# Minimum-methods

##### Methods for functions Minimum and Maximum in Package `distr'

Minimum and Maximum-methods

- Keywords
- methods, distribution

##### Usage

```
Minimum(e1, e2, ...)
Maximum(e1, e2, ...)
# S4 method for AbscontDistribution,AbscontDistribution
Minimum(e1,e2, ...)
# S4 method for DiscreteDistribution,DiscreteDistribution
Minimum(e1,e2, ...)
# S4 method for AbscontDistribution,Dirac
Minimum(e1,e2,
withSimplify = getdistrOption("simplifyD"))
# S4 method for AcDcLcDistribution,AcDcLcDistribution
Minimum(e1,e2,
withSimplify = getdistrOption("simplifyD"))
# S4 method for AcDcLcDistribution,AcDcLcDistribution
Maximum(e1,e2,
withSimplify = getdistrOption("simplifyD"))
# S4 method for AbscontDistribution,numeric
Minimum(e1,e2, ...)
# S4 method for DiscreteDistribution,numeric
Minimum(e1,e2, ...)
# S4 method for AcDcLcDistribution,numeric
Minimum(e1,e2,
withSimplify = getdistrOption("simplifyD"))
# S4 method for AcDcLcDistribution,numeric
Maximum(e1,e2,
withSimplify = getdistrOption("simplifyD"))
```

##### Arguments

- e1
distribution object

- e2
distribution object or numeric

- …
further arguments (to be able to call various methods with the same arguments

- withSimplify
logical; is result to be piped through a call to

`simplifyD`

?

##### Value

the corresponding distribution of the minimum / maximum

##### Methods

- Minimum
`signature(e1 = "AbscontDistribution", e2 = "AbscontDistribution")`

: returns the distribution of`min(X1,X2)`

, if`X1`

,`X2`

are independent and distributed according to`e1`

and`e2`

respectively; the result is again of class`"AbscontDistribution"`

- Minimum
`signature(e1 = "DiscreteDistribution", e2 = "DiscreteDistribution")`

: returns the distribution of`min(X1,X2)`

, if`X1`

,`X2`

are independent and distributed according to`e1`

and`e2`

respectively; the result is again of class`"DiscreteDistribution"`

- Minimum
`signature(e1 = "AbscontDistribution", e2 = "Dirac")`

: returns the distribution of`min(X1,X2)`

, if`X1`

,`X2`

are distributed according to`e1`

and`e2`

respectively; the result is of class`"UnivarLebDecDistribution"`

- Minimum
`signature(e1 = "AcDcLcDistribution", e2 = "AcDcLcDistribution")`

: returns the distribution of`min(X1,X2)`

, if`X1`

,`X2`

are distributed according to`e1`

and`e2`

respectively; the result is of class`"UnivarLebDecDistribution"`

- Minimum
`signature(e1 = "AcDcLcDistribution", e2 = "numeric")`

: if`e2`

= \(n\), returns the distribution of`min(X1,X2,...,Xn)`

, if`X1`

,`X2`

, ...,`Xn`

are i.i.d. according to`e1`

; the result is of class`"UnivarLebDecDistribution"`

- Maximum
`signature(e1 = "AcDcLcDistribution", e2 = "AcDcLcDistribution")`

: returns the distribution of`max(X1,X2)`

, if`X1`

,`X2`

are distributed according to`e1`

and`e2`

respectively; translates into`-Minimum(-e1,-e2)`

; the result is of class`"UnivarLebDecDistribution"`

- Maximum
`signature(e1 = "AcDcLcDistribution", e2 = "numeric")`

: if`e2`

= \(n\), returns the distribution of`max(X1,X2,...,Xn)`

, if`X1`

,`X2`

, ...,`Xn`

are i.i.d. according to`e1`

; translates into`-Minimum(-e1,e2)`

; the result is of class`"UnivarLebDecDistribution"`

##### See Also

##### Examples

```
# NOT RUN {
plot(Maximum(Unif(0,1), Minimum(Unif(0,1), Unif(0,1))))
plot(Minimum(Exp(4),4))
## a sometimes lengthy example...
# }
# NOT RUN {
plot(Minimum(Norm(),Pois()))
# }
```

*Documentation reproduced from package distr, version 2.7.0, License: LGPL-3*