pig {ig} | R Documentation |
Cumulative distribution function for the IGDT with mean mu, scale parameter lambda and associated kernel g.
pig(q, mu = 1, lambda = 1, kernel = "normal", parameter.nu = 1, lower.tail = TRUE, log.p = FALSE)
q |
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. |
lower.tail |
Logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]. |
log.p |
Logical; if TRUE, probabilities p are given as log(p). |
The IGTD has cdf given by
F_T(t) = F_Z(a_t)+int^{infty}_{b_t} c , g(u^2- frac{4 , λ}{μ}) mbox{d}u,
where b_t=sqrt{λ/μ} [sqrt{t/μ} + sqrt{μ/t}], μ is the mean, λ the scale parameter, g is the kernel of the pdf of the associated symmetrical distribution, c the normalization constant and F_Z(cdot) denotes the cdf of the associated symmetrical distribution.
pig()
gives the cdf of an IGTD.
Víctor Leiva <victor.leiva@uv.cl>, Hugo Hernández <hugo.hernandez@msn.com>, and Antonio Sanhueza <asanhue@ufro.cl>.
Sanhueza, A., Leiva, V. and Balakrishnan, N. (2007). A new class of inverse Gaussian type distributions. Metrika (in press).
## Compute the cdf for a vector q with mu=1, lambda=1 and g="normal" ## At the end we have the graph of the cdf of the IGTD with g="normal". x <- seq(0, 4,by=0.01) px <- pig(x,mu=1.0,lambda=1.0,kernel="normal") print(px) plot(x, px, main = "cdf of the IGTD (g='normal')", ylab="F(x)")