mazTRI: Triangular Distribution bounded between [0,1]

Description Usage Arguments Details Value References See Also Examples

View source: R/Triangle.R

Description

These functions provide the ability for generating probability density values, cumulative probability density values and moments about zero values for the Triangular Distribution bounded between [0,1]

Usage

1

Arguments

r

vector of moments

mode

single value for mode

Details

Setting min=0 and max=1 mode=c in the triangular distribution a unit bounded triangular distribution can be obtained. The probability density function and cumulative density function of a unit bounded triangular distribution with random variable P are given by

g_{P}(p)= \frac{2p}{c}

; 0 ≤ p < c

g_{P}(p)= \frac{2(1-p)}{(1-c)}

; c ≤ p ≤ 1

G_{P}(p)= \frac{p^2}{c}

; 0 ≤ p < c

G_{P}(p)= 1-\frac{(1-p)^2}{(1-c)}

; c ≤ p ≤ 1

0 ≤ mode=c ≤ 1

The mean and the variance are denoted by

E[P]= \frac{(a+b+c)}{3}= \frac{(1+c)}{3}

var[P]= \frac{a^2+b^2+c^2-ab-ac-bc}{18}= \frac{(1+c^2-c)}{18}

Moments about zero is denoted as

E[P^r]= \frac{2c^{r+2}}{c(r+2)}+\frac{2(1-c^{r+1})}{(1-c)(r+1)}+\frac{2(c^{r+2}-1)}{(1-c)(r+2)}

r = 1,2,3,...

NOTE : If input parameters are not in given domain conditions necessary error messages will be provided to go further

Value

The output of mazTRI give the moments about zero in vector form.

References

Horsnell, G. (1957). Economic acceptance sampling schemes. Journal of the Royal Statistical Society, Series A, 120:148-191.

Johnson, N. L., Kotz, S. and Balakrishnan, N. (1994) Continuous Univariate Distributions, Vol. 2, Wiley Series in Probability and Mathematical Statistics, Wiley

Karlis, D. & Xekalaki, E., 2008. The Polygonal Distribution. In Advances in Mathematical and Statistical Modeling. Boston: Birkhuser Boston, pp. 21-33.

Available at: http://dx.doi.org/10.1007/978-0-8176-4626-4_2 .

Okagbue, H. et al., 2014. Using the Average of the Extreme Values of a Triangular Distribution for a Transformation, and Its Approximant via the Continuous Uniform Distribution. British Journal of Mathematics & Computer Science, 4(24), pp.3497-3507.

Available at: http://www.sciencedomain.org/abstract.php?iid=699&id=6&aid=6427 .

See Also

triangle

—————

Triangular

Examples

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#plotting the random variables and probability values
col<-rainbow(4)
x<-seq(0.2,0.8,by=0.2)
plot(0,0,main="Probability density graph",xlab="Random variable",
ylab="Probability density values",xlim = c(0,1),ylim = c(0,3))
for (i in 1:4)
{
lines(seq(0,1,by=0.01),dTRI(seq(0,1,by=0.01),x[i])$pdf,col = col[i])
}

dTRI(seq(0,1,by=0.05),0.3)$pdf     #extracting the pdf values
dTRI(seq(0,1,by=0.01),0.3)$mean    #extracting the mean
dTRI(seq(0,1,by=0.01),0.3)$var     #extracting the variance

#plotting the random variables and cumulative probability values
col<-rainbow(4)
x<-seq(0.2,0.8,by=0.2)
plot(0,0,main="Cumulative density graph",xlab="Random variable",
ylab="Cumulative density values",xlim = c(0,1),ylim = c(0,1))
for (i in 1:4)
{
lines(seq(0,1,by=0.01),pTRI(seq(0,1,by=0.01),x[i]),col = col[i])
}

pTRI(seq(0,1,by=0.05),0.3)      #acquiring the cumulative probability values
mazTRI(1.4,.3)                  #acquiring the moment about zero values
mazTRI(2,.3)-mazTRI(1,.3)^2     #variance for when is mode 0.3
#only the integer value of moments is taken here because moments cannot be decimal
mazTRI(1.9,0.5)

Amalan-ConStat/R-fitODBOD documentation built on Oct. 1, 2018, 7:13 p.m.