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# Copyright 2018 Rob Carnell
#' The Log-Triangle Distribution
#'
#' @description These functions provide information about the triangle distribution on the
#' logarithmic interval from \code{a} to \code{b} with a maximum at \code{c}. \code{dltriangle}
#' gives the density, \code{pltriangle} gives the distribution function,
#' \code{qltriangle} gives the quantile function, and \code{rltriangle} generates
#' \code{n} random deviates.
#'
#' @details All probabilities are lower tailed probabilties. \code{a},
#' \code{b}, and \code{c} may be appropriate length vectors except in the
#' case of \code{rtriangle}.
#'
#' @param x,q vector of quantiles.
#' @param a lower limit of the distribution.
#' @param b upper limit of the distribution.
#' @param c mode of the distribution.
#' @param p vector of probabilities.
#' @param n number of observations. If \code{length(n) > 1}, the length is taken to be the number required.
#' @param logbase the base of the logarithmic scale to use (default to 10)
#'
#' @return \code{dltriangle} gives the density, \code{pltriangle} gives the
#' distribution function, \code{qltriangle} gives the quantile function, and
#' \code{rltraingle} generates random deviates. Invalid arguments will
#' result in return value \code{NaN} or \code{NA}.
#' @references
#' Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) \emph{The New S Language}. Wadsworth & Brooks/Cole.
#' @seealso
#' \code{\link{.Random.seed}} about random number generation,
#' \code{\link{runif}}, etc for other distributions.
#' @keywords distribution
#'
#' @name ltriangle
#' @importFrom stats runif
#' @export
#'
#' @examples
#' tri <- rltriangle(100000, 1, 100, 10)
#' hist(log10(tri), breaks=100, main="Triangle Distribution", xlab="x")
#' dltriangle(10, 1, 100, 10) # 2/(log10(b)-log10(a)) = 1
#' qltriangle(pltriangle(10)) # 10
rltriangle <- function(n=1, a=1, b=100, c=10^((log10(a) + log10(b))/2), logbase=10)
{
stopifnot(length(n) == 1)
if (n < 1 | is.na(n)) stop(paste("invalid argument: n =", n))
n <- floor(n)
if (any(is.na(c(a,b,c)))) return(rep(NaN, times = n)) # to match behavior of runif
if (any(a > c | b < c)) return(rep(NaN, times = n)) # to match behavior of runif
if (any(is.infinite(c(a, b, c)))) return(rep(NaN, times = n))
if (any(c(a,b,c) == 0)) return(rep(-Inf, times = n))
if (any(c(a,b,c) < 0)) return(rep(NaN, times = n))
lp <- runif(n)
stopifnot(length(logbase) == 1)
if (logbase == 10)
{
la <- log10(a)
lb <- log10(b)
lc <- log10(c)
} else
{
la <- log(a)/log(logbase)
lb <- log(b)/log(logbase)
lc <- log(c)/log(logbase)
}
if (a != c)
{
# if a = c then i is always true
i <- which((la + sqrt(lp * (lb - la)*(lc - la))) <= lc)
j <- which((lb - sqrt((1 - lp) * (lb - la) * (lb - lc))) > lc)
} else
{
i <- which((la + sqrt(lp * (lb - la)*(lc - la))) < lc)
j <- which((lb - sqrt((1 - lp) * (lb - la) * (lb - lc))) >= lc)
}
if (length(i) != 0)
lp[i] <- la + sqrt(lp[i] * (lb - la) * (lc - la))
if (length(j) != 0)
lp[j] <- lb - sqrt((1 - lp[j]) * (lb - la) * (lb - lc))
p <- logbase^lp
return(p)
}
#' @rdname ltriangle
#' @export
dltriangle <- function(x, a=1, b=100, c=10^((log10(a) + log10(b))/2), logbase=10) {
x1 <- length(x)
a1 <- length(a)
b1 <- length(b)
c1 <- length(c)
stopifnot(length(logbase) == 1)
if (logbase == 10)
{
la <- log10(a)
lb <- log10(b)
lc <- log10(c)
lx <- log10(x)
} else
{
la <- log(a)/log(logbase)
lb <- log(b)/log(logbase)
lc <- log(c)/log(logbase)
lx <- log(x)/log(logbase)
}
dTest <- function(X){
if (any(is.na(X)))
{
# is.na is TRUE for NA, NaN, and FALSE
if (any(is.nan(X))) return(NaN) # to conform to qunif
else return(NA) # to conform to qunif
} else if (X[2] > X[4] | X[3] < X[4] | (X[1] == X[2] & X[2] == X[4]))
{
warning("values required to be a <= c <= b (at least one strict inequality)")
return(NaN) # to conform to behavior of qunif
} else if (any(is.infinite(X[2:4])))
{
return(NaN)
} else if (X[1] <= X[2])
{
return(0)
} else if (X[2] != X[4] & X[1] < X[4])
{
