Truncated mean of the Uniform distribution

Truncated mean of the Uniform distribution with min \(a\) and max \(b\).

Etrunc_unif(d, min = 0, max = 1, less.than.d = TRUE)

Arguments

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

Value

Function :

• E_unif gives the expected value.

• V_unif gives the variance.

• kthmoment_unif gives the kth moment.

• Etrunc_unif gives the truncated mean.

• SL_unif gives the stop-loss.

• Elim_unif gives the limited mean.

• Mexcess_unif gives the mean excess loss.

• TVaR_unif gives the Tail Value-at-Risk.

• VaR_unif gives the 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 \(x \in [a, b]\).

See also

Other Continuous Uniform Distribution: E_unif(), Elim_unif(), Mexcess_unif(), SL_unif(), TVaR_unif(), V_unif(), VaR_unif(), kthmoment_unif()

Examples

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

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