 method for class 'univdist'
log(x, base = exp(1))

## S3 method for class 'trans_univdist'
log(x, base = exp(1))

## S3 method for class 'univdist'
exp(x)

## S3 method for class 'trans_univdist'
exp(x)

## S3 method for class 'univdist'
e1 ^ e2

## S3 method for class 'trans_univdist'
e1 ^ e2

## S3 method for class 'normdist'
e1 + e2

## S3 method for class 'normdist'
e1 * e2

## S3 method for class 'normdist'
exp(x)

## S3 method for class 'expdist'
e1 * e2

## S3 method for class 'expdist'
e1 ^ e2

## S3 method for class 'unifdist'
e1 + e2

## S3 method for class 'unifdist'
e1 * e2

## S3 method for class 'tdist'
e1 ^ e2

## S3 method for class 'fdist'
e1 ^ e2

## S3 method for class 'betadist'
e1 - e2 = NULL

## S3 method for class 'binomdist'
e1 - e2 = NULL

## S3 method for class 'gammadist'
e1 * e2

## S3 method for class 'cauchydist'
e1 + e2

## S3 method for class 'cauchydist'
e1 * e2

## S3 method for class 'cauchydist'
e1 ^ e2

## S3 method for class 'lnormdist'
e1 * e2

## S3 method for class 'lnormdist'
log(x, base = exp(1))

## S3 method for class 'lnormdist'
e1 ^ e2

## S3 method for class 'weibulldist'
e1 * e2

## S3 method for class 'gumbeldist'
e1 + e2

## S3 method for class 'gumbeldist'
e1 * e2

## S3 method for class 'frechetdist'
e1 + e2

## S3 method for class 'frechetdist'
e1 * e2

## S3 method for class 'paretodist'
e1 * e2

## S3 method for class 'GPDdist'
e1 + e2

## S3 method for class 'GPDdist'
e1 * e2

Arguments

e1

distribution object or numeric of length one.

e2

distribution object or numeric of length one.

x

distribution object.

base

a positive number: the base with respect to which logarithms are computed.

Details

The offered arithmetic operators +, -, *, /, ^, log, exp, sqrt create an object that represents transformed random variable.

The functions, using the expressions manipulation, prepare expressions for transformation, inverse transformation, derivative of the inverse transformation and print. These expressions are then used later when the distribution is evaluated.

The transformation framework also keeps track on history of the transformations and so is able to recognize some inverse transformations of previous transformations or update the last transformation. Additionally, the methods are able to recognize some invariant and direct transformations, and so rather change the parameters or distribution family than to loose this information.

Value

Object representing a transformed random variable.

Examples

# transformation
B  <- binomdist(10, 0.3)
B2 <- - 3*log(B)
B2

# invariant transformation
N  <- normdist(1, 3)
N2 <- - 3*N + 5
N2

# direct transformation
N3 <- exp(N2)
N3

# recognize inverse
B3 <- exp(B2/-3)
B3
# update
B4 <- B + 5
B4 + 3