sfig {ig} | R Documentation |
Survival function for the IGTD with mean parameter mu, scale parameter lambda and associated kernel g.
sfig(t, mu = 1, lambda = 1, kernel = "normal", parameter.nu = 1)
t |
Vector of quantiles. |
mu |
Mean. |
lambda |
Scale parameter. |
kernel |
Kernel of the pdf of the associated symmetrical distribution by means of which the IGTD is obtained. The kernels: "Laplace" , "logistic" , "normal" and "t" are available. |
parameter.nu |
Additional parameter of the IGTD when the t kernel is used. This parameter corresponds to a shape parameter and it is also known as "degree of freedom" . For default nu=1 , in which case the Cauchy distribution is obtained. The Student-t distribution has always degrees of kurtosis greater than normal distribution. This aspect is transferred to the IGTD and produces robust parameter estimates for the IGTD. |
The IGTD has sf given by
S_T(t)= F_Z(-a_t)-int^{infty}_{b_t} c , g(u^2- frac{4 , λ}{μ}) mbox{d}u; t >0.
sfig()
gives the sf of an IGTD.
Víctor Leiva <victor.leiva@uv.cl>, Hugo Hernández <hugo.hernandez@msn.com>, and Antonio Sanhueza <asanhue@ufro.cl>.
## Compute the sf of the IGTD with g="normal" for a vector x with mu=1, lambda=1 ## At the end we have the graph of the IGTD sf x <- seq(0, 4,by=0.01) sx <- sfig(x,mu=1.0,lambda=1.0,kernel="normal") print(sx) plot(x, sx, main = "Survival of the IGTD (classical case)", ylab="S(x)")