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Diffstat (limited to 'R/pmt.R')
-rw-r--r-- | R/pmt.R | 53 |
1 files changed, 53 insertions, 0 deletions
@@ -0,0 +1,53 @@ +# Copyright © 2016 by Justin Bedő +# +# Permission to use, copy, modify, and/or distribute this software for any +# purpose with or without fee is hereby granted, provided that the above +# copyright notice and this permission notice appear in all copies. +# +# THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES +# WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF +# MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR +# ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES +# WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN +# ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF +# OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + +pmt <- function(a, b, two.sided=F) { + ce <- function(mu){ + pt1 <- mapply(function(xa, mu, rho) logsumexp(cumsum(log(((1 + rho) * (xa - (0:xa-1))/(2 * mu))))), a, mu, rho) + pt2 <- mapply(function(xb, mu, rho) logsumexp(cumsum(log((2*mu*rho) / ((1 + rho)*(xb + (1:100)))))), b, mu, rho) + rho + rho * (exp(pt1) - exp(pt2)) + } + + logsumexp <- function(x) { + x <- sort(x, decreasing=T) + log1p(sum(exp(x[-1] - x[1]))) + x[1] + } + + Ra <- sum(a) + Rb <- sum(b) + chi <- a/b + rho <- rep(Ra/Rb, length(a)) + + msk <- a/Ra > b/Rb + rho[msk] <- 1/rho[msk] + tmp <- a[msk] + a[msk] <- b[msk] + b[msk] <- tmp + chi[msk] <- 1/chi[msk] + + lb <- (rho - chi + sqrt(((rho - chi)^2 + 4 * chi * rho * (1 + rho)))) / (4 * rho) * b * 0.75 + ub <- (1 + chi) * (1 + rho) / (2 * rho + 1) * b * 1.25 + + while(max(ub - lb) > 1e-6){ + mu <- (ub + lb) / 2 + scmu <- ce(mu) >= 0 + ub <- ub * scmu + mu * (1 - scmu) + lb <- lb * (1 - scmu) + mu * scmu + } + + t1 <- mapply(function(xa, mu, rho) { i <- 0:xa; logsumexp(i * log(2 * mu) - lfactorial(i) - i * log(1 + rho))}, a, mu, rho) + t2 <- mapply(function(xb, mu, rho) { j <- xb:(xb*100); logsumexp(j * log(2 * mu * rho) - lfactorial(j) - j * log(1 + rho))}, b, mu, rho) + + (2*mu-t1-t2) / log(10) +} |