Displaying 5 results from an estimated 5 matches for "bes1".
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2010 Jan 26
1
newton method for single nonlinear equation
...")
z <- pars[1]
## Constant value
alp <- 2.0165 ; rho <- 0.868;
c <- sqrt(pi)/(gamma(alp)*(1-rho)^alp)
for (i in 1:n)
{ t1 <- exp(-pars[1]/(1-rho))
t2 <- (pars[1]*(1-rho)/(2*sqrt(rho)))^(alp-0.5)
bes1 <- besselI(pars[1]*sqrt(rho)/(1-rho),alp-0.5)
bes2 <- besselI(pars[1]*sqrt(rho)/(1-rho),alp-1.5)
bes3 <- besselI(pars[1]*sqrt(rho)/(1-rho),alp+0.5)
## Equation
f <- c*t1*t2*bes1 - runi
## derivative
fprime <- c*t1*t2*( -bes1/(1-rho) + (alp-0....
2010 Feb 10
1
looping problem
...ave this code here:
library(numDeriv)
fprime <- function(z)
{ alp <- 2.0165;
rho <- 0.868;
# simplified expressions
a <- alp-0.5
c1 <- sqrt(pi)/(gamma(alp)*(1-rho)^alp)
c2 <- sqrt(rho)/(1-rho)
t1 <- exp(-z/(1-rho))
t2 <- (z/(2*c2))^a
bes1 <- besselI(z*c2,a)
t1bes1 <- t1*bes1
c1*t1bes1*t2
}
## Newton iteration
newton_gam <- function(z)
{ n <- length(z)
r <- runif(n)
tol <- 1E-6
cdf <- vector(length=n, mode="numeric")
for (i in 1:1000)
{ # numerical intergration to find the cdf
...
2010 Jan 26
1
Newton method
...")
z <- pars[1]
## Constant value
alp <- 2.0165 ; rho <- 0.868;
c <- sqrt(pi)/(gamma(alp)*(1-rho)^alp)
for (i in 1:n)
{ t1 <- exp(-pars[1]/(1-rho))
t2 <- (pars[1]*(1-rho)/(2*sqrt(rho)))^(alp-0.5)
bes1 <- besselI(pars[1]*sqrt(rho)/(1-rho),alp-0.5)
bes2 <- besselI(pars[1]*sqrt(rho)/(1-rho),alp-1.5)
bes3 <- besselI(pars[1]*sqrt(rho)/(1-rho),alp+0.5)
## Equation
f <- c*t1*t2*bes1 - runi
## derivative
fprime <- c*t1*t2*( -bes1/(1-rho) + (alp-0....
2010 Feb 09
1
how to adjust the output
...at I can carry out the calculation.
integrand <- function(z)
{ alp <- 2.0165
rho <- 0.868
# simplified expressions
a <- alp-0.5
c1 <- sqrt(pi)/(gamma(alp)*(1-rho)^alp)
c2 <- sqrt(rho)/(1-rho)
t1 <- exp(-z/(1-rho))
t2 <- (z/(2*c2))^a
bes1 <- besselI(z*c2,a)
t1bes1 <- t1*bes1
c1*t1bes1*t2
}
z1 <- 20
cdf <- integrate(integrand, lower = 0, upper = z1,abs.tol = FALSE)
r <- runif(1)
## Newton iteration
z2 <- z1 - (cdf - r)/integrand(z1)
Output
> z1 <- 20
> cdf <- integrate(integrand,...
2010 Feb 09
0
For and while in looping
...re is the code:
library(numDeriv)
fprime <- function(z)
{ alp <- 2.0165;
rho <- 0.868;
# simplified expressions
a <- alp-0.5
c1 <- sqrt(pi)/(gamma(alp)*(1-rho)^alp)
c2 <- sqrt(rho)/(1-rho)
t1 <- exp(-z/(1-rho))
t2 <- (z/(2*c2))^a
bes1 <- besselI(z*c2,a)
t1bes1 <- t1*bes1
c1*t1bes1*t2
}
## Newton iteration
newton_gam <- function(z)
{ n <- length(z)
r <- runif(n)
tol <- 1E-6
for (i in 1:n)
{ # numerical intergration to find the cdf
cdf[i] <- integrate(fprime, lower = 0, upper = z...