Distribution Functions and Parameter Estimates for the Triangle Distribution • triangle

An R package to work with the triangle distribution and logarithmic triangle distribution

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See the package documentation here:

Getting Started

Install the R package:

# Stable CRAN version
install.packages(triangle)

# OR development version from GitHub
require(devtools)
devtools::install_github("bertcarnell/triangle")

use the functions:

a = minimum
b = maximum
c = mode

require(triangle)

Triangle distribution

# rtriangle(n, a, b, c)
set.seed(42)
rtriangle(5, 1, 5, 2)

## [1] 3.988898 4.131038 2.073171 3.573596 2.926584

# ptriangle(x, a, b, c)
ptriangle(0:5, 0, 10, 5)

## [1] 0.00 0.02 0.08 0.18 0.32 0.50

# qtriangle(p, a, b, c)
qtriangle(seq(0, 1, by = 0.2), 1, 10, 3)

## [1]  1.000000  2.897367  3.851830  4.980040  6.450352 10.000000

# dtriangle(x, a, b, c)
dtriangle(0:4, 0, 10, 5)

## [1] 0.00 0.04 0.08 0.12 0.16

Logarithmic triangle distribution

# rltriangle(n, a, b, c, logbase)
set.seed(2001)
rltriangle(5, 1, 100, 10)

## [1] 20.195183 13.001831  4.579489  4.753026  3.572658

# pltriangle(x, a, b, c, logbase)
pltriangle(10^(0:3), 1, 1000, 10)

## [1] 0.0000000 0.3333333 0.8333333 1.0000000

# qltriangle(p, a, b, c, logbase)
qltriangle(seq(0, 1, by = 0.2), 1, 100, 20)

## [1]   1.00000   5.26497  10.47630  17.76210  29.59642 100.00000

# dltriangle(x, a, b, c, logbase)
dltriangle(0:5, 1, 10, 5)

## [1] 0.0000000 0.0000000 0.8613531 1.3652124 1.7227062 2.0000000

Parameter estimates

triangle method of moments estimates

x <- rtriangle(20, 0, 2, 1.5)
triangle_mom(x)

##         a         b         c 
## 0.6341961 1.9096262 1.4197678

triangle maximum likelihood estimates

x <- c(0.1, 0.25, 0.3, 0.4, 0.45, 0.6, 0.75, 0.8)
# triangle_mle(x, debug = FALSE, maxiter = 100)
triangle_mle(x)

## Triangle Maximum Likelihood Estimates
## 
## Call:  triangle_mle(x = x) 
## 
## Estimates:
##    Estimate Std.Err
## a 0.0076277  0.0996
## b 0.9939370  0.1649
## c 0.3000000  0.0861
## 
## Convergence Code:  0
##   CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH

# standard triangle (0,1) likelihood estimates
standard_triangle_mle(x)

## Triangle Maximum Likelihood Estimates
## 
## Call:  standard_triangle_mle(x = x) 
## 
## Estimates:
##   Estimate Std.Err
## a      0.0  0.0000
## b      1.0  0.0000
## c      0.3  0.0871
## 
## Convergence Code:  NA
##

set.seed(1976)
x <- rtriangle(100, 1, 5, 3.5)
triangle_mle(x)

## Triangle Maximum Likelihood Estimates
## 
## Call:  triangle_mle(x = x) 
## 
## Estimates:
##   Estimate Std.Err
## a   0.9060  0.1259
## b   4.8254  0.0770
## c   3.6853  0.0924
## 
## Convergence Code:  0
##   CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH