SMNGmoments {BayesLN} | R Documentation |
Functions that implement the mean, the generic moments (both raw and centered) and the moment generating function of the SMNG distribution.
SMNG_MGF(
r,
mu = 0,
delta,
gamma,
lambda,
beta = 0,
inf_sum = FALSE,
rel_tol = 1e-05
)
meanSMNG(mu, delta, gamma, lambda, beta)
SMNGmoment(j, mu, delta, gamma, lambda, beta, type = "central")
r |
Coefficient of the MGF. Can be viewed also as the order of the logSMNG moments. |
mu |
Location parameter, default set to 0. |
delta |
Concentration parameter, must be positive. |
gamma |
Tail parameter, must be positive. |
lambda |
Shape parameter. |
beta |
Skewness parameter, default set to 0 (symmetric case). |
inf_sum |
Logical: if FALSE (default), the integral representation of the SMNG density is used, otherwise the infinite sum is employed. |
rel_tol |
Level of relative tolerance required for the |
j |
Order of the moment. |
type |
String that indicate the kind of moment to comupute. Could be |
If the mean (i.e. the first order raw moment) of the SMNG distribution is required, then the function meanSMNG
could be use.
On the other hand, to obtain the generic j-th moment both "raw"
or "centered"
around the mean, the function momentSMNG
could be used.
Finally, to evaluate the Moment Generating Function (MGF) of the SMNG distribution in the point r
, the function SMNG_MGF
is provided.
It is defined only for points that are lower then the parameter gamma
, and for integer values of r
it could also considered as the
r-th raw moment of the logSMNG distribution. The last function is implemented both in the integral form, which uses the routine integrate
,
or in the infinite sum structure.
### Comparisons sample quantities vs true values
sample <- rSMNG(n=50000,mu = 0,delta = 2,gamma = 2,lambda = 1,beta = 2)
mean(sample)
meanSMNG(mu = 0,delta = 2,gamma = 2,lambda = 1,beta = 2)
var(sample)
SMNGmoment(j = 2,mu = 0,delta = 2,gamma = 2,lambda = 1,beta = 2,type = "central")
SMNGmoment(j = 2,mu = 0,delta = 2,gamma = 2,lambda = 1,beta = 2,type = "raw")-
meanSMNG(mu = 0,delta = 2,gamma = 2,lambda = 1,beta = 2)^2
mean(exp(sample))
SMNG_MGF(r = 1,mu = 0,delta = 2,gamma = 2,lambda = 1,beta = 2)