Implements some aspects of the stable lambda (SL) distribution
rqsl(n, t = 1, nu0 = 0, theta = 1, convo = 1, beta.a = 0, mu = 0)rsl(n, t = 1, nu0 = 0, theta = 1, convo = 1, beta.a = 0, mu = 0,
lambda = 4)
dsl(x, t = 1, nu0 = 0, theta = 1, convo = 1, beta.a = 0, mu = 0,
lambda = 4)
dqsl(x, t = 1, nu0 = 0, theta = 1, convo = 1, beta.a = 0, mu = 0)
kqsl(t = 1, nu0 = 0, theta = 1, convo = 1, beta.a = 0, mu = 0)
ksl(t = 1, nu0 = 0, theta = 1, convo = 1, beta.a = 0, mu = 0,
lambda = 4)
qsl_kurtosis_analytic(t = 1, nu0 = 0, theta = 1, convo = 1,
beta.a = 0)
qsl_skewness_analytic(t = 1, nu0 = 0, theta = 1, convo = 1,
beta.a = 0)
qsl_variance_analytic(t = 1, nu0 = 0, theta = 1, convo = 1,
beta.a = 0)
qsl_std_pdf0_analytic(t = 1, nu0 = 0, theta = 1, convo = 1,
beta.a = 0)
qsl_pdf_integrand_analytic(x, nu, t = 1, nu0 = 0, theta = 1, convo = 1,
beta.a = 0, mu = 0)
cfqsl(s, t = 1, nu0 = 0, theta = 1, convo = 1, beta.a = 0, mu = 0,
method = "a")
cfsl(s, t = 1, nu0 = 0, theta = 1, convo = 1, beta.a = 0, mu = 0,
lambda = 4, method = "a")
numeric, number of observations.
numeric, the time parameter, where the variance is t, default is 1.
numeric, the location parameter, default is 0.
numeric, the scale parameter, default is 1.
numeric, the convolution number, default is 1.
numeric, the skewness parameter, default is 0. This number is annualized by sqrt(t).
numeric, the location parameter, default is 0.
numeric, the shape parameter, default is 4.
numeric, vector of responses.
numeric, vector of nu in the pdf integrand, starting from 0 (not nu0).
numeric, vector of responses for characteristic function.
character, method of characteristic function (CF) calculation. Default is "a". Method a uses cflihnlap x dstablecnt. Method b uses dlihnlap x cfstablecnt. Method c uses direct integration on PDF up to 50 stdev. They should yield the same result.
numeric, standard convention is followed: d* returns the density, p* returns the distribution function, q* returns the quantile function, and r* generates random deviates. The following are our extensions: k* returns the first 4 cumulants, skewness, and kurtosis, cf* returns the characteristic function.