Description Usage Arguments Details Value Examples
Pareto distribution with shape parameter alpha and rate parameter lambda.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | dPareto(x, shape, rate = 1/scale, scale = 1/rate)
pPareto(q, shape, rate = 1/scale, scale = 1/rate, lower.tail = TRUE)
expValPareto(shape, rate = 1/scale, scale = 1/rate)
varPareto(shape, rate = 1/scale, scale = 1/rate)
kthMomentPareto(k, shape, rate = 1/scale, scale = 1/rate)
expValLimPareto(d, shape, rate = 1/scale, scale = 1/rate)
expValTruncPareto(d, shape, rate = 1/scale, scale = 1/rate, less.than.d = TRUE)
stopLossPareto(d, shape, rate = 1/scale, scale = 1/rate)
meanExcessPareto(d, shape, rate = 1/scale, scale = 1/rate)
VatRPareto(kap, shape, rate = 1/scale, scale = 1/rate)
TVatRPareto(kap, shape, rate = 1/scale, scale = 1/rate)
|
x |
vector of quantiles. |
shape |
shape parameter alpha, must be positive. |
rate |
rate parameter lambda, must be positive. |
scale |
alternative parameterization to the rate parameter, scale = 1 / rate. |
q |
vector of quantiles. |
lower.tail |
logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x]. |
k |
kth-moment. |
d |
cut-off value. |
less.than.d |
logical; if |
kap |
probability. |
The Pareto distribution with rate parameter lam as well as shape parameter a has density:
f(x) = (a lam^a)/ (lam + x)^(a + 1)
for x > 0, a, lam > 0.
Function :
dPareto
gives the probability density function (PDF).
pPareto
gives the cumulative density function (CDF).
expValPareto
gives the expected value.
varPareto
gives the variance.
kthMomentPareto
gives the kth moment.
expValLimPareto
gives the limited mean.
expValTruncPareto
gives the truncated mean.
stopLossPareto
gives the stop-loss.
meanExcessPareto
gives the mean excess loss.
VatRPareto
gives the Value-at-Risk.
TVatRPareto
gives the Tail Value-at-Risk.
Invalid parameter values will return an error detailing which parameter is problematic.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 | # With scale parameter
dPareto(x = 2, shape = 2, scale = 5)
# With rate parameter
dPareto(x = 2, shape = 2, rate = .20)
# With scale parameter
pPareto(q = 2, shape = 2, scale = 5)
# With rate parameter
pPareto(q = 2, shape = 2, rate = 0.20)
# Survival function
pPareto(q = 2, shape = 2, rate = 0.20, lower.tail = FALSE)
# With scale parameter
expValPareto(shape = 5, scale = 0.5)
# With rate parameter
expValPareto(shape = 5, rate = 2)
# With scale parameter
varPareto(shape = 5, scale = 0.5)
# With rate parameter
varPareto(shape = 5, rate = 2)
# With scale parameter
kthMomentPareto(k = 4, shape = 5, scale = 0.5)
# With rate parameter
kthMomentPareto(k = 4, shape = 5, rate = 2)
# With scale parameter
expValLimPareto(d = 4, shape = 5, scale = 0.5)
# With rate parameter
expValLimPareto(d = 4, shape = 5, rate = 2)
# With scale parameter
expValTruncPareto(d = 4, shape = 5, scale = 0.5)
# With rate parameter
expValTruncPareto(d = 4, shape = 5, rate = 2)
# With scale parameter
stopLossPareto(d = 2, shape = 5, scale = 0.5)
# With rate parameter
stopLossPareto(d = 2, shape = 5, rate = 2)
# With scale parameter
meanExcessPareto(d = 6, shape = 5, scale = 0.5)
# With rate parameter
meanExcessPareto(d = 6, shape = 5, rate = 2)
# With scale parameter
VatRPareto(kap = .99, shape = 5, scale = 0.5)
# With rate parameter
VatRPareto(kap = .99, shape = 5, rate = 2)
# With scale parameter
TVatRPareto(kap = .99, shape = 5, scale = 0.5)
# With rate parameter
TVatRPareto(kap = .99, shape = 5, rate = 2)
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