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)lower and upper limits of the distribution. Must be finite.
kth-moment.
cut-off value.
logical; if TRUE (default) truncated mean for values <= d, otherwise, for values > d.
probability.
t.
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.
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 \(x \in [a, b]\).
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