Uniform distribution with min $$a$$ and max $$b$$.

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, 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.

## 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.

## Details

The (continuous) uniform distribution with min and max parameters $$a$$ and $$b$$ respectively has density: $$f(x) = \frac{1}{b - a} \times \bm{1}_{\{x \in [a, b] \}}$$ for $$x \in [a, b]$$.

## Examples

expValUnif(min = 3, max = 4)
#> [1] 3.5

varUnif(min = 3, max = 4)
#> [1] 0.08333333

kthMomentUnif(k = 2, min = 3, max = 4)
#> [1] 12.33333

expValLimUnif(d = 3, min = 2, max = 4)
#> [1] 2.75

expValTruncUnif(d = 3, min = 2, max = 4)
#> [1] 1.25

# Values greather than d
expValTruncUnif(d = 3, min = 2, max = 4, less.than.d = FALSE)
#> [1] 1.75

stopLossUnif(d = 3, min = 2, max = 4)
#> [1] 0.25

meanExcessUnif(d = 2, min = 2, max = 4)
#> [1] 1

VatRUnif(kap = .99, min = 3, max = 4)
#> [1] 3.99

TVatRUnif(kap = .99, min = 3, max = 4)
#> [1] 3.995

mgfUnif(t = 2, min = 0, max = 1)
#> [1] 3.194528