Compare multiple triangle distributions fits

Description

Compare multiple triangle distributions fits

Usage

compare_triangle_fit(
  y,
  cols = c("red", "blue", "green"),
  main = "Triangle Fit Comparison",
  ...
)

Arguments

Examples

set.seed(10304)
xtest <- rtriangle(100, 1, 5, 2)
compare_triangle_fit(xtest)

The Log-Triangle Distribution

Description

These functions provide information about the triangle distribution on the logarithmic interval from a to b with a maximum at c. dltriangle gives the density, pltriangle gives the distribution function, qltriangle gives the quantile function, and rltriangle generates n random deviates.

Usage

rltriangle(
  n = 1,
  a = 1,
  b = 100,
  c = 10^((log10(a) + log10(b))/2),
  logbase = 10
)

dltriangle(x, a = 1, b = 100, c = 10^((log10(a) + log10(b))/2), logbase = 10)

pltriangle(q, a = 1, b = 100, c = 10^((log10(a) + log10(b))/2), logbase = 10)

qltriangle(p, a = 1, b = 100, c = 10^((log10(a) + log10(b))/2), logbase = 10)

Arguments

Details

All probabilities are lower tailed probabilties. a, b, and c may be appropriate length vectors except in the case of rtriangle.

Value

dltriangle gives the density, pltriangle gives the distribution function, qltriangle gives the quantile function, and rltraingle generates random deviates. Invalid arguments will result in return value NaN or NA.

References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

See Also

.Random.seed about random number generation, runif, etc for other distributions.

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

Quantile-Quantile Plot for Triangle Distributed Data

Description

Quantile-Quantile Plot for Triangle Distributed Data

Usage

qqtriangle(
  y,
  a,
  b,
  c,
  main = "Triangle Q-Q Plot",
  xlab = "Theoretical Quantiles",
  ylab = "Sample Quantiles",
  ...
)

Arguments

Value

a list of x-y coordinates on the plot

Examples

set.seed(10304)
xtest <- rtriangle(100, 1, 5, 2)
theta <- coef(triangle_mle(xtest))
qqtriangle(xtest, theta[1], theta[2], theta[3])

Maximum likelihood estimate of the standard triangle distribution mode

Description

Maximum likelihood estimate of the standard triangle distribution mode

Usage

standard_triangle_mle(x, debug = FALSE)

Arguments

Value

an object of S3 class triangle_mle containing a list with the call, coefficients, variance co-variance matrix, minimum negative log likelihood, number of observations, and the sample

References

Samuel Kotz and Johan Rene van Dorp. Beyond Beta doi:10.1142/5720

Examples

xtest <- c(0.1, 0.25, 0.3, 0.4, 0.45, 0.6, 0.75, 0.8)
standard_triangle_mle(xtest)

Utility Methods for S3 class triangle_mle

Description

Utility Methods for S3 class triangle_mle

Usage

## S3 method for class 'triangle_mle'
summary(object, ...)

## S3 method for class 'triangle_mle'
print(x, ...)

## S3 method for class 'triangle_mle'
coef(object, ...)

## S3 method for class 'triangle_mle'
logLik(object, ...)

## S3 method for class 'triangle_mle'
AIC(object, ..., k = 2)

## S3 method for class 'triangle_mle'
BIC(object, ...)

## S3 method for class 'triangle_mle'
vcov(object, ...)

## S3 method for class 'triangle_mle'
profile(fitted, ...)

## S3 method for class 'triangle_mle'
confint(object, parm, level = 0.95, ...)

Arguments

Value

an object of class summary.mle

x invisibly

a vector of coefficients

an object of class logLik

the AIC

the BIC

the variance co-variance matrix

an object of class profile.mle

an object of class profile.mle

Examples

set.seed(1234)
x <- rtriangle(100, 0, 1, 0.5)
mle1 <- triangle_mle(x)
summary(mle1)
print(mle1)
coef(mle1)
logLik(mle1)
AIC(mle1)
BIC(mle1)
vcov(mle1)
## Not run: 
  prof <- profile(mle1)
  stats4::plot(prof)
  confint(mle1, 1:3, level = 0.95)

## End(Not run)

The Triangle Distribution

Description

These functions provide information about the triangle distribution on the interval from a to b with a maximum at c. dtriangle gives the density, ptriangle gives the distribution function, qtriangle gives the quantile function, and rtriangle generates n random deviates.

Usage

dtriangle(x, a = 0, b = 1, c = (a + b)/2)

ptriangle(q, a = 0, b = 1, c = (a + b)/2)

qtriangle(p, a = 0, b = 1, c = (a + b)/2)

rtriangle(n = 1, a = 0, b = 1, c = (a + b)/2)

Arguments

Details

All probabilities are lower tailed probabilities. a, b, and c may be appropriate length vectors except in the case of rtriangle. rtriangle is derived from a draw from runif. The triangle distribution has density:

f(x) = \frac{2(x-a)}{(b-a)(c-a)}

for a \le x < c.

f(x) = \frac{2(b-x)}{(b-a)(b-c)}

for c \le x \le b. f(x) = 0 elsewhere. The mean and variance are:

E(x) = \frac{(a + b + c)}{3}

V(x) = \frac{1}{18}(a^2 + b^2 + c^2 - ab - ac - bc)

Value

dtriangle gives the density, ptriangle gives the distribution function, qtriangle gives the quantile function, and rtriangle generates random deviates. Invalid arguments will result in return value NaN or NA.

References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

See Also

.Random.seed about random number generation, runif, etc for other distributions.

Examples

## view the distribution
tri <- rtriangle(100000, 1, 5, 3)
hist(tri, breaks=100, main="Triangle Distribution", xlab="x")
mean(tri) # 1/3*(1 + 5 + 3) = 3
var(tri)  # 1/18*(1^2 + 3^2 + 5^2 - 1*5 - 1*3 - 5*3) = 0.666667
dtriangle(0.5, 0, 1, 0.5) # 2/(b-a) = 2
qtriangle(ptriangle(0.7)) # 0.7

Triangle parameter estimates using a non-linear fit of the empirical CDF

Description

Triangle parameter estimates using a non-linear fit of the empirical CDF

Usage

triangle_cdfe(x, control = stats::nls.control(maxiter = 100, warnOnly = TRUE))

Arguments

Value

an object of class nls

Examples

set.seed(10304)
xtest <- rtriangle(100, 1, 5, 2)
cdfe <- triangle_cdfe(xtest)
print(cdfe)
summary(cdfe)
coef(cdfe)
## Not run: 
  confint(cdfe)

## End(Not run)

Maximum likelihood estimate of the triangle distribution parameters

Description

Maximum likelihood estimate of the triangle distribution parameters

Usage

triangle_mle(x, debug = FALSE, maxiter = 100)

Arguments

Value

an object of S3 class triangle_mle containing a list with the call, coefficients, variance co-variance matrix, minimum negative log likelihood, details of the optimization number of observations, and the sample

References

Samuel Kotz and Johan Rene van Dorp. Beyond Beta doi:10.1142/5720

Examples

xtest <- c(0.1, 0.25, 0.3, 0.4, 0.45, 0.6, 0.75, 0.8)
triangle_mle(xtest)

Triangle distribution method of moments estimate

Description

Triangle distribution method of moments estimate

Usage

triangle_mom(x)

Arguments

Value

a vector of the parameter estimates

Examples

set.seed(1204)
x <- rtriangle(20, 0, 2, 1.5)
triangle_mom(x)