Uniform Distribution

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

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.

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