return(2*(X[1] - X[2]) / (X[3] - X[2]) / (X[4] - X[2]))
} else if (X[4] != X[3] & X[1] >= X[4] & X[1] < X[3])
{
return(2*(X[3] - X[1]) / (X[3] - X[2]) / (X[3] - X[4]))
} else if (X[1] >= X[3]) {
return(0)
}
}
k <- max(x1, a1, b1, c1)
if (k == 1) return(dTest(c(lx, la, lb, lc)))
params <- matrix(nrow = k, ncol = 4)
tryCatch(
{
params[,1] <- lx
params[,2] <- la
params[,3] <- lb
params[,4] <- lc
}, error = function(X) {
stop(paste(" -- Argument Lengths: length of x = ", x1,
", a = ", a1, ", b = ", b1, ", c = ", c1, " -- ", X, sep = ""))
})
return(apply(params, 1, dTest))
}
#' @rdname ltriangle
#' @export
pltriangle <- function(q, a=1, b=100, c=10^((log10(a) + log10(b))/2), logbase=10)
{
q1 <- length(q)
a1 <- length(a)
b1 <- length(b)
c1 <- length(c)
stopifnot(length(logbase) == 1)
if (logbase == 10)
{
la <- log10(a)
lb <- log10(b)
lc <- log10(c)
lq <- log10(q)
} else
{
la <- log(a)/log(logbase)
lb <- log(b)/log(logbase)
lc <- log(c)/log(logbase)
lq <- log(q)/log(logbase)
}
pTest <- function(X)
{
if (any(is.na(X))) { # is.na is TRUE for NA, NaN, and FALSE
if (any(is.nan(X))) return(NaN) # to conform to qunif
else return(NA) # to conform to qunif
} else if (X[2] > X[4] | X[3] < X[4] | (X[1] == X[2] & X[2] == X[4]))
{
warning("values required to be a <= c <= b (at least one strict inequality)")
return(NaN) # to conform to behavior of qunif
} else if (any(is.infinite(X[2:4])))
{
return(NaN)
} else if (X[1] <= X[2])
{
return(0)
} else if (X[2] != X[4] & X[1] < X[4])
{
return((X[1] - X[2])^2 / (X[3] - X[2]) / (X[4] - X[2]))
} else if (X[4] != X[3] & X[1] >= X[4] & X[1] < X[3])
{
return(1 - (X[3] - X[1])^2 / (X[3] - X[2]) / (X[3] - X[4]))
} else if (X[1] >= X[3])
{
return(1)
}
}
k <- max(q1, a1, b1, c1)
if (k == 1) return(pTest(c(lq, la, lb, lc)))
params <- matrix(nrow = k, ncol = 4)
tryCatch(
{
params[,1] <- lq
params[,2] <- la
params[,3] <- lb
params[,4] <- lc
}, error = function(X) {
stop(paste(" -- Argument Lengths: length of q = ", q1,
", a = ", a1, ", b = ", b1, ", c = ", c1, " -- ", X, sep = ""))
})
return(apply(params, 1, pTest))
}
#' @rdname ltriangle
#' @export
qltriangle <- function(p, a=1, b=100, c=10^((log10(a) + log10(b))/2), logbase=10)
{
p1 <- length(p)
a1 <- length(a)
b1 <- length(b)
c1 <- length(c)
stopifnot(length(logbase) == 1)
if (logbase == 10)
{
la <- log10(a)
lb <- log10(b)
lc <- log10(c)
} else
{
la <- log(a)/log(logbase)
lb <- log(b)/log(logbase)
lc <- log(c)/log(logbase)
}
qTest <- function(X)
{
# X = c(p, a, b, c)
if (any(is.na(X))) { # is.na is TRUE for NA, NaN, and FALSE
if (any(is.nan(X))) return(NaN) # to conform to qunif
else return(NA) # to conform to qunif
} else if (X[2] > X[4] | X[3] < X[4])
{
warning("values required to be a <= c <= b (at least one strict inequality)")
return(NaN) # to conform to behavior of qunif
} else if (X[1] < 0 | X[1] > 1)
{
warning("at least one p is outside [0,1]")
return(NaN) # to conform to behavior of qunif
} else if (any(is.infinite(X)))
{
return(NaN)
} else if ((X[2] != X[4] &&
(X[2] + sqrt(X[1]*(X[3] - X[2])*(X[4] - X[2]))) <= X[4]) |
(X[2] == X[4] &&
(X[2] + sqrt(X[1]*(X[3] - X[2])*(X[4] - X[2]))) < X[4]))
{
return(logbase^(X[2] + sqrt(X[1]*(X[3] - X[2])*(X[4] - X[2]))))
} else if ((X[2] != X[4] &&
(X[3] - sqrt((1 - X[1])*(X[3] - X[2])*(X[3] - X[4]))) > X[4]) |
(X[2] == X[4] &&
(X[3] - sqrt((1 - X[1])*(X[3] - X[2])*(X[3] - X[4]))) >= X[4]))
{
return(logbase^(X[3] - sqrt((1 - X[1])*(X[3] - X[2])*(X[3] - X[4]))))
} else if (X[2] != X[4] && (X[2] + sqrt(X[1]*(X[3] - X[2])*(X[4] - X[2]))) - X[4] <= (X[3] - X[2])*.Machine$double.eps)
{
return(X[4])
} else stop("Unexpected Result")
}
k <- max(p1, a1, b1, c1)
if (k == 1) return(qTest(c(p,la,lb,lc)))
params <- matrix(nrow = k, ncol = 4)
tryCatch(
{
params[,1] <- p
params[,2] <- la
params[,3] <- lb
params[,4] <- lc
}, error = function(X) {
stop(paste(" -- Argument Lengths: length of p = ", p1,
", a = ", a1, ", b = ", b1, ", c = ", c1, " -- ", X, sep = ""))
})
return(apply(params, 1, qTest))
}
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