hfig {ig} | R Documentation |
Hazard function or failure rate for the IGTD with mean parameter mu, scale parameter lambda and associated kernel g
.
hfig(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 hf given by
h_T(t)=frac{f_Z(a_{t}) , frac{sqrt{λ}}{sqrt{t^{3}}}}{F_Z(-a_t)-int^{infty}_{b_t} c , g(u^2- frac{4 , λ}{μ}) mbox{footnotesize d}u}.
hfig()
gives the hf of an IGTD.
Víctor Leiva <victor.leiva@uv.cl>, Hugo Hernández <hugo.hernandez@msn.com>, and Antonio Sanhueza <asanhue@ufro.cl>.
## Computes the hf of the IGTD with g="normal" for a vector x with mu=1, lambda=1 and g="normal" ## At the end we have the graph of the IGTD hf x <- seq(0, 4,by=0.01) hx <- hfig(x,mu=1.0,lambda=1.0,kernel="normal") print(hx) plot(x, hx, main = "Hazard function of the IGTD (classical case)", ylab="h(x)")