# MinMaximum-methods: Methods for functions Minimum and Maximum in Package 'distr'

### Description

Minimum and Maximum-methods

### Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25``` ```Minimum(e1, e2, ...) Maximum(e1, e2, ...) ## S4 method for signature 'AbscontDistribution,AbscontDistribution' Minimum(e1,e2, ...) ## S4 method for signature 'DiscreteDistribution,DiscreteDistribution' Minimum(e1,e2, ...) ## S4 method for signature 'AbscontDistribution,Dirac' Minimum(e1,e2, withSimplify = getdistrOption("simplifyD")) ## S4 method for signature 'AcDcLcDistribution,AcDcLcDistribution' Minimum(e1,e2, withSimplify = getdistrOption("simplifyD")) ## S4 method for signature 'AcDcLcDistribution,AcDcLcDistribution' Maximum(e1,e2, withSimplify = getdistrOption("simplifyD")) ## S4 method for signature 'AbscontDistribution,numeric' Minimum(e1,e2, ...) ## S4 method for signature 'DiscreteDistribution,numeric' Minimum(e1,e2, ...) ## S4 method for signature 'AcDcLcDistribution,numeric' Minimum(e1,e2, withSimplify = getdistrOption("simplifyD")) ## S4 method for signature '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"`

`Huberize`, `Truncate`

### Examples

 ```1 2 3 4``` ```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())) ```

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