| dTLCAR {TLCAR} | R Documentation |
Probability Density Function (PDF) for the TLCAR Distribution
Description
Calculate the probability density at a given value using the TLCAR distribution.
Usage
dTLCAR(x, alpha, a, b, theta, m)
Arguments
x |
Value at which to calculate the PDF. |
alpha |
Parameter representing the distribution of the Topp-Leone component. |
a |
Parameter representing the scale (a) of the Cauchy component. |
b |
Parameter representing the position (b) of the Cauchy component. |
theta |
Parameter representing the scale of the Rayleigh component. |
m |
Additional parameter. |
Details
The probability density function (PDF) for the TLCAR distribution is defined as follows:
f(x)=\frac{2\alpha}{\pi a}\left[\frac{1+\left(\frac{x^2}{\theta^2}-1\right)e^{-\frac{x^2}{2\theta^2}}+m}{1+\left(\frac{x\left(1-e^{-\frac{x^2}{2\theta^2}}+m\right) -b}{a}\right)^2}\right]\left[\frac{1}{2}-\frac{1}{\pi}\arctan\frac{x\left(1-e^{-\frac{x^2}{2\theta^2}}+m\right) -b}{a}\right]\left[ 1-\left(\frac{1}{2}-\frac{1}{\pi}\arctan\frac{x\left(1-e^{-\frac{x^2}{2\theta^2}}+m\right)-b}{a}\right)^2\right]^{\alpha-1}
Value
Probability density at the given value.
Examples
dTLCAR(x = 1, alpha = 1, a = 1, b = 0, theta = 2, m = 0.5)