# Unif: Uniform Distribution In Distributacalcul: Probability Distribution Functions

## Description

Uniform distribution with min a and max b.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```expValUnif(min = 0, max = 1) varUnif(min = 0, max = 1) kthMomentUnif(k, min = 0, max = 1) expValLimUnif(d, min = 0, max = 1) expValTruncUnif(d, min = 0, max = 1, less.than.d = TRUE) stopLossUnif(d, min = 0, max = 1) meanExcessUnif(d, min = 0, max = 1) VatRUnif(kap, min = 0, max = 1) TVatRUnif(kap, min = 0, max = 1) mgfUnif(t, min = 0, max = 1) ```

## Arguments

 `min` lower and upper limits of the distribution. Must be finite. `max` lower and upper limits of the distribution. Must be finite. `k` kth-moment. `d` cut-off value. `less.than.d` logical; if `TRUE` (default) truncated mean for values <= d, otherwise, for values > d. `kap` probability. `t` t.

## Details

The (continuous) uniform distribution with min and max parameters a and b respectively has density:

f(x) = 1 / (b - a) x 1_{a <= x <= b}

for a <= x <= b.

## Value

Function :

• `expValUnif` gives the expected value.

• `varUnif` gives the variance.

• `kthMomentUnif` gives the kth moment.

• `expValLimUnif` gives the limited mean.

• `expValTruncUnif` gives the truncated mean.

• `stopLossUnif` gives the stop-loss.

• `meanExcessUnif` gives the mean excess loss.

• `VatRUnif` gives the Value-at-Risk.

• `TVatRUnif` gives the Tail Value-at-Risk.

Invalid parameter values will return an error detailing which parameter is problematic.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```expValUnif(min = 3, max = 4) varUnif(min = 3, max = 4) kthMomentUnif(k = 2, min = 3, max = 4) expValLimUnif(d = 3, min = 2, max = 4) expValTruncUnif(d = 3, min = 2, max = 4) # Values greather than d expValTruncUnif(d = 3, min = 2, max = 4, less.than.d = FALSE) stopLossUnif(d = 3, min = 2, max = 4) meanExcessUnif(d = 2, min = 2, max = 4) VatRUnif(kap = .99, min = 3, max = 4) TVatRUnif(kap = .99, min = 3, max = 4) mgfUnif(t = 2, min = 0, max = 1) ```

Distributacalcul documentation built on Sept. 13, 2020, 5:19 p.m.