Hi,
I'm estimating a MMNL model and testing some distributions like Normal, Log-Normal, Johnson's Sb, etc. I tested a triangular distribution based on this paper https://www.jstatsoft.org/article/view/v074i10 but it didn't work. Can anyone give an example of this distribution in Apollo? In the case of Johnson's Sb is it common estimate the l and u parameters: c = l + (u - l)*(exp(b)/(1+exp(b)), or just exp(b)/(1 + exp(b))?
Thanks,
Gabriel
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Triangular and Johnson's Sb distribution
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Re: Triangular and Johnson's Sb distribution
Hi
could you show us the code that you used and I'll help you improve it
Thanks
Stephane
could you show us the code that you used and I'll help you improve it
Thanks
Stephane
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Re: Triangular and Johnson's Sb distribution
Hi,
Following the code I used for the Sb (it worked, but my question is about the support parameters) and the symmetrical triangular distribution
Thanks,
Gabriel
Following the code I used for the Sb (it worked, but my question is about the support parameters) and the symmetrical triangular distribution
Code: Select all
### Set parameters for generating draws
apollo_draws = list(
interDrawsType = 'halton',
interNDraws = 200,
interNormDraws = c("draws_tt"),
interUnifDraws = c("draws_tc")
)
#create random coefficients
apollo_randCoeff <- function(apollo_beta,apollo_inputs){
randcoeff = list()
#Johnson's Sb distribution
randcoeff[['b_tt']] = exp(mu_b_tt + sigma_b_tt*draws_tt)/(1 + exp(mu_b_tt + sigma_b_tt*draws_tt))
#Johnson's Sb distribution with support parameters b_l and b_u
randcoeff[['b_tt']] = b_l + (b_u - b_l)*(exp(mu_b_tt + sigma_b_tt*draws_tt)/(1 + exp(mu_b_tt + sigma_b_tt*draws_tt)))
#symmetrical triangular distribution
randcoeff[['b_tc']] = if (draws_tc < 0.5) {
mu_b_tc + sigma_b_tt*(sqrt(2*draws_tc) - 1)
} else {
mu_b_tc + sigma_b_tc*(1 - sqrt(2*draws_tc))
}
return(randcoeff)
}
Gabriel
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- Site Admin
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Re: Triangular and Johnson's Sb distribution
Hi Gabriel
creating a symmetrical triangular is easy - it is simply the sum of two independent uniforms. Code below. I'm dividing the sum by 2 so that the range parameter is actually the range rather than half the range.
Stephane
creating a symmetrical triangular is easy - it is simply the sum of two independent uniforms. Code below. I'm dividing the sum by 2 so that the range parameter is actually the range rather than half the range.
Stephane
Code: Select all
apollo_draws = list(
interDrawsType = 'halton',
interNDraws = 200,
interNormDraws = c("draws_tt"),
interUnifDraws = c("draws_tc_a","draws_tc_b")
)
#create random coefficients
apollo_randCoeff <- function(apollo_beta,apollo_inputs){
randcoeff = list()
#Johnson's Sb distribution
randcoeff[['b_tt']] = exp(mu_b_tt + sigma_b_tt*draws_tt)/(1 + exp(mu_b_tt + sigma_b_tt*draws_tt))
#Johnson's Sb distribution with support parameters b_l and b_u
randcoeff[['b_tt']] = b_l + (b_u - b_l)*(exp(mu_b_tt + sigma_b_tt*draws_tt)/(1 + exp(mu_b_tt + sigma_b_tt*draws_tt)))
#symmetrical triangular distribution
randcoeff[['b_tc']] = bound_tt + range_tt * ( draws_tc_a + draws_tc_b ) / 2
return(randcoeff)
}
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- Contact:
Re: Triangular and Johnson's Sb distribution
Thanks prof Hess!
Best regards,
Gabriel
Best regards,
Gabriel